PC5214 wiki - User contributions [en]

Quantum Random Number Generator

2022-04-29T16:43:11Z

Zhang Munan: /* Randomness Extraction */

== '''Team Members''' ==
Wang Yang A0228753X

Xiao Yucan A0236278W

Zhang Munan A0236273E

== '''Idea''' ==
We live in an increasingly connected world, where a superior source of entropy is the key to data security. The effectiveness of any cryptographic system is determined by the strength of the keys it used. In turn, the strength of the key is determined by the degree of randomness used in its generation. Besides, large amount of random numbers are at the core of Monte Carlo simulations, which are widely used in scientific research. Methods produce random numbers from any algorithm are called pseudo-random number generator(PRNG). And random numbers generated by PRNG are deterministic by definition and therefore unsuitable for cryptographic purposes.

In order to generate unpredictable random numbers, hardware random number generators have been widely used. These physically generated random numbers are considered "truly" random because it is either practically or fundamentally impossible to predict the outcome of such a device. Quantum Random Number Generators (QRNGs) belong to a class of hardware random number generators and leverage the random properties of quantum physics to generate a true source of entropy, improving the quality of seed content for key generation.

Early QRNGs were based on radioactive decay. And more recently, QRNGs based on Poisson statistics of photons have been developed. The core idea is shown in the figure below. Single photons generated by a laser source are incident on a semi-transparent mirror and the mutually exclusive events (reflection/transmission) are detected and associated with ‘0’ or ‘1’ bit values respectively. The unpredictability of generated numbers is ensured by the quantum nature of the process. However, such a scheme needs a reliable single photon source as well as single photon detectors and it's not possible for our project. Here, we decided to build a QRNG based on measuring vacuum fluctuations of a light field as a random source. More details will be discussed in the principle part.
[[File:Principle schematic of QRNG.png|thumb|300px|'''Figure 1. Schematic of branching path quantum random number generators''']]

=== Benefits of having a quantum random number generator ===
* The source of randomness is unpredictable and controlled by quantum process.
* Live/real-time monitoring of entropy source is possible and highly effective as well.
* All attacks on the entropy source are detectable.

=== Application of quantum random number generator ===
* Securing data at rest in data centres
* Securing any kind of sensitive data
* Securing data in the cloud
* One-time pad for authentication in banking and other transactions
* Gaming applications and lottery
* Block-chain network
* Numerical simulations, statistical research
* IoT devices
* E-commerce and banking applications
* Cryptographic applications
* Telecom and 5G
* Monte Carlo Simulation

== '''Principles''' ==
[[File:Schematic of setup 2.png|thumb|300px|'''Figure 2. Schematic of setup''']]
Figure 2 schematically shows our setup. Such a setup is known as balanced homodyne detection and can extract the information of the electrical field in the second mode entering the polarizing beam-splitter (PBS) by measuring the photocurrent difference <math>i_1-i_2</math>. A continuous wave laser (wavelength 658 nm) is incident on one input port of the PBS and used as the local oscillator (LO), while another input port is empty. So the homodyne detection is trying to measure the vacuum state of the electromagnetic field. The randomness source in our setup is the fluctuations of the vacuum field. Here we tried to balance the optical power impinging on the two photodiodes, therefore any power fluctuation coming from the laser diode will be detected simultaneously and canceled in the photocurrent difference.

Alternatively, the randomness can be seen as coming from the shot noise of the photocurrents <math>i_1</math> and <math>i_2</math> with a power proportional to the average optical power. Since the shot noise currents from the diodes are uncorrelated, the y add up. And the amplitude fluctuations in the laser intensity (referred to as classical noise) can be eliminated by measuring the photocurrent difference.

== '''Setup''' ==
The practical setup (shown in Figure 3) was built with as few components as possible to create a baseline performance that we can compare.

[[File:Experimental setup.png|thumb|300px|'''Figure 3. Experimental setup''']]

==='''Tool list'''===
① Laser Diode
: Laser Diode is powered by a laser driving unit. The light intensity can be changed by changing the laser current.
② Focal Lens
: By adjusting the focal lens, the intensity of light that finally hits the photodiodes is adjusted.
③ RP: Rotatable Polarizer
: The polarization state of the light is adjusted by rotating the polarizer.
④ Mirror 1
: By adjusting mirror 1, the position of transmitted and reflected light spots hitting on PD1 and PD2 can be adjusted simultaneously.
⑤ PBS: Polarizing Beam Splitter
: The laser beam incident on the PBS can pass through or be reflected depending on the polarization state. If the incident beam is diagonal polarized (45°), the intensity of reflected and transmitted light is equal.
⑥ Mirror 2
: By adjusting mirror 2, the position of transmitted light spots hitting on PD2 can be tuned.
⑦&⑧ Photodiodes
: Detect the intensity of incident light.
⑩ Gain block
:A ready-made 60 dB gain Block from quantum optic lab.
⑪ High pass filter
:Designed cutoff frequency = 60 MHz.

==='''Description'''===
The total light power is changed by changing the laser current and adjusting the focal lens, while the power of the two output ports of the PBS is balanced by rotating the polarizer in front of the laser diode. Light leaving the PBS is detected by a pair of reverse-biased photodiodes connected in series to perform the current subtraction. By adjusting the orientation of M1 and M2, the light intensity incident on PD1 and PD2 can be adjusted and balanced. The balancing of the photocurrents is monitored by observing the voltage drop across a resister <math>R_{DC}</math> (DC port). Here we use a multimeter to measure the voltage. The fluctuations <math>\Delta(i_1-i_2)</math> are amplified by a 60 dB ready-made Gain block. And after that, a high pass filter (HPF) with a cutoff frequency of 60 MHz is used to filter out low frequency noise.

==='''Characterization list'''===
① Oscilloscope: Used to monitor the AC port and collect data.

② Spectrum Analyzer: Used to analyze the spectrum of total noise.

③ Multimeter
:Used to monitor the DC port and balance two photodiodes.

== '''Process''' ==
* '''26 February 2022:'''
* Did a basic characterization of photodiode
* Inputted a sine wave signal and a laser pointer light, observed the waveform of the photodiode
<gallery widths=300px heights=200px>
File:Basic characterization of photodiode test.jpeg|'''Figure 4. Basic characterization of photodiode'''
File:Schematic of basic characterization of photodiode test.png|'''Figure 5. Schematic of basic characterization of photodiode'''
</gallery>

:To understand the frequency response of the circuit shown in figure 5, we use a function generator to generate a sinusoidal signal to drive the LED, and use this circuit to measure the light output. When the frequency of the signal is low, we can see a relatively complete sine waveform on the oscilloscope. But when the frequency exceeds 1GHz, we could not observe a regular and stable waveform.
* '''5 March 2022:'''
* Used different resistors to test the frequency response of photodiode
<gallery widths=300px heights=200px>
File:Frequency of PD.png|'''Figure 6. Graph of the frequency response of photodiode'''
</gallery>
:We changed the resistors in Figure 6, from 1 kΩ to 11 kΩ and then 20 kΩ. We found that the higher the resistance of the resistor, the larger the output voltage but less sensitive to the high frequency. That is because a reverse-biased photodiode has a certain capacitance and forms an RC series circuit with the resistor. The larger the resistor, the larger the time constant <math>\tau=RC</math> of the RC circuit, and the slower the charge and discharge, which leads to a worse response to high frequency signals.
* '''12 March 2022:'''
* Build up the laser system and ensured the laser output
<gallery widths=300px heights=200px>
File:Laser diode.png|'''Figure 7. HL6501MG laser diode and schematic of internal circuit'''
File:Schematic of electronics laserconnector circuit.jpeg|'''Figure 8. Schematic of electronics laser connector circuit'''
File:Laser source setup.png|'''Figure 9. Laser source setup'''
</gallery>
:We used an HL6501MG laser diode, which is a 0.65 μm band AlGaInP laser diode (LD) with a multi-quantum well (MQW) structure. It is suitable as a light source for large-capacity optical disc memories and various other types of optical equipment. Hermetic sealing of the small package (φ=5.6 mm) assures high reliability.

:The Laser source consists of ① Laser diode; ② Thermostat; ③ Supply circuit for Laser diode and Thermostat; ④ Shell; ⑤ Focal lens; ⑥ Radiator. The Laser Diode is in the thermostat which is connected to the Radiator. We can set the temperature on the Laser power supply. The Thermostat and Radiator will keep the temperature of the laser diode as same as that set on the laser power supply. There is a focal lens in front of the laser diode. We can use it to change the focal length the enlarge the laser intensity hitting on the photodiodes. And a shell made of acrylic sheet and 4 balance posts.
* '''19 March 2022:'''
* Soldered photodiode driving circuit
* Test the feasibility
<gallery widths=300px heights=200px>
File:Photo diode outlines.png|'''Figure 10. S5972 Si PIN photodiode and schematic of internal circuit'''
File:Principle of photodiode driving circuit.png|'''Figure 11. Principle of photodiode driving circuit'''
File:Schematic photodiode driving circuit bolck.jpeg|'''Figure 12. Schematic photodiode driving circuit block'''
</gallery>

:We used an S5972 high-speed Si PIN photodiode to detect the light, which is designed for visible to near-infrared light detection. These photodiodes provide wideband characteristics at a low bias, making them suitable for optical communications and other high-speed photometry.

:We soldered all the components on the circuit chip as Figure 11 shows. After that, we tested its performance using a laser, it was approved that the optical signal was converted into the electrical signal and was measured by the oscilloscope.
* '''26 March 2022:'''
* Build up the whole system
* Tune the bias of two photodiodes
<gallery widths=300px heights=200px>
File:Whole setup.jpeg|'''Figure 13. The whole system setup'''
</gallery>
:We built up the whole setup on the optical platform. Then we tuned the bias of two photodiodes to make sure that the intensity of the laser hitting on both photodiodes is the same by adjusting the multimeter's voltage to around 0.
* '''2 April 2022:'''
* Focus the laser output
* Maximize the laser power output
* Characterize varaiation by varying optical power
<gallery widths=300px heights=200px>
File:Maximize the laser power output.jpeg|'''Figure 14. Maximize the laser power output'''
File:The detector noise power by varying the incident optical power.jpg|'''Figure 15. The plot of the detector noise power by varying the incident optical power'''
</gallery>
:We found that the laser output power in front of the polarizer was about 20 mW, but the power detected by each photodiode was only 0.4 mW. That is because the spot size of the laser was relatively large compared with the detection area of the photodiode. Therefore we needed to focus the lens in the laser block to maximize the detected laser power. To do this, we blocked one photodiode and used a multimeter to monitor the light power detected by another photodiode. After trials, we got a maximum value of voltage drop of 9.17 V, which corresponds to an optical power of 2.08 mW on each photodiode.

:Then, we characterized the change of noise level while rising incident optical power. And then we plotted a graph as shown in Figure 15, it is easy to find when the optical power is in a relatively low range, the noise level is flat which corresponds to the horizontal red line. While the optical power rises, the noise level increases with the optical power in a proportional manner. Therefore, we have enough reasons to believe that the overall noise is dominated by electronic noise in the low optical power range, while the noise level is dominated by shot noise in the high optical power range.
* '''9 April 2022:'''
* Soldered high pass filter
* Test its feasibility
<gallery widths=300px heights=200px>
File:Highpass filter principle circuit.png|'''Figure 16. Schematic of high pass filter circuit'''
File:Graph of theoretical high pass filter frequency response.jpg.png|'''Figure 17. Graph of theoretical high pass filter frequency response'''
File:Frequency of HPF.png|'''Figure 18. Graph of measured high pass filter frequency response'''
File:Schematic of high pass filter.jpeg|'''Figure 19. Setup of high pass filter'''
File:Setup of gain block and high pass filter.jpeg|'''Figure 20. Setup of gain block and high pass filter'''
</gallery>
:The measured total noise has a lot of low-frequency noise and is relatively flat power density in the range of 60-200 MHz. With a low pass filter of 200 MHz in the oscilloscope, we just needed a high pass filter of 60 MHz which compresses the low-frequency fluctuations. So we designed a high pass filter of 60 MHz and soldered the high pass filter.

:After that, we tested its performance. By comparing with the theoretical high pass filter graph, the measured high pass filter frequency response showed a high correspondence with it, which means it is feasible to apply it to the whole system to suppress the low-frequency fluctuations.
* '''16 April 2022:'''
* Apply the high pass filter to the circuit and test
* Record data and draw some graphs analysis
: In order to verify that the signals we obtained were quantum random numbers, we recorded the data at different sampling rates and performed autocorrelation calculations. These can be found in the "Result"-"Autocorrelation" part.

* '''23 April 2022:'''
* Processing experimental data
* Draw autocorrelation images
* Summarize and upload the experimental results

== '''Results''' ==
==='''Quantum noise'''===
*To ensure that the fluctuations at the amplifier output are dominated by quantum noise, the spectral power density is measured (in Figure 21. ).

[[File:Ampliﬁed noise levels measured into a resolution bandwidth B = 3 MHz..jpg|thumb|600px|center|'''Figure 21. Schematic of branching path quantum random number generators''']]

:Amplified noise levels measured into a resolution bandwidth B = 3 MHz. The total noise is measured from the photocurrent difference <math>i_1-i_2</math> with equal optical power impinging on both photodiodes. The current <math>i_1</math> of a single photodiode reveals colored classical noise. The electronic noise is measured without any optical input.
:In an alternative view, the laser beam can be seen as generating photocurrents <math>i_1</math> and <math>i_2</math> with a shot noise power proportional to the average optical power. The shot noise currents from the diodes add up as they are uncorrelated, while amplitude fluctuations in the laser intensity (referred to as classical noise) do not affect the photocurrent difference.

=== '''Autocorrelation'''===
*:Autocorrelation, sometimes known as serial correlation in the discrete-time case, is the correlation of a signal with a delayed copy of itself as a function of delay. Informally, it is the similarity between observations as a function of the time lag between them. In our experiment, if we obtain an ideal '''quantum random number generator''', the autocorrelation will be 1 when the time lag is 0, while the autocorrelation will be close to 0 when the time lag is not 0.

*:Given a signal <math>f(t)</math>, the continuous autocorrelation <math>R_{ff}(\tau)</math> is most often defined as the continuous cross-correlation integral of <math>f(t)</math> with itself, at lag <math>\tau</math>.

::::::::::::::::<math>R_{ff}(\tau) = \int_{-\infty}^\infty f(t+\tau)\overline{f(t)}\, {\rm d}t = \int_{-\infty}^\infty f(t) \overline{f(t-\tau)}\, {\rm d}t</math>

::where <math>\overline{f(t)}</math> represents the complex conjugate of <math>f(t)</math>. Note that the parameter <math>t</math> in the integral is a dummy variable and is only necessary to calculate the integral. It has no specific meaning.

*:'''Experimental result'''
:<gallery widths=500px heights=300px>
File:2.5 GHz (-20,20) After Highpass1.png|'''Figure 22. Autocorrelation of the total noise signal sampled at 2.5 GHz'''
File:500 kHz (-20,20) After Highpass1.png|'''Figure 23. Autocorrelation of the total noise signal sampled at 500 KHz'''
:</gallery>

:We recorded several sets of data with different sampling frequencies ( 2.5 GHz to 500 kHz) and obtained autocorrelation for each group. A very high correlation between any two adjacent points was observed when we use a 2.5 GHz sampling rate. This is simply because of an extremely high sampling rate which results in every two adjacent points being almost at the same position. We can get a better correlation by reducing the sampling frequency to such as 10 MHz or even lower.

:But the autocorrelation with a 500 kHz sampling rate is still not ideal. This is limited by our experimental setup. We caught up with too much electronic interference. A well-designed experimental setup with integrated photodiodes, amplifier, and high pass filter will stimulate a better result.

=== '''Randomness Extraction'''===
The amplified total noise is digitized into 16-bit words at a sampling rate of 10 MHz (because we get the best atuocorrelation result at this sampling rate) and recorded in binary form by an oscilloscope. All data are discrete values between <math>-2^{15}</math> and <math>2^{15}-1</math>. Figure 24 below shows the distribution of our raw data, which fits to a Gaussian distribution with a standard deviation <math>\sigma = 5240</math>.
[[File:Raw_data.png|thumb|600px|center|'''Figure 24. Distribution of row data and fitted with Gaussian distribution.''']]

In many applications, however, random numbers are required to be not only unpredictable but also uniformly distributed. Therefore the raw data collected by the oscilloscope cannot be used directly. Various randomness extractors, such as Trevisan's extractor and Linear Feedback Shift Register, have been used to convert non-uniformly distributed raw data in to a uniformly distributed binary stream. For simplicity, here we used random matrix multiplications to extract uniformly distributed random numbers.

Equation above shows how it works. Since our raw data is recorded in binary form, it is an N-row column vector <math>r_i</math> with all elements 0 or 1. And the <math>M \times N</math> binary matrix is an algorithmically generated pseudo-random matrix. Then the raw data and the random matrix are multiplied (binary OR and XOR) to produce a column vector <math>s_i</math> of M rows. As long as the size of the random matrix is large enough, 0 and 1 in the output <math>s_i</math> will be almost uniformly distributed. Here M can take any integer not greater than N. The reason is that, the voltage at AC port fluctuates around 0 V and the first few bits in each binary number are typically unused (all 0). Therefore the entropy in the raw data is smaller than the size of the data (e.g.6 bits of entropy per 8 bits sample). The standard approach would be to first estimate the entropy in the raw data and then choose the value of N to extract the randomness. Since in our project, we didn't do that, here we choose N = M.
[[File:Extracted.png|thumb|600px|center|'''Figure 25, Distribution of random data after the random matrix multiplication.''']]
Figure 25 shows the distribution of the data after randomness extraction. As we can see, all data fall within the <math>\pm3\sigma</math> bounds, so we have reason to believe that extracted data is almost uniformly distributed.
[[File:Contrast.png||thumb|600px|center|'''Figure 26. Distribution of random numbers before (blue) and after (red) the randomness extraction, shown in time domain (left) and histogram (right)''']]
Figure 26 shows the comparison between random numbers before and after the randomness extraction.

=== '''Randomness Test'''===
To verify the randomness of the experimental results we obtained, we used two compression protocols(rar and zip) to compress the random numbers we generated. The compressed file size does not change significantly compared with the original file(from 58k to 55k), which, to some extent, illustrates the randomness of our results.

== '''References''' ==
[1] Miguel Herrero-Collantes and Juan Carlos Garcia-Escartin, Quantum random number generators, Rev. Mod. Phys, 89, 015004.

[2] Shi, Yicheng, Brenda Chng, and Christian Kurtsiefer, Random numbers from vacuum fluctuations, Applied Physics Letters, 109.4 (2016): 041101.

[3] https://www.digchip.com/datasheets/parts/datasheet/625/HL6501MG-pdf.php

[4] https://www.farnell.com/datasheets/3171163.pdf

Quantum Random Number Generator

2022-04-29T16:41:18Z

Zhang Munan: /* Randomness Extraction */

== '''Team Members''' ==
Wang Yang A0228753X

Xiao Yucan A0236278W

Zhang Munan A0236273E

== '''Idea''' ==
We live in an increasingly connected world, where a superior source of entropy is the key to data security. The effectiveness of any cryptographic system is determined by the strength of the keys it used. In turn, the strength of the key is determined by the degree of randomness used in its generation. Besides, large amount of random numbers are at the core of Monte Carlo simulations, which are widely used in scientific research. Methods produce random numbers from any algorithm are called pseudo-random number generator(PRNG). And random numbers generated by PRNG are deterministic by definition and therefore unsuitable for cryptographic purposes.

In order to generate unpredictable random numbers, hardware random number generators have been widely used. These physically generated random numbers are considered "truly" random because it is either practically or fundamentally impossible to predict the outcome of such a device. Quantum Random Number Generators (QRNGs) belong to a class of hardware random number generators and leverage the random properties of quantum physics to generate a true source of entropy, improving the quality of seed content for key generation.

Early QRNGs were based on radioactive decay. And more recently, QRNGs based on Poisson statistics of photons have been developed. The core idea is shown in the figure below. Single photons generated by a laser source are incident on a semi-transparent mirror and the mutually exclusive events (reflection/transmission) are detected and associated with ‘0’ or ‘1’ bit values respectively. The unpredictability of generated numbers is ensured by the quantum nature of the process. However, such a scheme needs a reliable single photon source as well as single photon detectors and it's not possible for our project. Here, we decided to build a QRNG based on measuring vacuum fluctuations of a light field as a random source. More details will be discussed in the principle part.
[[File:Principle schematic of QRNG.png|thumb|300px|'''Figure 1. Schematic of branching path quantum random number generators''']]

=== Benefits of having a quantum random number generator ===
* The source of randomness is unpredictable and controlled by quantum process.
* Live/real-time monitoring of entropy source is possible and highly effective as well.
* All attacks on the entropy source are detectable.

=== Application of quantum random number generator ===
* Securing data at rest in data centres
* Securing any kind of sensitive data
* Securing data in the cloud
* One-time pad for authentication in banking and other transactions
* Gaming applications and lottery
* Block-chain network
* Numerical simulations, statistical research
* IoT devices
* E-commerce and banking applications
* Cryptographic applications
* Telecom and 5G
* Monte Carlo Simulation

== '''Principles''' ==
[[File:Schematic of setup 2.png|thumb|300px|'''Figure 2. Schematic of setup''']]
Figure 2 schematically shows our setup. Such a setup is known as balanced homodyne detection and can extract the information of the electrical field in the second mode entering the polarizing beam-splitter (PBS) by measuring the photocurrent difference <math>i_1-i_2</math>. A continuous wave laser (wavelength 658 nm) is incident on one input port of the PBS and used as the local oscillator (LO), while another input port is empty. So the homodyne detection is trying to measure the vacuum state of the electromagnetic field. The randomness source in our setup is the fluctuations of the vacuum field. Here we tried to balance the optical power impinging on the two photodiodes, therefore any power fluctuation coming from the laser diode will be detected simultaneously and canceled in the photocurrent difference.

Alternatively, the randomness can be seen as coming from the shot noise of the photocurrents <math>i_1</math> and <math>i_2</math> with a power proportional to the average optical power. Since the shot noise currents from the diodes are uncorrelated, the y add up. And the amplitude fluctuations in the laser intensity (referred to as classical noise) can be eliminated by measuring the photocurrent difference.

== '''Setup''' ==
The practical setup (shown in Figure 3) was built with as few components as possible to create a baseline performance that we can compare.

[[File:Experimental setup.png|thumb|300px|'''Figure 3. Experimental setup''']]

==='''Tool list'''===
① Laser Diode
: Laser Diode is powered by a laser driving unit. The light intensity can be changed by changing the laser current.
② Focal Lens
: By adjusting the focal lens, the intensity of light that finally hits the photodiodes is adjusted.
③ RP: Rotatable Polarizer
: The polarization state of the light is adjusted by rotating the polarizer.
④ Mirror 1
: By adjusting mirror 1, the position of transmitted and reflected light spots hitting on PD1 and PD2 can be adjusted simultaneously.
⑤ PBS: Polarizing Beam Splitter
: The laser beam incident on the PBS can pass through or be reflected depending on the polarization state. If the incident beam is diagonal polarized (45°), the intensity of reflected and transmitted light is equal.
⑥ Mirror 2
: By adjusting mirror 2, the position of transmitted light spots hitting on PD2 can be tuned.
⑦&⑧ Photodiodes
: Detect the intensity of incident light.
⑩ Gain block
:A ready-made 60 dB gain Block from quantum optic lab.
⑪ High pass filter
:Designed cutoff frequency = 60 MHz.

==='''Description'''===
The total light power is changed by changing the laser current and adjusting the focal lens, while the power of the two output ports of the PBS is balanced by rotating the polarizer in front of the laser diode. Light leaving the PBS is detected by a pair of reverse-biased photodiodes connected in series to perform the current subtraction. By adjusting the orientation of M1 and M2, the light intensity incident on PD1 and PD2 can be adjusted and balanced. The balancing of the photocurrents is monitored by observing the voltage drop across a resister <math>R_{DC}</math> (DC port). Here we use a multimeter to measure the voltage. The fluctuations <math>\Delta(i_1-i_2)</math> are amplified by a 60 dB ready-made Gain block. And after that, a high pass filter (HPF) with a cutoff frequency of 60 MHz is used to filter out low frequency noise.

==='''Characterization list'''===
① Oscilloscope: Used to monitor the AC port and collect data.

② Spectrum Analyzer: Used to analyze the spectrum of total noise.

③ Multimeter
:Used to monitor the DC port and balance two photodiodes.

== '''Process''' ==
* '''26 February 2022:'''
* Did a basic characterization of photodiode
* Inputted a sine wave signal and a laser pointer light, observed the waveform of the photodiode
<gallery widths=300px heights=200px>
File:Basic characterization of photodiode test.jpeg|'''Figure 4. Basic characterization of photodiode'''
File:Schematic of basic characterization of photodiode test.png|'''Figure 5. Schematic of basic characterization of photodiode'''
</gallery>

:To understand the frequency response of the circuit shown in figure 5, we use a function generator to generate a sinusoidal signal to drive the LED, and use this circuit to measure the light output. When the frequency of the signal is low, we can see a relatively complete sine waveform on the oscilloscope. But when the frequency exceeds 1GHz, we could not observe a regular and stable waveform.
* '''5 March 2022:'''
* Used different resistors to test the frequency response of photodiode
<gallery widths=300px heights=200px>
File:Frequency of PD.png|'''Figure 6. Graph of the frequency response of photodiode'''
</gallery>
:We changed the resistors in Figure 6, from 1 kΩ to 11 kΩ and then 20 kΩ. We found that the higher the resistance of the resistor, the larger the output voltage but less sensitive to the high frequency. That is because a reverse-biased photodiode has a certain capacitance and forms an RC series circuit with the resistor. The larger the resistor, the larger the time constant <math>\tau=RC</math> of the RC circuit, and the slower the charge and discharge, which leads to a worse response to high frequency signals.
* '''12 March 2022:'''
* Build up the laser system and ensured the laser output
<gallery widths=300px heights=200px>
File:Laser diode.png|'''Figure 7. HL6501MG laser diode and schematic of internal circuit'''
File:Schematic of electronics laserconnector circuit.jpeg|'''Figure 8. Schematic of electronics laser connector circuit'''
File:Laser source setup.png|'''Figure 9. Laser source setup'''
</gallery>
:We used an HL6501MG laser diode, which is a 0.65 μm band AlGaInP laser diode (LD) with a multi-quantum well (MQW) structure. It is suitable as a light source for large-capacity optical disc memories and various other types of optical equipment. Hermetic sealing of the small package (φ=5.6 mm) assures high reliability.

:The Laser source consists of ① Laser diode; ② Thermostat; ③ Supply circuit for Laser diode and Thermostat; ④ Shell; ⑤ Focal lens; ⑥ Radiator. The Laser Diode is in the thermostat which is connected to the Radiator. We can set the temperature on the Laser power supply. The Thermostat and Radiator will keep the temperature of the laser diode as same as that set on the laser power supply. There is a focal lens in front of the laser diode. We can use it to change the focal length the enlarge the laser intensity hitting on the photodiodes. And a shell made of acrylic sheet and 4 balance posts.
* '''19 March 2022:'''
* Soldered photodiode driving circuit
* Test the feasibility
<gallery widths=300px heights=200px>
File:Photo diode outlines.png|'''Figure 10. S5972 Si PIN photodiode and schematic of internal circuit'''
File:Principle of photodiode driving circuit.png|'''Figure 11. Principle of photodiode driving circuit'''
File:Schematic photodiode driving circuit bolck.jpeg|'''Figure 12. Schematic photodiode driving circuit block'''
</gallery>

:We used an S5972 high-speed Si PIN photodiode to detect the light, which is designed for visible to near-infrared light detection. These photodiodes provide wideband characteristics at a low bias, making them suitable for optical communications and other high-speed photometry.

:We soldered all the components on the circuit chip as Figure 11 shows. After that, we tested its performance using a laser, it was approved that the optical signal was converted into the electrical signal and was measured by the oscilloscope.
* '''26 March 2022:'''
* Build up the whole system
* Tune the bias of two photodiodes
<gallery widths=300px heights=200px>
File:Whole setup.jpeg|'''Figure 13. The whole system setup'''
</gallery>
:We built up the whole setup on the optical platform. Then we tuned the bias of two photodiodes to make sure that the intensity of the laser hitting on both photodiodes is the same by adjusting the multimeter's voltage to around 0.
* '''2 April 2022:'''
* Focus the laser output
* Maximize the laser power output
* Characterize varaiation by varying optical power
<gallery widths=300px heights=200px>
File:Maximize the laser power output.jpeg|'''Figure 14. Maximize the laser power output'''
File:The detector noise power by varying the incident optical power.jpg|'''Figure 15. The plot of the detector noise power by varying the incident optical power'''
</gallery>
:We found that the laser output power in front of the polarizer was about 20 mW, but the power detected by each photodiode was only 0.4 mW. That is because the spot size of the laser was relatively large compared with the detection area of the photodiode. Therefore we needed to focus the lens in the laser block to maximize the detected laser power. To do this, we blocked one photodiode and used a multimeter to monitor the light power detected by another photodiode. After trials, we got a maximum value of voltage drop of 9.17 V, which corresponds to an optical power of 2.08 mW on each photodiode.

:Then, we characterized the change of noise level while rising incident optical power. And then we plotted a graph as shown in Figure 15, it is easy to find when the optical power is in a relatively low range, the noise level is flat which corresponds to the horizontal red line. While the optical power rises, the noise level increases with the optical power in a proportional manner. Therefore, we have enough reasons to believe that the overall noise is dominated by electronic noise in the low optical power range, while the noise level is dominated by shot noise in the high optical power range.
* '''9 April 2022:'''
* Soldered high pass filter
* Test its feasibility
<gallery widths=300px heights=200px>
File:Highpass filter principle circuit.png|'''Figure 16. Schematic of high pass filter circuit'''
File:Graph of theoretical high pass filter frequency response.jpg.png|'''Figure 17. Graph of theoretical high pass filter frequency response'''
File:Frequency of HPF.png|'''Figure 18. Graph of measured high pass filter frequency response'''
File:Schematic of high pass filter.jpeg|'''Figure 19. Setup of high pass filter'''
File:Setup of gain block and high pass filter.jpeg|'''Figure 20. Setup of gain block and high pass filter'''
</gallery>
:The measured total noise has a lot of low-frequency noise and is relatively flat power density in the range of 60-200 MHz. With a low pass filter of 200 MHz in the oscilloscope, we just needed a high pass filter of 60 MHz which compresses the low-frequency fluctuations. So we designed a high pass filter of 60 MHz and soldered the high pass filter.

:After that, we tested its performance. By comparing with the theoretical high pass filter graph, the measured high pass filter frequency response showed a high correspondence with it, which means it is feasible to apply it to the whole system to suppress the low-frequency fluctuations.
* '''16 April 2022:'''
* Apply the high pass filter to the circuit and test
* Record data and draw some graphs analysis
: In order to verify that the signals we obtained were quantum random numbers, we recorded the data at different sampling rates and performed autocorrelation calculations. These can be found in the "Result"-"Autocorrelation" part.

* '''23 April 2022:'''
* Processing experimental data
* Draw autocorrelation images
* Summarize and upload the experimental results

== '''Results''' ==
==='''Quantum noise'''===
*To ensure that the fluctuations at the amplifier output are dominated by quantum noise, the spectral power density is measured (in Figure 21. ).

[[File:Ampliﬁed noise levels measured into a resolution bandwidth B = 3 MHz..jpg|thumb|600px|center|'''Figure 21. Schematic of branching path quantum random number generators''']]

:Amplified noise levels measured into a resolution bandwidth B = 3 MHz. The total noise is measured from the photocurrent difference <math>i_1-i_2</math> with equal optical power impinging on both photodiodes. The current <math>i_1</math> of a single photodiode reveals colored classical noise. The electronic noise is measured without any optical input.
:In an alternative view, the laser beam can be seen as generating photocurrents <math>i_1</math> and <math>i_2</math> with a shot noise power proportional to the average optical power. The shot noise currents from the diodes add up as they are uncorrelated, while amplitude fluctuations in the laser intensity (referred to as classical noise) do not affect the photocurrent difference.

=== '''Autocorrelation'''===
*:Autocorrelation, sometimes known as serial correlation in the discrete-time case, is the correlation of a signal with a delayed copy of itself as a function of delay. Informally, it is the similarity between observations as a function of the time lag between them. In our experiment, if we obtain an ideal '''quantum random number generator''', the autocorrelation will be 1 when the time lag is 0, while the autocorrelation will be close to 0 when the time lag is not 0.

*:Given a signal <math>f(t)</math>, the continuous autocorrelation <math>R_{ff}(\tau)</math> is most often defined as the continuous cross-correlation integral of <math>f(t)</math> with itself, at lag <math>\tau</math>.

::::::::::::::::<math>R_{ff}(\tau) = \int_{-\infty}^\infty f(t+\tau)\overline{f(t)}\, {\rm d}t = \int_{-\infty}^\infty f(t) \overline{f(t-\tau)}\, {\rm d}t</math>

::where <math>\overline{f(t)}</math> represents the complex conjugate of <math>f(t)</math>. Note that the parameter <math>t</math> in the integral is a dummy variable and is only necessary to calculate the integral. It has no specific meaning.

*:'''Experimental result'''
:<gallery widths=500px heights=300px>
File:2.5 GHz (-20,20) After Highpass1.png|'''Figure 22. Autocorrelation of the total noise signal sampled at 2.5 GHz'''
File:500 kHz (-20,20) After Highpass1.png|'''Figure 23. Autocorrelation of the total noise signal sampled at 500 KHz'''
:</gallery>

:We recorded several sets of data with different sampling frequencies ( 2.5 GHz to 500 kHz) and obtained autocorrelation for each group. A very high correlation between any two adjacent points was observed when we use a 2.5 GHz sampling rate. This is simply because of an extremely high sampling rate which results in every two adjacent points being almost at the same position. We can get a better correlation by reducing the sampling frequency to such as 10 MHz or even lower.

:But the autocorrelation with a 500 kHz sampling rate is still not ideal. This is limited by our experimental setup. We caught up with too much electronic interference. A well-designed experimental setup with integrated photodiodes, amplifier, and high pass filter will stimulate a better result.

=== '''Randomness Extraction'''===
The amplified total noise is digitized into 16-bit words at a sampling rate of 10 MHz (because we get the best atuocorrelation result at this sampling rate) and recorded in binary form by an oscilloscope. All data are discrete values between <math>-2^{15}</math> and <math>2^{15}-1</math>. Figure 24 below shows the distribution of our raw data, which fits to a Gaussian distribution with a standard deviation <math>\sigma = 5240</math>.
[[File:Raw_data.png|thumb|600px|center|'''Figure 24. Distribution of row data and fitted with Gaussian distribution.''']]

In many applications, however, random numbers are required to be not only unpredictable but also uniformly distributed. Therefore the raw data collected by the oscilloscope cannot be used directly. Various randomness extractors, such as Trevisan's extractor and Linear Feedback Shift Register, have been used to convert non-uniformly distributed raw data in to a uniformly distributed binary stream. For simplicity, here we used random matrix multiplications to extract uniformly distributed random numbers.

Equation above shows how it works. Since our raw data is recorded in binary form, it is an N-row column vector <math>r_i</math> with all elements 0 or 1. And the <math>M \times N</math> binary matrix is an algorithmically generated pseudo-random matrix. Then the raw data and the random matrix are multiplied （binary OR and XOR） to produce a column vector <math>s_i</math> of M rows. As long as the size of the random matrix is large enough, 0 and 1 in the output <math>s_i</math> will be almost uniformly distributed. Here M can take any integer not greater than N. The reason is that, the voltage at AC port fluctuates around 0 V and the first few bits in each binary number are typically unused (all 0). Therefore the entropy in the raw data is smaller than the size of the data (e.g.6 bits of entropy per 8 bits sample). The standard approach would be to first estimate the entropy in the raw data and then choose the value of N to extract the randomness. Since in our project, we didn't do that, here we choose N = M.
[[File:Extracted.png|thumb|600px|center|'''Figure 25, Distribution of random data after the random matrix multiplication.''']]
Figure 25 shows the distribution of the data after randomness extraction. As we can see, all data fall within the <math>\pm3\sigma</math> bounds, so we have reason to believe that extracted data is almost uniformly distributed.
[[File:Contrast.png||thumb|600px|center|'''Figure 26. Distribution of random numbers before (blue) and after (red) the randomness extraction, shown in time domain (left) and histogram (right)''']]
Figure 26 shows the comparison between random numbers before and after the randomness extraction.

=== '''Randomness Test'''===
To verify the randomness of the experimental results we obtained, we used two compression protocols(rar and zip) to compress the random numbers we generated. The compressed file size does not change significantly compared with the original file(from 58k to 55k), which, to some extent, illustrates the randomness of our results.

== '''References''' ==
[1] Miguel Herrero-Collantes and Juan Carlos Garcia-Escartin, Quantum random number generators, Rev. Mod. Phys, 89, 015004.

[2] Shi, Yicheng, Brenda Chng, and Christian Kurtsiefer, Random numbers from vacuum fluctuations, Applied Physics Letters, 109.4 (2016): 041101.

[3] https://www.digchip.com/datasheets/parts/datasheet/625/HL6501MG-pdf.php

[4] https://www.farnell.com/datasheets/3171163.pdf

Quantum Random Number Generator

2022-04-29T16:39:12Z

Zhang Munan: /* Randomness Test */

== '''Team Members''' ==
Wang Yang A0228753X

Xiao Yucan A0236278W

Zhang Munan A0236273E

== '''Idea''' ==
We live in an increasingly connected world, where a superior source of entropy is the key to data security. The effectiveness of any cryptographic system is determined by the strength of the keys it used. In turn, the strength of the key is determined by the degree of randomness used in its generation. Besides, large amount of random numbers are at the core of Monte Carlo simulations, which are widely used in scientific research. Methods produce random numbers from any algorithm are called pseudo-random number generator(PRNG). And random numbers generated by PRNG are deterministic by definition and therefore unsuitable for cryptographic purposes.

In order to generate unpredictable random numbers, hardware random number generators have been widely used. These physically generated random numbers are considered "truly" random because it is either practically or fundamentally impossible to predict the outcome of such a device. Quantum Random Number Generators (QRNGs) belong to a class of hardware random number generators and leverage the random properties of quantum physics to generate a true source of entropy, improving the quality of seed content for key generation.

Early QRNGs were based on radioactive decay. And more recently, QRNGs based on Poisson statistics of photons have been developed. The core idea is shown in the figure below. Single photons generated by a laser source are incident on a semi-transparent mirror and the mutually exclusive events (reflection/transmission) are detected and associated with ‘0’ or ‘1’ bit values respectively. The unpredictability of generated numbers is ensured by the quantum nature of the process. However, such a scheme needs a reliable single photon source as well as single photon detectors and it's not possible for our project. Here, we decided to build a QRNG based on measuring vacuum fluctuations of a light field as a random source. More details will be discussed in the principle part.
[[File:Principle schematic of QRNG.png|thumb|300px|'''Figure 1. Schematic of branching path quantum random number generators''']]

=== Benefits of having a quantum random number generator ===
* The source of randomness is unpredictable and controlled by quantum process.
* Live/real-time monitoring of entropy source is possible and highly effective as well.
* All attacks on the entropy source are detectable.

=== Application of quantum random number generator ===
* Securing data at rest in data centres
* Securing any kind of sensitive data
* Securing data in the cloud
* One-time pad for authentication in banking and other transactions
* Gaming applications and lottery
* Block-chain network
* Numerical simulations, statistical research
* IoT devices
* E-commerce and banking applications
* Cryptographic applications
* Telecom and 5G
* Monte Carlo Simulation

== '''Principles''' ==
[[File:Schematic of setup 2.png|thumb|300px|'''Figure 2. Schematic of setup''']]
Figure 2 schematically shows our setup. Such a setup is known as balanced homodyne detection and can extract the information of the electrical field in the second mode entering the polarizing beam-splitter (PBS) by measuring the photocurrent difference <math>i_1-i_2</math>. A continuous wave laser (wavelength 658 nm) is incident on one input port of the PBS and used as the local oscillator (LO), while another input port is empty. So the homodyne detection is trying to measure the vacuum state of the electromagnetic field. The randomness source in our setup is the fluctuations of the vacuum field. Here we tried to balance the optical power impinging on the two photodiodes, therefore any power fluctuation coming from the laser diode will be detected simultaneously and canceled in the photocurrent difference.

Alternatively, the randomness can be seen as coming from the shot noise of the photocurrents <math>i_1</math> and <math>i_2</math> with a power proportional to the average optical power. Since the shot noise currents from the diodes are uncorrelated, the y add up. And the amplitude fluctuations in the laser intensity (referred to as classical noise) can be eliminated by measuring the photocurrent difference.

== '''Setup''' ==
The practical setup (shown in Figure 3) was built with as few components as possible to create a baseline performance that we can compare.

[[File:Experimental setup.png|thumb|300px|'''Figure 3. Experimental setup''']]

==='''Tool list'''===
① Laser Diode
: Laser Diode is powered by a laser driving unit. The light intensity can be changed by changing the laser current.
② Focal Lens
: By adjusting the focal lens, the intensity of light that finally hits the photodiodes is adjusted.
③ RP: Rotatable Polarizer
: The polarization state of the light is adjusted by rotating the polarizer.
④ Mirror 1
: By adjusting mirror 1, the position of transmitted and reflected light spots hitting on PD1 and PD2 can be adjusted simultaneously.
⑤ PBS: Polarizing Beam Splitter
: The laser beam incident on the PBS can pass through or be reflected depending on the polarization state. If the incident beam is diagonal polarized (45°), the intensity of reflected and transmitted light is equal.
⑥ Mirror 2
: By adjusting mirror 2, the position of transmitted light spots hitting on PD2 can be tuned.
⑦&⑧ Photodiodes
: Detect the intensity of incident light.
⑩ Gain block
:A ready-made 60 dB gain Block from quantum optic lab.
⑪ High pass filter
:Designed cutoff frequency = 60 MHz.

==='''Description'''===
The total light power is changed by changing the laser current and adjusting the focal lens, while the power of the two output ports of the PBS is balanced by rotating the polarizer in front of the laser diode. Light leaving the PBS is detected by a pair of reverse-biased photodiodes connected in series to perform the current subtraction. By adjusting the orientation of M1 and M2, the light intensity incident on PD1 and PD2 can be adjusted and balanced. The balancing of the photocurrents is monitored by observing the voltage drop across a resister <math>R_{DC}</math> (DC port). Here we use a multimeter to measure the voltage. The fluctuations <math>\Delta(i_1-i_2)</math> are amplified by a 60 dB ready-made Gain block. And after that, a high pass filter (HPF) with a cutoff frequency of 60 MHz is used to filter out low frequency noise.

==='''Characterization list'''===
① Oscilloscope: Used to monitor the AC port and collect data.

② Spectrum Analyzer: Used to analyze the spectrum of total noise.

③ Multimeter
:Used to monitor the DC port and balance two photodiodes.

== '''Process''' ==
* '''26 February 2022:'''
* Did a basic characterization of photodiode
* Inputted a sine wave signal and a laser pointer light, observed the waveform of the photodiode
<gallery widths=300px heights=200px>
File:Basic characterization of photodiode test.jpeg|'''Figure 4. Basic characterization of photodiode'''
File:Schematic of basic characterization of photodiode test.png|'''Figure 5. Schematic of basic characterization of photodiode'''
</gallery>

:To understand the frequency response of the circuit shown in figure 5, we use a function generator to generate a sinusoidal signal to drive the LED, and use this circuit to measure the light output. When the frequency of the signal is low, we can see a relatively complete sine waveform on the oscilloscope. But when the frequency exceeds 1GHz, we could not observe a regular and stable waveform.
* '''5 March 2022:'''
* Used different resistors to test the frequency response of photodiode
<gallery widths=300px heights=200px>
File:Frequency of PD.png|'''Figure 6. Graph of the frequency response of photodiode'''
</gallery>
:We changed the resistors in Figure 6, from 1 kΩ to 11 kΩ and then 20 kΩ. We found that the higher the resistance of the resistor, the larger the output voltage but less sensitive to the high frequency. That is because a reverse-biased photodiode has a certain capacitance and forms an RC series circuit with the resistor. The larger the resistor, the larger the time constant <math>\tau=RC</math> of the RC circuit, and the slower the charge and discharge, which leads to a worse response to high frequency signals.
* '''12 March 2022:'''
* Build up the laser system and ensured the laser output
<gallery widths=300px heights=200px>
File:Laser diode.png|'''Figure 7. HL6501MG laser diode and schematic of internal circuit'''
File:Schematic of electronics laserconnector circuit.jpeg|'''Figure 8. Schematic of electronics laser connector circuit'''
File:Laser source setup.png|'''Figure 9. Laser source setup'''
</gallery>
:We used an HL6501MG laser diode, which is a 0.65 μm band AlGaInP laser diode (LD) with a multi-quantum well (MQW) structure. It is suitable as a light source for large-capacity optical disc memories and various other types of optical equipment. Hermetic sealing of the small package (φ=5.6 mm) assures high reliability.

:The Laser source consists of ① Laser diode; ② Thermostat; ③ Supply circuit for Laser diode and Thermostat; ④ Shell; ⑤ Focal lens; ⑥ Radiator. The Laser Diode is in the thermostat which is connected to the Radiator. We can set the temperature on the Laser power supply. The Thermostat and Radiator will keep the temperature of the laser diode as same as that set on the laser power supply. There is a focal lens in front of the laser diode. We can use it to change the focal length the enlarge the laser intensity hitting on the photodiodes. And a shell made of acrylic sheet and 4 balance posts.
* '''19 March 2022:'''
* Soldered photodiode driving circuit
* Test the feasibility
<gallery widths=300px heights=200px>
File:Photo diode outlines.png|'''Figure 10. S5972 Si PIN photodiode and schematic of internal circuit'''
File:Principle of photodiode driving circuit.png|'''Figure 11. Principle of photodiode driving circuit'''
File:Schematic photodiode driving circuit bolck.jpeg|'''Figure 12. Schematic photodiode driving circuit block'''
</gallery>

:We used an S5972 high-speed Si PIN photodiode to detect the light, which is designed for visible to near-infrared light detection. These photodiodes provide wideband characteristics at a low bias, making them suitable for optical communications and other high-speed photometry.

:We soldered all the components on the circuit chip as Figure 11 shows. After that, we tested its performance using a laser, it was approved that the optical signal was converted into the electrical signal and was measured by the oscilloscope.
* '''26 March 2022:'''
* Build up the whole system
* Tune the bias of two photodiodes
<gallery widths=300px heights=200px>
File:Whole setup.jpeg|'''Figure 13. The whole system setup'''
</gallery>
:We built up the whole setup on the optical platform. Then we tuned the bias of two photodiodes to make sure that the intensity of the laser hitting on both photodiodes is the same by adjusting the multimeter's voltage to around 0.
* '''2 April 2022:'''
* Focus the laser output
* Maximize the laser power output
* Characterize varaiation by varying optical power
<gallery widths=300px heights=200px>
File:Maximize the laser power output.jpeg|'''Figure 14. Maximize the laser power output'''
File:The detector noise power by varying the incident optical power.jpg|'''Figure 15. The plot of the detector noise power by varying the incident optical power'''
</gallery>
:We found that the laser output power in front of the polarizer was about 20 mW, but the power detected by each photodiode was only 0.4 mW. That is because the spot size of the laser was relatively large compared with the detection area of the photodiode. Therefore we needed to focus the lens in the laser block to maximize the detected laser power. To do this, we blocked one photodiode and used a multimeter to monitor the light power detected by another photodiode. After trials, we got a maximum value of voltage drop of 9.17 V, which corresponds to an optical power of 2.08 mW on each photodiode.

:Then, we characterized the change of noise level while rising incident optical power. And then we plotted a graph as shown in Figure 15, it is easy to find when the optical power is in a relatively low range, the noise level is flat which corresponds to the horizontal red line. While the optical power rises, the noise level increases with the optical power in a proportional manner. Therefore, we have enough reasons to believe that the overall noise is dominated by electronic noise in the low optical power range, while the noise level is dominated by shot noise in the high optical power range.
* '''9 April 2022:'''
* Soldered high pass filter
* Test its feasibility
<gallery widths=300px heights=200px>
File:Highpass filter principle circuit.png|'''Figure 16. Schematic of high pass filter circuit'''
File:Graph of theoretical high pass filter frequency response.jpg.png|'''Figure 17. Graph of theoretical high pass filter frequency response'''
File:Frequency of HPF.png|'''Figure 18. Graph of measured high pass filter frequency response'''
File:Schematic of high pass filter.jpeg|'''Figure 19. Setup of high pass filter'''
File:Setup of gain block and high pass filter.jpeg|'''Figure 20. Setup of gain block and high pass filter'''
</gallery>
:The measured total noise has a lot of low-frequency noise and is relatively flat power density in the range of 60-200 MHz. With a low pass filter of 200 MHz in the oscilloscope, we just needed a high pass filter of 60 MHz which compresses the low-frequency fluctuations. So we designed a high pass filter of 60 MHz and soldered the high pass filter.

:After that, we tested its performance. By comparing with the theoretical high pass filter graph, the measured high pass filter frequency response showed a high correspondence with it, which means it is feasible to apply it to the whole system to suppress the low-frequency fluctuations.
* '''16 April 2022:'''
* Apply the high pass filter to the circuit and test
* Record data and draw some graphs analysis
: In order to verify that the signals we obtained were quantum random numbers, we recorded the data at different sampling rates and performed autocorrelation calculations. These can be found in the "Result"-"Autocorrelation" part.

* '''23 April 2022:'''
* Processing experimental data
* Draw autocorrelation images
* Summarize and upload the experimental results

== '''Results''' ==
==='''Quantum noise'''===
*To ensure that the fluctuations at the amplifier output are dominated by quantum noise, the spectral power density is measured (in Figure 21. ).

[[File:Ampliﬁed noise levels measured into a resolution bandwidth B = 3 MHz..jpg|thumb|600px|center|'''Figure 21. Schematic of branching path quantum random number generators''']]

:Amplified noise levels measured into a resolution bandwidth B = 3 MHz. The total noise is measured from the photocurrent difference <math>i_1-i_2</math> with equal optical power impinging on both photodiodes. The current <math>i_1</math> of a single photodiode reveals colored classical noise. The electronic noise is measured without any optical input.
:In an alternative view, the laser beam can be seen as generating photocurrents <math>i_1</math> and <math>i_2</math> with a shot noise power proportional to the average optical power. The shot noise currents from the diodes add up as they are uncorrelated, while amplitude fluctuations in the laser intensity (referred to as classical noise) do not affect the photocurrent difference.

=== '''Autocorrelation'''===
*:Autocorrelation, sometimes known as serial correlation in the discrete-time case, is the correlation of a signal with a delayed copy of itself as a function of delay. Informally, it is the similarity between observations as a function of the time lag between them. In our experiment, if we obtain an ideal '''quantum random number generator''', the autocorrelation will be 1 when the time lag is 0, while the autocorrelation will be close to 0 when the time lag is not 0.

*:Given a signal <math>f(t)</math>, the continuous autocorrelation <math>R_{ff}(\tau)</math> is most often defined as the continuous cross-correlation integral of <math>f(t)</math> with itself, at lag <math>\tau</math>.

::::::::::::::::<math>R_{ff}(\tau) = \int_{-\infty}^\infty f(t+\tau)\overline{f(t)}\, {\rm d}t = \int_{-\infty}^\infty f(t) \overline{f(t-\tau)}\, {\rm d}t</math>

::where <math>\overline{f(t)}</math> represents the complex conjugate of <math>f(t)</math>. Note that the parameter <math>t</math> in the integral is a dummy variable and is only necessary to calculate the integral. It has no specific meaning.

*:'''Experimental result'''
:<gallery widths=500px heights=300px>
File:2.5 GHz (-20,20) After Highpass1.png|'''Figure 22. Autocorrelation of the total noise signal sampled at 2.5 GHz'''
File:500 kHz (-20,20) After Highpass1.png|'''Figure 23. Autocorrelation of the total noise signal sampled at 500 KHz'''
:</gallery>

:We recorded several sets of data with different sampling frequencies ( 2.5 GHz to 500 kHz) and obtained autocorrelation for each group. A very high correlation between any two adjacent points was observed when we use a 2.5 GHz sampling rate. This is simply because of an extremely high sampling rate which results in every two adjacent points being almost at the same position. We can get a better correlation by reducing the sampling frequency to such as 10 MHz or even lower.

:But the autocorrelation with a 500 kHz sampling rate is still not ideal. This is limited by our experimental setup. We caught up with too much electronic interference. A well-designed experimental setup with integrated photodiodes, amplifier, and high pass filter will stimulate a better result.

=== '''Randomness Extraction'''===
The amplified total noise is digitized into 16-bit words at a sampling rate of 10 MHz (because we get the best atuocorrelation result at this sampling rate) and recorded by an oscilloscope. All data are discrete values between <math>-2^{15}</math> and <math>2^{15}-1</math>. Figure 24 below shows the distribution of our raw data, which fits to a Gaussian distribution with a standard deviation <math>\sigma = 5240</math>.
[[File:Raw_data.png|thumb|600px|center|'''Figure 24. Distribution of row data and fitted with Gaussian distribution.''']]

In many applications, however, random numbers are required to be not only unpredictable but also uniformly distributed. Therefore the raw data collected by the oscilloscope cannot be used directly. Various randomness extractors, such as Trevisan's extractor and Linear Feedback Shift Register, have been used to convert non-uniformly distributed raw data in to a uniformly distributed binary stream. For simplicity, here we used random matrix multiplications to extract uniformly distributed random numbers.

Equation above shows how it works. Since our raw data is recorded in binary form, it is an N-row column vector <math>r_i</math> with all elements 0 or 1. And the <math>M \times N</math> binary matrix is an algorithmically generated pseudo-random matrix. Then the raw data and the random matrix are multiplied （binary OR and XOR） to produce a column vector <math>s_i</math> of M rows. As long as the size of the random matrix is large enough, 0 and 1 in the output <math>s_i</math> will be almost uniformly distributed. Here M can take any integer not greater than N. The reason is that, the voltage at AC port fluctuates around 0 V and the first few bits in each binary number are typically unused (all 0). Therefore the entropy in the raw data is smaller than the size of the data (e.g.6 bits of entropy per 8 bits sample). The standard approach would be to first estimate the entropy in the raw data and then choose the value of N to extract the randomness. Since in our project, we didn't do that, here we choose N = M.
[[File:Extracted.png|thumb|600px|center|'''Figure 25, Distribution of random data after the random matrix multiplication.''']]
Figure 25 shows the distribution of the data after randomness extraction. As we can see, all data fall within the <math>\pm3\sigma</math> bounds, so we have reason to believe that extracted data is almost uniformly distributed.
[[File:Contrast.png||thumb|600px|center|'''Figure 26. Distribution of random numbers before (blue) and after (red) the randomness extraction, shown in time domain (left) and histogram (right)''']]
Figure 26 shows the comparison between random numbers before and after the randomness extraction.

=== '''Randomness Test'''===
To verify the randomness of the experimental results we obtained, we used two compression protocols(rar and zip) to compress the random numbers we generated. The compressed file size does not change significantly compared with the original file(from 58k to 55k), which, to some extent, illustrates the randomness of our results.

== '''References''' ==
[1] Miguel Herrero-Collantes and Juan Carlos Garcia-Escartin, Quantum random number generators, Rev. Mod. Phys, 89, 015004.

[2] Shi, Yicheng, Brenda Chng, and Christian Kurtsiefer, Random numbers from vacuum fluctuations, Applied Physics Letters, 109.4 (2016): 041101.

[3] https://www.digchip.com/datasheets/parts/datasheet/625/HL6501MG-pdf.php

[4] https://www.farnell.com/datasheets/3171163.pdf

Quantum Random Number Generator

2022-04-29T16:36:52Z

Zhang Munan: /* Randomness Extraction */

== '''Team Members''' ==
Wang Yang A0228753X

Xiao Yucan A0236278W

Zhang Munan A0236273E

== '''Idea''' ==
We live in an increasingly connected world, where a superior source of entropy is the key to data security. The effectiveness of any cryptographic system is determined by the strength of the keys it used. In turn, the strength of the key is determined by the degree of randomness used in its generation. Besides, large amount of random numbers are at the core of Monte Carlo simulations, which are widely used in scientific research. Methods produce random numbers from any algorithm are called pseudo-random number generator(PRNG). And random numbers generated by PRNG are deterministic by definition and therefore unsuitable for cryptographic purposes.

In order to generate unpredictable random numbers, hardware random number generators have been widely used. These physically generated random numbers are considered "truly" random because it is either practically or fundamentally impossible to predict the outcome of such a device. Quantum Random Number Generators (QRNGs) belong to a class of hardware random number generators and leverage the random properties of quantum physics to generate a true source of entropy, improving the quality of seed content for key generation.

Early QRNGs were based on radioactive decay. And more recently, QRNGs based on Poisson statistics of photons have been developed. The core idea is shown in the figure below. Single photons generated by a laser source are incident on a semi-transparent mirror and the mutually exclusive events (reflection/transmission) are detected and associated with ‘0’ or ‘1’ bit values respectively. The unpredictability of generated numbers is ensured by the quantum nature of the process. However, such a scheme needs a reliable single photon source as well as single photon detectors and it's not possible for our project. Here, we decided to build a QRNG based on measuring vacuum fluctuations of a light field as a random source. More details will be discussed in the principle part.
[[File:Principle schematic of QRNG.png|thumb|300px|'''Figure 1. Schematic of branching path quantum random number generators''']]

=== Benefits of having a quantum random number generator ===
* The source of randomness is unpredictable and controlled by quantum process.
* Live/real-time monitoring of entropy source is possible and highly effective as well.
* All attacks on the entropy source are detectable.

=== Application of quantum random number generator ===
* Securing data at rest in data centres
* Securing any kind of sensitive data
* Securing data in the cloud
* One-time pad for authentication in banking and other transactions
* Gaming applications and lottery
* Block-chain network
* Numerical simulations, statistical research
* IoT devices
* E-commerce and banking applications
* Cryptographic applications
* Telecom and 5G
* Monte Carlo Simulation

== '''Principles''' ==
[[File:Schematic of setup 2.png|thumb|300px|'''Figure 2. Schematic of setup''']]
Figure 2 schematically shows our setup. Such a setup is known as balanced homodyne detection and can extract the information of the electrical field in the second mode entering the polarizing beam-splitter (PBS) by measuring the photocurrent difference <math>i_1-i_2</math>. A continuous wave laser (wavelength 658 nm) is incident on one input port of the PBS and used as the local oscillator (LO), while another input port is empty. So the homodyne detection is trying to measure the vacuum state of the electromagnetic field. The randomness source in our setup is the fluctuations of the vacuum field. Here we tried to balance the optical power impinging on the two photodiodes, therefore any power fluctuation coming from the laser diode will be detected simultaneously and canceled in the photocurrent difference.

Alternatively, the randomness can be seen as coming from the shot noise of the photocurrents <math>i_1</math> and <math>i_2</math> with a power proportional to the average optical power. Since the shot noise currents from the diodes are uncorrelated, the y add up. And the amplitude fluctuations in the laser intensity (referred to as classical noise) can be eliminated by measuring the photocurrent difference.

== '''Setup''' ==
The practical setup (shown in Figure 3) was built with as few components as possible to create a baseline performance that we can compare.

[[File:Experimental setup.png|thumb|300px|'''Figure 3. Experimental setup''']]

==='''Tool list'''===
① Laser Diode
: Laser Diode is powered by a laser driving unit. The light intensity can be changed by changing the laser current.
② Focal Lens
: By adjusting the focal lens, the intensity of light that finally hits the photodiodes is adjusted.
③ RP: Rotatable Polarizer
: The polarization state of the light is adjusted by rotating the polarizer.
④ Mirror 1
: By adjusting mirror 1, the position of transmitted and reflected light spots hitting on PD1 and PD2 can be adjusted simultaneously.
⑤ PBS: Polarizing Beam Splitter
: The laser beam incident on the PBS can pass through or be reflected depending on the polarization state. If the incident beam is diagonal polarized (45°), the intensity of reflected and transmitted light is equal.
⑥ Mirror 2
: By adjusting mirror 2, the position of transmitted light spots hitting on PD2 can be tuned.
⑦&⑧ Photodiodes
: Detect the intensity of incident light.
⑩ Gain block
:A ready-made 60 dB gain Block from quantum optic lab.
⑪ High pass filter
:Designed cutoff frequency = 60 MHz.

==='''Description'''===
The total light power is changed by changing the laser current and adjusting the focal lens, while the power of the two output ports of the PBS is balanced by rotating the polarizer in front of the laser diode. Light leaving the PBS is detected by a pair of reverse-biased photodiodes connected in series to perform the current subtraction. By adjusting the orientation of M1 and M2, the light intensity incident on PD1 and PD2 can be adjusted and balanced. The balancing of the photocurrents is monitored by observing the voltage drop across a resister <math>R_{DC}</math> (DC port). Here we use a multimeter to measure the voltage. The fluctuations <math>\Delta(i_1-i_2)</math> are amplified by a 60 dB ready-made Gain block. And after that, a high pass filter (HPF) with a cutoff frequency of 60 MHz is used to filter out low frequency noise.

==='''Characterization list'''===
① Oscilloscope: Used to monitor the AC port and collect data.

② Spectrum Analyzer: Used to analyze the spectrum of total noise.

③ Multimeter
:Used to monitor the DC port and balance two photodiodes.

== '''Process''' ==
* '''26 February 2022:'''
* Did a basic characterization of photodiode
* Inputted a sine wave signal and a laser pointer light, observed the waveform of the photodiode
<gallery widths=300px heights=200px>
File:Basic characterization of photodiode test.jpeg|'''Figure 4. Basic characterization of photodiode'''
File:Schematic of basic characterization of photodiode test.png|'''Figure 5. Schematic of basic characterization of photodiode'''
</gallery>

:To understand the frequency response of the circuit shown in figure 5, we use a function generator to generate a sinusoidal signal to drive the LED, and use this circuit to measure the light output. When the frequency of the signal is low, we can see a relatively complete sine waveform on the oscilloscope. But when the frequency exceeds 1GHz, we could not observe a regular and stable waveform.
* '''5 March 2022:'''
* Used different resistors to test the frequency response of photodiode
<gallery widths=300px heights=200px>
File:Frequency of PD.png|'''Figure 6. Graph of the frequency response of photodiode'''
</gallery>
:We changed the resistors in Figure 6, from 1 kΩ to 11 kΩ and then 20 kΩ. We found that the higher the resistance of the resistor, the larger the output voltage but less sensitive to the high frequency. That is because a reverse-biased photodiode has a certain capacitance and forms an RC series circuit with the resistor. The larger the resistor, the larger the time constant <math>\tau=RC</math> of the RC circuit, and the slower the charge and discharge, which leads to a worse response to high frequency signals.
* '''12 March 2022:'''
* Build up the laser system and ensured the laser output
<gallery widths=300px heights=200px>
File:Laser diode.png|'''Figure 7. HL6501MG laser diode and schematic of internal circuit'''
File:Schematic of electronics laserconnector circuit.jpeg|'''Figure 8. Schematic of electronics laser connector circuit'''
File:Laser source setup.png|'''Figure 9. Laser source setup'''
</gallery>
:We used an HL6501MG laser diode, which is a 0.65 μm band AlGaInP laser diode (LD) with a multi-quantum well (MQW) structure. It is suitable as a light source for large-capacity optical disc memories and various other types of optical equipment. Hermetic sealing of the small package (φ=5.6 mm) assures high reliability.

:The Laser source consists of ① Laser diode; ② Thermostat; ③ Supply circuit for Laser diode and Thermostat; ④ Shell; ⑤ Focal lens; ⑥ Radiator. The Laser Diode is in the thermostat which is connected to the Radiator. We can set the temperature on the Laser power supply. The Thermostat and Radiator will keep the temperature of the laser diode as same as that set on the laser power supply. There is a focal lens in front of the laser diode. We can use it to change the focal length the enlarge the laser intensity hitting on the photodiodes. And a shell made of acrylic sheet and 4 balance posts.
* '''19 March 2022:'''
* Soldered photodiode driving circuit
* Test the feasibility
<gallery widths=300px heights=200px>
File:Photo diode outlines.png|'''Figure 10. S5972 Si PIN photodiode and schematic of internal circuit'''
File:Principle of photodiode driving circuit.png|'''Figure 11. Principle of photodiode driving circuit'''
File:Schematic photodiode driving circuit bolck.jpeg|'''Figure 12. Schematic photodiode driving circuit block'''
</gallery>

:We used an S5972 high-speed Si PIN photodiode to detect the light, which is designed for visible to near-infrared light detection. These photodiodes provide wideband characteristics at a low bias, making them suitable for optical communications and other high-speed photometry.

:We soldered all the components on the circuit chip as Figure 11 shows. After that, we tested its performance using a laser, it was approved that the optical signal was converted into the electrical signal and was measured by the oscilloscope.
* '''26 March 2022:'''
* Build up the whole system
* Tune the bias of two photodiodes
<gallery widths=300px heights=200px>
File:Whole setup.jpeg|'''Figure 13. The whole system setup'''
</gallery>
:We built up the whole setup on the optical platform. Then we tuned the bias of two photodiodes to make sure that the intensity of the laser hitting on both photodiodes is the same by adjusting the multimeter's voltage to around 0.
* '''2 April 2022:'''
* Focus the laser output
* Maximize the laser power output
* Characterize varaiation by varying optical power
<gallery widths=300px heights=200px>
File:Maximize the laser power output.jpeg|'''Figure 14. Maximize the laser power output'''
File:The detector noise power by varying the incident optical power.jpg|'''Figure 15. The plot of the detector noise power by varying the incident optical power'''
</gallery>
:We found that the laser output power in front of the polarizer was about 20 mW, but the power detected by each photodiode was only 0.4 mW. That is because the spot size of the laser was relatively large compared with the detection area of the photodiode. Therefore we needed to focus the lens in the laser block to maximize the detected laser power. To do this, we blocked one photodiode and used a multimeter to monitor the light power detected by another photodiode. After trials, we got a maximum value of voltage drop of 9.17 V, which corresponds to an optical power of 2.08 mW on each photodiode.

:Then, we characterized the change of noise level while rising incident optical power. And then we plotted a graph as shown in Figure 15, it is easy to find when the optical power is in a relatively low range, the noise level is flat which corresponds to the horizontal red line. While the optical power rises, the noise level increases with the optical power in a proportional manner. Therefore, we have enough reasons to believe that the overall noise is dominated by electronic noise in the low optical power range, while the noise level is dominated by shot noise in the high optical power range.
* '''9 April 2022:'''
* Soldered high pass filter
* Test its feasibility
<gallery widths=300px heights=200px>
File:Highpass filter principle circuit.png|'''Figure 16. Schematic of high pass filter circuit'''
File:Graph of theoretical high pass filter frequency response.jpg.png|'''Figure 17. Graph of theoretical high pass filter frequency response'''
File:Frequency of HPF.png|'''Figure 18. Graph of measured high pass filter frequency response'''
File:Schematic of high pass filter.jpeg|'''Figure 19. Setup of high pass filter'''
File:Setup of gain block and high pass filter.jpeg|'''Figure 20. Setup of gain block and high pass filter'''
</gallery>
:The measured total noise has a lot of low-frequency noise and is relatively flat power density in the range of 60-200 MHz. With a low pass filter of 200 MHz in the oscilloscope, we just needed a high pass filter of 60 MHz which compresses the low-frequency fluctuations. So we designed a high pass filter of 60 MHz and soldered the high pass filter.

:After that, we tested its performance. By comparing with the theoretical high pass filter graph, the measured high pass filter frequency response showed a high correspondence with it, which means it is feasible to apply it to the whole system to suppress the low-frequency fluctuations.
* '''16 April 2022:'''
* Apply the high pass filter to the circuit and test
* Record data and draw some graphs analysis
: In order to verify that the signals we obtained were quantum random numbers, we recorded the data at different sampling rates and performed autocorrelation calculations. These can be found in the "Result"-"Autocorrelation" part.

* '''23 April 2022:'''
* Processing experimental data
* Draw autocorrelation images
* Summarize and upload the experimental results

== '''Results''' ==
==='''Quantum noise'''===
*To ensure that the fluctuations at the amplifier output are dominated by quantum noise, the spectral power density is measured (in Figure 21. ).

[[File:Ampliﬁed noise levels measured into a resolution bandwidth B = 3 MHz..jpg|thumb|600px|center|'''Figure 21. Schematic of branching path quantum random number generators''']]

:Amplified noise levels measured into a resolution bandwidth B = 3 MHz. The total noise is measured from the photocurrent difference <math>i_1-i_2</math> with equal optical power impinging on both photodiodes. The current <math>i_1</math> of a single photodiode reveals colored classical noise. The electronic noise is measured without any optical input.
:In an alternative view, the laser beam can be seen as generating photocurrents <math>i_1</math> and <math>i_2</math> with a shot noise power proportional to the average optical power. The shot noise currents from the diodes add up as they are uncorrelated, while amplitude fluctuations in the laser intensity (referred to as classical noise) do not affect the photocurrent difference.

=== '''Autocorrelation'''===
*:Autocorrelation, sometimes known as serial correlation in the discrete-time case, is the correlation of a signal with a delayed copy of itself as a function of delay. Informally, it is the similarity between observations as a function of the time lag between them. In our experiment, if we obtain an ideal '''quantum random number generator''', the autocorrelation will be 1 when the time lag is 0, while the autocorrelation will be close to 0 when the time lag is not 0.

*:Given a signal <math>f(t)</math>, the continuous autocorrelation <math>R_{ff}(\tau)</math> is most often defined as the continuous cross-correlation integral of <math>f(t)</math> with itself, at lag <math>\tau</math>.

::::::::::::::::<math>R_{ff}(\tau) = \int_{-\infty}^\infty f(t+\tau)\overline{f(t)}\, {\rm d}t = \int_{-\infty}^\infty f(t) \overline{f(t-\tau)}\, {\rm d}t</math>

::where <math>\overline{f(t)}</math> represents the complex conjugate of <math>f(t)</math>. Note that the parameter <math>t</math> in the integral is a dummy variable and is only necessary to calculate the integral. It has no specific meaning.

*:'''Experimental result'''
:<gallery widths=500px heights=300px>
File:2.5 GHz (-20,20) After Highpass1.png|'''Figure 22. Autocorrelation of the total noise signal sampled at 2.5 GHz'''
File:500 kHz (-20,20) After Highpass1.png|'''Figure 23. Autocorrelation of the total noise signal sampled at 500 KHz'''
:</gallery>

:We recorded several sets of data with different sampling frequencies ( 2.5 GHz to 500 kHz) and obtained autocorrelation for each group. A very high correlation between any two adjacent points was observed when we use a 2.5 GHz sampling rate. This is simply because of an extremely high sampling rate which results in every two adjacent points being almost at the same position. We can get a better correlation by reducing the sampling frequency to such as 10 MHz or even lower.

:But the autocorrelation with a 500 kHz sampling rate is still not ideal. This is limited by our experimental setup. We caught up with too much electronic interference. A well-designed experimental setup with integrated photodiodes, amplifier, and high pass filter will stimulate a better result.

=== '''Randomness Extraction'''===
The amplified total noise is digitized into 16-bit words at a sampling rate of 10 MHz (because we get the best atuocorrelation result at this sampling rate) and recorded by an oscilloscope. All data are discrete values between <math>-2^{15}</math> and <math>2^{15}-1</math>. Figure 24 below shows the distribution of our raw data, which fits to a Gaussian distribution with a standard deviation <math>\sigma = 5240</math>.
[[File:Raw_data.png|thumb|600px|center|'''Figure 24. Distribution of row data and fitted with Gaussian distribution.''']]

In many applications, however, random numbers are required to be not only unpredictable but also uniformly distributed. Therefore the raw data collected by the oscilloscope cannot be used directly. Various randomness extractors, such as Trevisan's extractor and Linear Feedback Shift Register, have been used to convert non-uniformly distributed raw data in to a uniformly distributed binary stream. For simplicity, here we used random matrix multiplications to extract uniformly distributed random numbers.

Equation above shows how it works. Since our raw data is recorded in binary form, it is an N-row column vector <math>r_i</math> with all elements 0 or 1. And the <math>M \times N</math> binary matrix is an algorithmically generated pseudo-random matrix. Then the raw data and the random matrix are multiplied （binary OR and XOR） to produce a column vector <math>s_i</math> of M rows. As long as the size of the random matrix is large enough, 0 and 1 in the output <math>s_i</math> will be almost uniformly distributed. Here M can take any integer not greater than N. The reason is that, the voltage at AC port fluctuates around 0 V and the first few bits in each binary number are typically unused (all 0). Therefore the entropy in the raw data is smaller than the size of the data (e.g.6 bits of entropy per 8 bits sample). The standard approach would be to first estimate the entropy in the raw data and then choose the value of N to extract the randomness. Since in our project, we didn't do that, here we choose N = M.
[[File:Extracted.png|thumb|600px|center|'''Figure 25, Distribution of random data after the random matrix multiplication.''']]
Figure 25 shows the distribution of the data after randomness extraction. As we can see, all data fall within the <math>\pm3\sigma</math> bounds, so we have reason to believe that extracted data is almost uniformly distributed.
[[File:Contrast.png||thumb|600px|center|'''Figure 26. Distribution of random numbers before (blue) and after (red) the randomness extraction, shown in time domain (left) and histogram (right)''']]
Figure 26 shows the comparison between random numbers before and after the randomness extraction.

=== '''Randomness Test'''===
*:To verify the randomness of the experimental results we obtained, we used two compression protocols(rar and zip) to compress the random numbers we generated. The compressed file size does not change significantly compared with the original file(from 58k to 55k), which, to some extent, illustrates the randomness of our results.

== '''References''' ==
[1] Miguel Herrero-Collantes and Juan Carlos Garcia-Escartin, Quantum random number generators, Rev. Mod. Phys, 89, 015004.

[2] Shi, Yicheng, Brenda Chng, and Christian Kurtsiefer, Random numbers from vacuum fluctuations, Applied Physics Letters, 109.4 (2016): 041101.

[3] https://www.digchip.com/datasheets/parts/datasheet/625/HL6501MG-pdf.php

[4] https://www.farnell.com/datasheets/3171163.pdf

Quantum Random Number Generator

2022-04-29T16:17:42Z

Zhang Munan: /* Randomness Extraction */

== '''Team Members''' ==
Wang Yang A0228753X

Xiao Yucan A0236278W

Zhang Munan A0236273E

== '''Idea''' ==
We live in an increasingly connected world, where a superior source of entropy is the key to data security. The effectiveness of any cryptographic system is determined by the strength of the keys it used. In turn, the strength of the key is determined by the degree of randomness used in its generation. Besides, large amount of random numbers are at the core of Monte Carlo simulations, which are widely used in scientific research. Methods produce random numbers from any algorithm are called pseudo-random number generator(PRNG). And random numbers generated by PRNG are deterministic by definition and therefore unsuitable for cryptographic purposes.

In order to generate unpredictable random numbers, hardware random number generators have been widely used. These physically generated random numbers are considered "truly" random because it is either practically or fundamentally impossible to predict the outcome of such a device. Quantum Random Number Generators (QRNGs) belong to a class of hardware random number generators and leverage the random properties of quantum physics to generate a true source of entropy, improving the quality of seed content for key generation.

Early QRNGs were based on radioactive decay. And more recently, QRNGs based on Poisson statistics of photons have been developed. The core idea is shown in the figure below. Single photons generated by a laser source are incident on a semi-transparent mirror and the mutually exclusive events (reflection/transmission) are detected and associated with ‘0’ or ‘1’ bit values respectively. The unpredictability of generated numbers is ensured by the quantum nature of the process. However, such a scheme needs a reliable single photon source as well as single photon detectors and it's not possible for our project. Here, we decided to build a QRNG based on measuring vacuum fluctuations of a light field as a random source. More details will be discussed in the principle part.
[[File:Principle schematic of QRNG.png|thumb|300px|'''Figure 1. Schematic of branching path quantum random number generators''']]

=== Benefits of having a quantum random number generator ===
* The source of randomness is unpredictable and controlled by quantum process.
* Live/real-time monitoring of entropy source is possible and highly effective as well.
* All attacks on the entropy source are detectable.

=== Application of quantum random number generator ===
* Securing data at rest in data centres
* Securing any kind of sensitive data
* Securing data in the cloud
* One-time pad for authentication in banking and other transactions
* Gaming applications and lottery
* Block-chain network
* Numerical simulations, statistical research
* IoT devices
* E-commerce and banking applications
* Cryptographic applications
* Telecom and 5G
* Monte Carlo Simulation

== '''Principles''' ==
[[File:Schematic of setup 2.png|thumb|300px|'''Figure 2. Schematic of setup''']]
Figure 2 schematically shows our setup. Such a setup is known as balanced homodyne detection and can extract the information of the electrical field in the second mode entering the polarizing beam-splitter (PBS) by measuring the photocurrent difference <math>i_1-i_2</math>. A continuous wave laser (wavelength 658 nm) is incident on one input port of the PBS and used as the local oscillator (LO), while another input port is empty. So the homodyne detection is trying to measure the vacuum state of the electromagnetic field. The randomness source in our setup is the fluctuations of the vacuum field. Here we tried to balance the optical power impinging on the two photodiodes, therefore any power fluctuation coming from the laser diode will be detected simultaneously and canceled in the photocurrent difference.

Alternatively, the randomness can be seen as coming from the shot noise of the photocurrents <math>i_1</math> and <math>i_2</math> with a power proportional to the average optical power. Since the shot noise currents from the diodes are uncorrelated, the y add up. And the amplitude fluctuations in the laser intensity (referred to as classical noise) can be eliminated by measuring the photocurrent difference.

== '''Setup''' ==
The practical setup (shown in Figure 3) was built with as few components as possible to create a baseline performance that we can compare.

[[File:Experimental setup.png|thumb|300px|'''Figure 3. Experimental setup''']]

==='''Tool list'''===
① Laser Diode
: Laser Diode is powered by a laser driving unit. The light intensity can be changed by changing the laser current.
② Focal Lens
: By adjusting the focal lens, the intensity of light that finally hits the photodiodes is adjusted.
③ RP: Rotatable Polarizer
: The polarization state of the light is adjusted by rotating the polarizer.
④ Mirror 1
: By adjusting mirror 1, the position of transmitted and reflected light spots hitting on PD1 and PD2 can be adjusted simultaneously.
⑤ PBS: Polarizing Beam Splitter
: The laser beam incident on the PBS can pass through or be reflected depending on the polarization state. If the incident beam is diagonal polarized (45°), the intensity of reflected and transmitted light is equal.
⑥ Mirror 2
: By adjusting mirror 2, the position of transmitted light spots hitting on PD2 can be tuned.
⑦&⑧ Photodiodes
: Detect the intensity of incident light.
⑩ Gain block
:A ready-made 60 dB gain Block from quantum optic lab.
⑪ High pass filter
:Designed cutoff frequency = 60 MHz.

==='''Description'''===
The total light power is changed by changing the laser current and adjusting the focal lens, while the power of the two output ports of the PBS is balanced by rotating the polarizer in front of the laser diode. Light leaving the PBS is detected by a pair of reverse-biased photodiodes connected in series to perform the current subtraction. By adjusting the orientation of M1 and M2, the light intensity incident on PD1 and PD2 can be adjusted and balanced. The balancing of the photocurrents is monitored by observing the voltage drop across a resister <math>R_{DC}</math> (DC port). Here we use a multimeter to measure the voltage. The fluctuations <math>\Delta(i_1-i_2)</math> are amplified by a 60 dB ready-made Gain block. And after that, a high pass filter (HPF) with a cutoff frequency of 60 MHz is used to filter out low frequency noise.

==='''Characterization list'''===
① Oscilloscope: Used to monitor the AC port and collect data.

② Spectrum Analyzer: Used to analyze the spectrum of total noise.

③ Multimeter
:Used to monitor the DC port and balance two photodiodes.

== '''Process''' ==
* '''26 February 2022:'''
* Did a basic characterization of photodiode
* Inputted a sine wave signal and a laser pointer light, observed the waveform of the photodiode
<gallery widths=300px heights=200px>
File:Basic characterization of photodiode test.jpeg|'''Figure 4. Basic characterization of photodiode'''
File:Schematic of basic characterization of photodiode test.png|'''Figure 5. Schematic of basic characterization of photodiode'''
</gallery>

:To understand the frequency response of the circuit shown in figure 5, we use a function generator to generate a sinusoidal signal to drive the LED, and use this circuit to measure the light output. When the frequency of the signal is low, we can see a relatively complete sine waveform on the oscilloscope. But when the frequency exceeds 1GHz, we could not observe a regular and stable waveform.
* '''5 March 2022:'''
* Used different resistors to test the frequency response of photodiode
<gallery widths=300px heights=200px>
File:Frequency of PD.png|'''Figure 6. Graph of the frequency response of photodiode'''
</gallery>
:We changed the resistors in Figure 6, from 1 kΩ to 11 kΩ and then 20 kΩ. We found that the higher the resistance of the resistor, the larger the output voltage but less sensitive to the high frequency. That is because a reverse-biased photodiode has a certain capacitance and forms an RC series circuit with the resistor. The larger the resistor, the larger the time constant <math>\tau=RC</math> of the RC circuit, and the slower the charge and discharge, which leads to a worse response to high frequency signals.
* '''12 March 2022:'''
* Build up the laser system and ensured the laser output
<gallery widths=300px heights=200px>
File:Laser diode.png|'''Figure 7. HL6501MG laser diode and schematic of internal circuit'''
File:Schematic of electronics laserconnector circuit.jpeg|'''Figure 8. Schematic of electronics laser connector circuit'''
File:Laser source setup.png|'''Figure 9. Laser source setup'''
</gallery>
:We used an HL6501MG laser diode, which is a 0.65 μm band AlGaInP laser diode (LD) with a multi-quantum well (MQW) structure. It is suitable as a light source for large-capacity optical disc memories and various other types of optical equipment. Hermetic sealing of the small package (φ=5.6 mm) assures high reliability.

:The Laser source consists of ① Laser diode; ② Thermostat; ③ Supply circuit for Laser diode and Thermostat; ④ Shell; ⑤ Focal lens; ⑥ Radiator. The Laser Diode is in the thermostat which is connected to the Radiator. We can set the temperature on the Laser power supply. The Thermostat and Radiator will keep the temperature of the laser diode as same as that set on the laser power supply. There is a focal lens in front of the laser diode. We can use it to change the focal length the enlarge the laser intensity hitting on the photodiodes. And a shell made of acrylic sheet and 4 balance posts.
* '''19 March 2022:'''
* Soldered photodiode driving circuit
* Test the feasibility
<gallery widths=300px heights=200px>
File:Photo diode outlines.png|'''Figure 10. S5972 Si PIN photodiode and schematic of internal circuit'''
File:Principle of photodiode driving circuit.png|'''Figure 11. Principle of photodiode driving circuit'''
File:Schematic photodiode driving circuit bolck.jpeg|'''Figure 12. Schematic photodiode driving circuit block'''
</gallery>

:We used an S5972 high-speed Si PIN photodiode to detect the light, which is designed for visible to near-infrared light detection. These photodiodes provide wideband characteristics at a low bias, making them suitable for optical communications and other high-speed photometry.

:We soldered all the components on the circuit chip as Figure 11 shows. After that, we tested its performance using a laser, it was approved that the optical signal was converted into the electrical signal and was measured by the oscilloscope.
* '''26 March 2022:'''
* Build up the whole system
* Tune the bias of two photodiodes
<gallery widths=300px heights=200px>
File:Whole setup.jpeg|'''Figure 13. The whole system setup'''
</gallery>
:We built up the whole setup on the optical platform. Then we tuned the bias of two photodiodes to make sure that the intensity of the laser hitting on both photodiodes is the same by adjusting the multimeter's voltage to around 0.
* '''2 April 2022:'''
* Focus the laser output
* Maximize the laser power output
* Characterize varaiation by varying optical power
<gallery widths=300px heights=200px>
File:Maximize the laser power output.jpeg|'''Figure 14. Maximize the laser power output'''
File:The detector noise power by varying the incident optical power.jpg|'''Figure 15. The plot of the detector noise power by varying the incident optical power'''
</gallery>
:We found that the laser output power in front of the polarizer was about 20 mW, but the power detected by each photodiode was only 0.4 mW. That is because the spot size of the laser was relatively large compared with the detection area of the photodiode. Therefore we needed to focus the lens in the laser block to maximize the detected laser power. To do this, we blocked one photodiode and used a multimeter to monitor the light power detected by another photodiode. After trials, we got a maximum value of voltage drop of 9.17 V, which corresponds to an optical power of 2.08 mW on each photodiode.

:Then, we characterized the change of noise level while rising incident optical power. And then we plotted a graph as shown in Figure 15, it is easy to find when the optical power is in a relatively low range, the noise level is flat which corresponds to the horizontal red line. While the optical power rises, the noise level increases with the optical power in a proportional manner. Therefore, we have enough reasons to believe that the overall noise is dominated by electronic noise in the low optical power range, while the noise level is dominated by shot noise in the high optical power range.
* '''9 April 2022:'''
* Soldered high pass filter
* Test its feasibility
<gallery widths=300px heights=200px>
File:Highpass filter principle circuit.png|'''Figure 16. Schematic of high pass filter circuit'''
File:Graph of theoretical high pass filter frequency response.jpg.png|'''Figure 17. Graph of theoretical high pass filter frequency response'''
File:Frequency of HPF.png|'''Figure 18. Graph of measured high pass filter frequency response'''
File:Schematic of high pass filter.jpeg|'''Figure 19. Setup of high pass filter'''
File:Setup of gain block and high pass filter.jpeg|'''Figure 20. Setup of gain block and high pass filter'''
</gallery>
:The measured total noise has a lot of low-frequency noise and is relatively flat power density in the range of 60-200 MHz. With a low pass filter of 200 MHz in the oscilloscope, we just needed a high pass filter of 60 MHz which compresses the low-frequency fluctuations. So we designed a high pass filter of 60 MHz and soldered the high pass filter.

:After that, we tested its performance. By comparing with the theoretical high pass filter graph, the measured high pass filter frequency response showed a high correspondence with it, which means it is feasible to apply it to the whole system to suppress the low-frequency fluctuations.
* '''16 April 2022:'''
* Apply the high pass filter to the circuit and test
* Record data and draw some graphs analysis
: In order to verify that the signals we obtained were quantum random numbers, we recorded the data at different sampling rates and performed autocorrelation calculations. These can be found in the "Result"-"Autocorrelation" part.

* '''23 April 2022:'''
* Processing experimental data
* Draw autocorrelation images
* Summarize and upload the experimental results

== '''Results''' ==
==='''Quantum noise'''===
*To ensure that the fluctuations at the amplifier output are dominated by quantum noise, the spectral power density is measured (in Figure 21. ).

[[File:Ampliﬁed noise levels measured into a resolution bandwidth B = 3 MHz..jpg|thumb|600px|center|'''Figure 21. Schematic of branching path quantum random number generators''']]

:Amplified noise levels measured into a resolution bandwidth B = 3 MHz. The total noise is measured from the photocurrent difference <math>i_1-i_2</math> with equal optical power impinging on both photodiodes. The current <math>i_1</math> of a single photodiode reveals colored classical noise. The electronic noise is measured without any optical input.
:In an alternative view, the laser beam can be seen as generating photocurrents <math>i_1</math> and <math>i_2</math> with a shot noise power proportional to the average optical power. The shot noise currents from the diodes add up as they are uncorrelated, while amplitude fluctuations in the laser intensity (referred to as classical noise) do not affect the photocurrent difference.

=== '''Autocorrelation'''===
*:Autocorrelation, sometimes known as serial correlation in the discrete-time case, is the correlation of a signal with a delayed copy of itself as a function of delay. Informally, it is the similarity between observations as a function of the time lag between them. In our experiment, if we obtain an ideal '''quantum random number generator''', the autocorrelation will be 1 when the time lag is 0, while the autocorrelation will be close to 0 when the time lag is not 0.

*:Given a signal <math>f(t)</math>, the continuous autocorrelation <math>R_{ff}(\tau)</math> is most often defined as the continuous cross-correlation integral of <math>f(t)</math> with itself, at lag <math>\tau</math>.

::::::::::::::::<math>R_{ff}(\tau) = \int_{-\infty}^\infty f(t+\tau)\overline{f(t)}\, {\rm d}t = \int_{-\infty}^\infty f(t) \overline{f(t-\tau)}\, {\rm d}t</math>

::where <math>\overline{f(t)}</math> represents the complex conjugate of <math>f(t)</math>. Note that the parameter <math>t</math> in the integral is a dummy variable and is only necessary to calculate the integral. It has no specific meaning.

*:'''Experimental result'''
:<gallery widths=500px heights=300px>
File:2.5 GHz (-20,20) After Highpass1.png|'''Figure 22. Autocorrelation of the total noise signal sampled at 2.5 GHz'''
File:500 kHz (-20,20) After Highpass1.png|'''Figure 23. Autocorrelation of the total noise signal sampled at 500 KHz'''
:</gallery>

:We recorded several sets of data with different sampling frequencies ( 2.5 GHz to 500 kHz) and obtained autocorrelation for each group. A very high correlation between any two adjacent points was observed when we use a 2.5 GHz sampling rate. This is simply because of an extremely high sampling rate which results in every two adjacent points being almost at the same position. We can get a better correlation by reducing the sampling frequency to such as 10 MHz or even lower.

:But the autocorrelation with a 500 kHz sampling rate is still not ideal. This is limited by our experimental setup. We caught up with too much electronic interference. A well-designed experimental setup with integrated photodiodes, amplifier, and high pass filter will stimulate a better result.

=== '''Randomness Extraction'''===
The amplified total noise is digitized into 16-bit words at a sampling rate of 10 MHz (because we get the best atuocorrelation result at this sampling rate) and recorded by an oscilloscope. All data are discrete values between <math>-2^{15}</math> and <math>2^{15}-1</math>. Figure 24 below shows the distribution of our raw data, which fits to a Gaussian distribution with a standard deviation <math>\sigma = 5240</math>.
[[File:Raw_data.png|thumb|600px|center|'''Figure 24 765876486''']]

In many applications, however, random numbers are required to be not only unpredictable but also uniformly distributed. Therefore the raw data collected by the oscilloscope cannot be used directly. Various randomness extractors, such as Trevisan's extractor and Linear Feedback Shift Register, have been used to convert non-uniformly distributed raw data in to a uniformly distributed binary stream. For simplicity, here we used random matrix multiplications to extract uniformly distributed random numbers.

Equation above shows how it works. Since our raw data is recorded in binary form, it is an N-row column vector <math>r_i</math> with all elements 0 or 1. And the <math>M \times N</math> binary matrix is an algorithmically generated pseudo-random matrix. Then the raw data and the random matrix are multiplied （binary OR and XOR） to produce a column vector <math>s_i</math> of M rows. As long as the size of the random matrix is large enough, 0 and 1 in the output <math>s_i</math> will be almost uniformly distributed. Here M can take any integer not greater than N. The reason is that, the voltage at AC port fluctuates around 0 V and the first few bits in each binary number are typically unused (all 0). Therefore the entropy in the raw data is smaller than the size of the data (e.g.6 bits of entropy per 8 bits sample). The standard approach would be to first estimate the entropy in the raw data and then choose the value of N to extract the randomness. Since in our project, we didn't do that, here we choose N = M.
[[File:Extracted.png|thumb|600px|center|'''Figure 25''']]
[[File:Contrast.png||thumb|600px|center|'''Figure 26''']]

=== '''Randomness Test'''===
*:To verify the randomness of the experimental results we obtained, we used two compression protocols(rar and zip) to compress the random numbers we generated. The compressed file size does not change significantly compared with the original file(from 58k to 55k), which, to some extent, illustrates the randomness of our results.

== '''References''' ==
[1] Miguel Herrero-Collantes and Juan Carlos Garcia-Escartin, Quantum random number generators, Rev. Mod. Phys, 89, 015004.

[2] Shi, Yicheng, Brenda Chng, and Christian Kurtsiefer, Random numbers from vacuum fluctuations, Applied Physics Letters, 109.4 (2016): 041101.

[3] https://www.digchip.com/datasheets/parts/datasheet/625/HL6501MG-pdf.php

[4] https://www.farnell.com/datasheets/3171163.pdf

Quantum Random Number Generator

2022-04-29T16:01:03Z

Zhang Munan: /* Randomness Extraction */

== '''Team Members''' ==
Wang Yang A0228753X

Xiao Yucan A0236278W

Zhang Munan A0236273E

== '''Idea''' ==
We live in an increasingly connected world, where a superior source of entropy is the key to data security. The effectiveness of any cryptographic system is determined by the strength of the keys it used. In turn, the strength of the key is determined by the degree of randomness used in its generation. Besides, large amount of random numbers are at the core of Monte Carlo simulations, which are widely used in scientific research. Methods produce random numbers from any algorithm are called pseudo-random number generator(PRNG). And random numbers generated by PRNG are deterministic by definition and therefore unsuitable for cryptographic purposes.

In order to generate unpredictable random numbers, hardware random number generators have been widely used. These physically generated random numbers are considered "truly" random because it is either practically or fundamentally impossible to predict the outcome of such a device. Quantum Random Number Generators (QRNGs) belong to a class of hardware random number generators and leverage the random properties of quantum physics to generate a true source of entropy, improving the quality of seed content for key generation.

Early QRNGs were based on radioactive decay. And more recently, QRNGs based on Poisson statistics of photons have been developed. The core idea is shown in the figure below. Single photons generated by a laser source are incident on a semi-transparent mirror and the mutually exclusive events (reflection/transmission) are detected and associated with ‘0’ or ‘1’ bit values respectively. The unpredictability of generated numbers is ensured by the quantum nature of the process. However, such a scheme needs a reliable single photon source as well as single photon detectors and it's not possible for our project. Here, we decided to build a QRNG based on measuring vacuum fluctuations of a light field as a random source. More details will be discussed in the principle part.
[[File:Principle schematic of QRNG.png|thumb|300px|'''Figure 1. Schematic of branching path quantum random number generators''']]

=== Benefits of having a quantum random number generator ===
* The source of randomness is unpredictable and controlled by quantum process.
* Live/real-time monitoring of entropy source is possible and highly effective as well.
* All attacks on the entropy source are detectable.

=== Application of quantum random number generator ===
* Securing data at rest in data centres
* Securing any kind of sensitive data
* Securing data in the cloud
* One-time pad for authentication in banking and other transactions
* Gaming applications and lottery
* Block-chain network
* Numerical simulations, statistical research
* IoT devices
* E-commerce and banking applications
* Cryptographic applications
* Telecom and 5G
* Monte Carlo Simulation

== '''Principles''' ==
[[File:Schematic of setup 2.png|thumb|300px|'''Figure 2. Schematic of setup''']]
Figure 2 schematically shows our setup. Such a setup is known as balanced homodyne detection and can extract the information of the electrical field in the second mode entering the polarizing beam-splitter (PBS) by measuring the photocurrent difference <math>i_1-i_2</math>. A continuous wave laser (wavelength 658 nm) is incident on one input port of the PBS and used as the local oscillator (LO), while another input port is empty. So the homodyne detection is trying to measure the vacuum state of the electromagnetic field. The randomness source in our setup is the fluctuations of the vacuum field. Here we tried to balance the optical power impinging on the two photodiodes, therefore any power fluctuation coming from the laser diode will be detected simultaneously and canceled in the photocurrent difference.

Alternatively, the randomness can be seen as coming from the shot noise of the photocurrents <math>i_1</math> and <math>i_2</math> with a power proportional to the average optical power. Since the shot noise currents from the diodes are uncorrelated, the y add up. And the amplitude fluctuations in the laser intensity (referred to as classical noise) can be eliminated by measuring the photocurrent difference.

== '''Setup''' ==
The practical setup (shown in Figure 3) was built with as few components as possible to create a baseline performance that we can compare.

[[File:Experimental setup.png|thumb|300px|'''Figure 3. Experimental setup''']]

==='''Tool list'''===
① Laser Diode
: Laser Diode is powered by a laser driving unit. The light intensity can be changed by changing the laser current.
② Focal Lens
: By adjusting the focal lens, the intensity of light that finally hits the photodiodes is adjusted.
③ RP: Rotatable Polarizer
: The polarization state of the light is adjusted by rotating the polarizer.
④ Mirror 1
: By adjusting mirror 1, the position of transmitted and reflected light spots hitting on PD1 and PD2 can be adjusted simultaneously.
⑤ PBS: Polarizing Beam Splitter
: The laser beam incident on the PBS can pass through or be reflected depending on the polarization state. If the incident beam is diagonal polarized (45°), the intensity of reflected and transmitted light is equal.
⑥ Mirror 2
: By adjusting mirror 2, the position of transmitted light spots hitting on PD2 can be tuned.
⑦&⑧ Photodiodes
: Detect the intensity of incident light.
⑩ Gain block
:A ready-made 60 dB gain Block from quantum optic lab.
⑪ High pass filter
:Designed cutoff frequency = 60 MHz.

==='''Description'''===
The total light power is changed by changing the laser current and adjusting the focal lens, while the power of the two output ports of the PBS is balanced by rotating the polarizer in front of the laser diode. Light leaving the PBS is detected by a pair of reverse-biased photodiodes connected in series to perform the current subtraction. By adjusting the orientation of M1 and M2, the light intensity incident on PD1 and PD2 can be adjusted and balanced. The balancing of the photocurrents is monitored by observing the voltage drop across a resister <math>R_{DC}</math> (DC port). Here we use a multimeter to measure the voltage. The fluctuations <math>\Delta(i_1-i_2)</math> are amplified by a 60 dB ready-made Gain block. And after that, a high pass filter (HPF) with a cutoff frequency of 60 MHz is used to filter out low frequency noise.

==='''Characterization list'''===
① Oscilloscope: Used to monitor the AC port and collect data.

② Spectrum Analyzer: Used to analyze the spectrum of total noise.

③ Multimeter
:Used to monitor the DC port and balance two photodiodes.

== '''Process''' ==
* '''26 February 2022:'''
* Did a basic characterization of photodiode
* Inputted a sine wave signal and a laser pointer light, observed the waveform of the photodiode
<gallery widths=300px heights=200px>
File:Basic characterization of photodiode test.jpeg|'''Figure 4. Basic characterization of photodiode'''
File:Schematic of basic characterization of photodiode test.png|'''Figure 5. Schematic of basic characterization of photodiode'''
</gallery>

:To understand the frequency response of the circuit shown in figure 5, we use a function generator to generate a sinusoidal signal to drive the LED, and use this circuit to measure the light output. When the frequency of the signal is low, we can see a relatively complete sine waveform on the oscilloscope. But when the frequency exceeds 1GHz, we could not observe a regular and stable waveform.
* '''5 March 2022:'''
* Used different resistors to test the frequency response of photodiode
<gallery widths=300px heights=200px>
File:Frequency of PD.png|'''Figure 6. Graph of the frequency response of photodiode'''
</gallery>
:We changed the resistors in Figure 6, from 1 kΩ to 11 kΩ and then 20 kΩ. We found that the higher the resistance of the resistor, the larger the output voltage but less sensitive to the high frequency. That is because a reverse-biased photodiode has a certain capacitance and forms an RC series circuit with the resistor. The larger the resistor, the larger the time constant <math>\tau=RC</math> of the RC circuit, and the slower the charge and discharge, which leads to a worse response to high frequency signals.
* '''12 March 2022:'''
* Build up the laser system and ensured the laser output
<gallery widths=300px heights=200px>
File:Laser diode.png|'''Figure 7. HL6501MG laser diode and schematic of internal circuit'''
File:Schematic of electronics laserconnector circuit.jpeg|'''Figure 8. Schematic of electronics laser connector circuit'''
File:Laser source setup.png|'''Figure 9. Laser source setup'''
</gallery>
:We used an HL6501MG laser diode, which is a 0.65 μm band AlGaInP laser diode (LD) with a multi-quantum well (MQW) structure. It is suitable as a light source for large-capacity optical disc memories and various other types of optical equipment. Hermetic sealing of the small package (φ=5.6 mm) assures high reliability.

:The Laser source consists of ① Laser diode; ② Thermostat; ③ Supply circuit for Laser diode and Thermostat; ④ Shell; ⑤ Focal lens; ⑥ Radiator. The Laser Diode is in the thermostat which is connected to the Radiator. We can set the temperature on the Laser power supply. The Thermostat and Radiator will keep the temperature of the laser diode as same as that set on the laser power supply. There is a focal lens in front of the laser diode. We can use it to change the focal length the enlarge the laser intensity hitting on the photodiodes. And a shell made of acrylic sheet and 4 balance posts.
* '''19 March 2022:'''
* Soldered photodiode driving circuit
* Test the feasibility
<gallery widths=300px heights=200px>
File:Photo diode outlines.png|'''Figure 10. S5972 Si PIN photodiode and schematic of internal circuit'''
File:Principle of photodiode driving circuit.png|'''Figure 11. Principle of photodiode driving circuit'''
File:Schematic photodiode driving circuit bolck.jpeg|'''Figure 12. Schematic photodiode driving circuit block'''
</gallery>

:We used an S5972 high-speed Si PIN photodiode to detect the light, which is designed for visible to near-infrared light detection. These photodiodes provide wideband characteristics at a low bias, making them suitable for optical communications and other high-speed photometry.

:We soldered all the components on the circuit chip as Figure 11 shows. After that, we tested its performance using a laser, it was approved that the optical signal was converted into the electrical signal and was measured by the oscilloscope.
* '''26 March 2022:'''
* Build up the whole system
* Tune the bias of two photodiodes
<gallery widths=300px heights=200px>
File:Whole setup.jpeg|'''Figure 13. The whole system setup'''
</gallery>
:We built up the whole setup on the optical platform. Then we tuned the bias of two photodiodes to make sure that the intensity of the laser hitting on both photodiodes is the same by adjusting the multimeter's voltage to around 0.
* '''2 April 2022:'''
* Focus the laser output
* Maximize the laser power output
* Characterize varaiation by varying optical power
<gallery widths=300px heights=200px>
File:Maximize the laser power output.jpeg|'''Figure 14. Maximize the laser power output'''
File:The detector noise power by varying the incident optical power.jpg|'''Figure 15. The plot of the detector noise power by varying the incident optical power'''
</gallery>
:We found that the laser output power in front of the polarizer was about 20 mW, but the power detected by each photodiode was only 0.4 mW. That is because the spot size of the laser was relatively large compared with the detection area of the photodiode. Therefore we needed to focus the lens in the laser block to maximize the detected laser power. To do this, we blocked one photodiode and used a multimeter to monitor the light power detected by another photodiode. After trials, we got a maximum value of voltage drop of 9.17 V, which corresponds to an optical power of 2.08 mW on each photodiode.

:Then, we characterized the change of noise level while rising incident optical power. And then we plotted a graph as shown in Figure 15, it is easy to find when the optical power is in a relatively low range, the noise level is flat which corresponds to the horizontal red line. While the optical power rises, the noise level increases with the optical power in a proportional manner. Therefore, we have enough reasons to believe that the overall noise is dominated by electronic noise in the low optical power range, while the noise level is dominated by shot noise in the high optical power range.
* '''9 April 2022:'''
* Soldered high pass filter
* Test its feasibility
<gallery widths=300px heights=200px>
File:Highpass filter principle circuit.png|'''Figure 16. Schematic of high pass filter circuit'''
File:Graph of theoretical high pass filter frequency response.jpg.png|'''Figure 17. Graph of theoretical high pass filter frequency response'''
File:Frequency of HPF.png|'''Figure 18. Graph of measured high pass filter frequency response'''
File:Schematic of high pass filter.jpeg|'''Figure 19. Setup of high pass filter'''
File:Setup of gain block and high pass filter.jpeg|'''Figure 20. Setup of gain block and high pass filter'''
</gallery>
:The measured total noise has a lot of low-frequency noise and is relatively flat power density in the range of 60-200 MHz. With a low pass filter of 200 MHz in the oscilloscope, we just needed a high pass filter of 60 MHz which compresses the low-frequency fluctuations. So we designed a high pass filter of 60 MHz and soldered the high pass filter.

:After that, we tested its performance. By comparing with the theoretical high pass filter graph, the measured high pass filter frequency response showed a high correspondence with it, which means it is feasible to apply it to the whole system to suppress the low-frequency fluctuations.
* '''16 April 2022:'''
* Apply the high pass filter to the circuit and test
* Record data and draw some graphs analysis
: In order to verify that the signals we obtained were quantum random numbers, we recorded the data at different sampling rates and performed autocorrelation calculations. These can be found in the "Result"-"Autocorrelation" part.

* '''23 April 2022:'''
* Processing experimental data
* Draw autocorrelation images
* Summarize and upload the experimental results

== '''Results''' ==
==='''Quantum noise'''===
*To ensure that the fluctuations at the amplifier output are dominated by quantum noise, the spectral power density is measured (in Figure 21. ).

[[File:Ampliﬁed noise levels measured into a resolution bandwidth B = 3 MHz..jpg|thumb|600px|center|'''Figure 21. Schematic of branching path quantum random number generators''']]

:Amplified noise levels measured into a resolution bandwidth B = 3 MHz. The total noise is measured from the photocurrent difference <math>i_1-i_2</math> with equal optical power impinging on both photodiodes. The current <math>i_1</math> of a single photodiode reveals colored classical noise. The electronic noise is measured without any optical input.
:In an alternative view, the laser beam can be seen as generating photocurrents <math>i_1</math> and <math>i_2</math> with a shot noise power proportional to the average optical power. The shot noise currents from the diodes add up as they are uncorrelated, while amplitude fluctuations in the laser intensity (referred to as classical noise) do not affect the photocurrent difference.

=== '''Autocorrelation'''===
*:Autocorrelation, sometimes known as serial correlation in the discrete-time case, is the correlation of a signal with a delayed copy of itself as a function of delay. Informally, it is the similarity between observations as a function of the time lag between them. In our experiment, if we obtain an ideal '''quantum random number generator''', the autocorrelation will be 1 when the time lag is 0, while the autocorrelation will be close to 0 when the time lag is not 0.

*:Given a signal <math>f(t)</math>, the continuous autocorrelation <math>R_{ff}(\tau)</math> is most often defined as the continuous cross-correlation integral of <math>f(t)</math> with itself, at lag <math>\tau</math>.

::::::::::::::::<math>R_{ff}(\tau) = \int_{-\infty}^\infty f(t+\tau)\overline{f(t)}\, {\rm d}t = \int_{-\infty}^\infty f(t) \overline{f(t-\tau)}\, {\rm d}t</math>

::where <math>\overline{f(t)}</math> represents the complex conjugate of <math>f(t)</math>. Note that the parameter <math>t</math> in the integral is a dummy variable and is only necessary to calculate the integral. It has no specific meaning.

*:'''Experimental result'''
:<gallery widths=500px heights=300px>
File:2.5 GHz (-20,20) After Highpass1.png|'''Figure 22. Autocorrelation of the total noise signal sampled at 2.5 GHz'''
File:500 kHz (-20,20) After Highpass1.png|'''Figure 23. Autocorrelation of the total noise signal sampled at 500 KHz'''
:</gallery>

:We recorded several sets of data with different sampling frequencies ( 2.5 GHz to 500 kHz) and obtained autocorrelation for each group. A very high correlation between any two adjacent points was observed when we use a 2.5 GHz sampling rate. This is simply because of an extremely high sampling rate which results in every two adjacent points being almost at the same position. We can get a better correlation by reducing the sampling frequency to such as 10 MHz or even lower.

:But the autocorrelation with a 500 kHz sampling rate is still not ideal. This is limited by our experimental setup. We caught up with too much electronic interference. A well-designed experimental setup with integrated photodiodes, amplifier, and high pass filter will stimulate a better result.

=== '''Randomness Extraction'''===
The amplified total noise is digitized into 16-bit words at a sampling rate of 10 MHz (because we get the best atuocorrelation result at this sampling rate) and recorded by an oscilloscope. All data are discrete values between <math>-2^{15}</math> and <math>2^{15}-1</math>. Figure 24 below shows the distribution of our raw data, which fits to a Gaussian distribution with a standard deviation <math>\sigma = 5240</math>.
[[File:Raw_data.png|thumb|600px|center|'''Figure 24 765876486''']]

In many applications, however, random numbers are required to be not only unpredictable but also uniformly distributed. Therefore the raw data collected by the oscilloscope cannot be used directly. Various randomness extractors, such as Trevisan's extractor and Linear Feedback Shift Register, have been used to convert non-uniformly distributed raw data in to a uniformly distributed binary stream. For simplicity, here we used random matrix multiplications to extract uniformly distributed random numbers.

Equation above shows how it works. Since our raw data is recorded in binary form, it is an N-row column vector <math>r_i</math> with all elements 0 or 1. And the <math>M \times N</math> binary matrix is an algorithmically generated pseudo-random matrix. Then the raw data and the random matrix are multiplied （binary OR and XOR） to produce a column vector <math>s_i</math> of M rows. As long as the size of the random matrix is large enough, 0 and 1 in the output <math>s_i</math> will be almost uniformly distributed.
[[File:Extracted.png|thumb|600px|center|'''Figure 25''']]
[[File:Contrast.png||thumb|600px|center|'''Figure 26''']]

=== '''Randomness Test'''===
*:To verify the randomness of the experimental results we obtained, we used two compression protocols(rar and zip) to compress the random numbers we generated. The compressed file size does not change significantly compared with the original file(from 58k to 55k), which, to some extent, illustrates the randomness of our results.

== '''References''' ==
[1] Miguel Herrero-Collantes and Juan Carlos Garcia-Escartin, Quantum random number generators, Rev. Mod. Phys, 89, 015004.

[2] Shi, Yicheng, Brenda Chng, and Christian Kurtsiefer, Random numbers from vacuum fluctuations, Applied Physics Letters, 109.4 (2016): 041101.

[3] https://www.digchip.com/datasheets/parts/datasheet/625/HL6501MG-pdf.php

[4] https://www.farnell.com/datasheets/3171163.pdf

Quantum Random Number Generator

2022-04-29T15:01:59Z

Zhang Munan: /* Randomness Extraction */

== '''Team Members''' ==
Wang Yang A0228753X

Xiao Yucan A0236278W

Zhang Munan A0236273E

== '''Idea''' ==
We live in an increasingly connected world, where a superior source of entropy is the key to data security. The effectiveness of any cryptographic system is determined by the strength of the keys it used. In turn, the strength of the key is determined by the degree of randomness used in its generation. Besides, large amount of random numbers are at the core of Monte Carlo simulations, which are widely used in scientific research. Methods produce random numbers from any algorithm are called pseudo-random number generator(PRNG). And random numbers generated by PRNG are deterministic by definition and therefore unsuitable for cryptographic purposes.

In order to generate unpredictable random numbers, hardware random number generators have been widely used. These physically generated random numbers are considered "truly" random because it is either practically or fundamentally impossible to predict the outcome of such a device. Quantum Random Number Generators (QRNGs) belong to a class of hardware random number generators and leverage the random properties of quantum physics to generate a true source of entropy, improving the quality of seed content for key generation.

Early QRNGs were based on radioactive decay. And more recently, QRNGs based on Poisson statistics of photons have been developed. The core idea is shown in the figure below. Single photons generated by a laser source are incident on a semi-transparent mirror and the mutually exclusive events (reflection/transmission) are detected and associated with ‘0’ or ‘1’ bit values respectively. The unpredictability of generated numbers is ensured by the quantum nature of the process. However, such a scheme needs a reliable single photon source as well as single photon detectors and it's not possible for our project. Here, we decided to build a QRNG based on measuring vacuum fluctuations of a light field as a random source. More details will be discussed in the principle part.
[[File:Principle schematic of QRNG.png|thumb|300px|'''Figure 1. Schematic of branching path quantum random number generators''']]

=== Benefits of having a quantum random number generator ===
* The source of randomness is unpredictable and controlled by quantum process.
* Live/real-time monitoring of entropy source is possible and highly effective as well.
* All attacks on the entropy source are detectable.

=== Application of quantum random number generator ===
* Securing data at rest in data centres
* Securing any kind of sensitive data
* Securing data in the cloud
* One-time pad for authentication in banking and other transactions
* Gaming applications and lottery
* Block-chain network
* Numerical simulations, statistical research
* IoT devices
* E-commerce and banking applications
* Cryptographic applications
* Telecom and 5G
* Monte Carlo Simulation

== '''Principles''' ==
[[File:Schematic of setup 2.png|thumb|300px|'''Figure 2. Schematic of setup''']]
Figure 2 schematically shows our setup. Such a setup is known as balanced homodyne detection and can extract the information of the electrical field in the second mode entering the polarizing beam-splitter (PBS) by measuring the photocurrent difference <math>i_1-i_2</math>. A continuous wave laser (wavelength 658 nm) is incident on one input port of the PBS and used as the local oscillator (LO), while another input port is empty. So the homodyne detection is trying to measure the vacuum state of the electromagnetic field. The randomness source in our setup is the fluctuations of the vacuum field. Here we tried to balance the optical power impinging on the two photodiodes, therefore any power fluctuation coming from the laser diode will be detected simultaneously and canceled in the photocurrent difference.

Alternatively, the randomness can be seen as coming from the shot noise of the photocurrents <math>i_1</math> and <math>i_2</math> with a power proportional to the average optical power. Since the shot noise currents from the diodes are uncorrelated, the y add up. And the amplitude fluctuations in the laser intensity (referred to as classical noise) can be eliminated by measuring the photocurrent difference.

== '''Setup''' ==
The practical setup (shown in Figure 3) was built with as few components as possible to create a baseline performance that we can compare.

[[File:Experimental setup.png|thumb|300px|'''Figure 3. Experimental setup''']]

==='''Tool list'''===
① Laser Diode
: Laser Diode is powered by a laser driving unit. The light intensity can be changed by changing the laser current.
② Focal Lens
: By adjusting the focal lens, the intensity of light that finally hits the photodiodes is adjusted.
③ RP: Rotatable Polarizer
: The polarization state of the light is adjusted by rotating the polarizer.
④ Mirror 1
: By adjusting mirror 1, the position of transmitted and reflected light spots hitting on PD1 and PD2 can be adjusted simultaneously.
⑤ PBS: Polarizing Beam Splitter
: The laser beam incident on the PBS can pass through or be reflected depending on the polarization state. If the incident beam is diagonal polarized (45°), the intensity of reflected and transmitted light is equal.
⑥ Mirror 2
: By adjusting mirror 2, the position of transmitted light spots hitting on PD2 can be tuned.
⑦&⑧ Photodiodes
: Detect the intensity of incident light.
⑩ Gain block
:A ready-made 60 dB gain Block from quantum optic lab.
⑪ High pass filter
:Designed cutoff frequency = 60 MHz.

==='''Description'''===
The total light power is changed by changing the laser current and adjusting the focal lens, while the power of the two output ports of the PBS is balanced by rotating the polarizer in front of the laser diode. Light leaving the PBS is detected by a pair of reverse-biased photodiodes connected in series to perform the current subtraction. By adjusting the orientation of M1 and M2, the light intensity incident on PD1 and PD2 can be adjusted and balanced. The balancing of the photocurrents is monitored by observing the voltage drop across a resister <math>R_{DC}</math> (DC port). Here we use a multimeter to measure the voltage. The fluctuations <math>\Delta(i_1-i_2)</math> are amplified by a 60 dB ready-made Gain block. And after that, a high pass filter (HPF) with a cutoff frequency of 60 MHz is used to filter out low frequency noise.

==='''Characterization list'''===
① Oscilloscope: Used to monitor the AC port and collect data.

② Spectrum Analyzer: Used to analyze the spectrum of total noise.

③ Multimeter
:Used to monitor the DC port and balance two photodiodes.

== '''Process''' ==
* '''26 February 2022:'''
* Did a basic characterization of photodiode
* Inputted a sine wave signal and a laser pointer light, observed the waveform of the photodiode
<gallery widths=300px heights=200px>
File:Basic characterization of photodiode test.jpeg|'''Figure 4. Basic characterization of photodiode'''
File:Schematic of basic characterization of photodiode test.png|'''Figure 5. Schematic of basic characterization of photodiode'''
</gallery>

:To understand the frequency response of the circuit shown in figure 5, we use a function generator to generate a sinusoidal signal to drive the LED, and use this circuit to measure the light output. When the frequency of the signal is low, we can see a relatively complete sine waveform on the oscilloscope. But when the frequency exceeds 1GHz, we could not observe a regular and stable waveform.
* '''5 March 2022:'''
* Used different resistors to test the frequency response of photodiode
<gallery widths=300px heights=200px>
File:Frequency of PD.png|'''Figure 6. Graph of the frequency response of photodiode'''
</gallery>
:We changed the resistors in Figure 6, from 1 kΩ to 11 kΩ and then 20 kΩ. We found that the higher the resistance of the resistor, the larger the output voltage but less sensitive to the high frequency. That is because a reverse-biased photodiode has a certain capacitance and forms an RC series circuit with the resistor. The larger the resistor, the larger the time constant <math>\tau=RC</math> of the RC circuit, and the slower the charge and discharge, which leads to a worse response to high frequency signals.
* '''12 March 2022:'''
* Build up the laser system and ensured the laser output
<gallery widths=300px heights=200px>
File:Laser diode.png|'''Figure 7. HL6501MG laser diode and schematic of internal circuit'''
File:Schematic of electronics laserconnector circuit.jpeg|'''Figure 8. Schematic of electronics laser connector circuit'''
File:Laser source setup.png|'''Figure 9. Laser source setup'''
</gallery>
:We used an HL6501MG laser diode, which is a 0.65 μm band AlGaInP laser diode (LD) with a multi-quantum well (MQW) structure. It is suitable as a light source for large-capacity optical disc memories and various other types of optical equipment. Hermetic sealing of the small package (φ=5.6 mm) assures high reliability.

:The Laser source consists of ① Laser diode; ② Thermostat; ③ Supply circuit for Laser diode and Thermostat; ④ Shell; ⑤ Focal lens; ⑥ Radiator. The Laser Diode is in the thermostat which is connected to the Radiator. We can set the temperature on the Laser power supply. The Thermostat and Radiator will keep the temperature of the laser diode as same as that set on the laser power supply. There is a focal lens in front of the laser diode. We can use it to change the focal length the enlarge the laser intensity hitting on the photodiodes. And a shell made of acrylic sheet and 4 balance posts.
* '''19 March 2022:'''
* Soldered photodiode driving circuit
* Test the feasibility
<gallery widths=300px heights=200px>
File:Photo diode outlines.png|'''Figure 10. S5972 Si PIN photodiode and schematic of internal circuit'''
File:Principle of photodiode driving circuit.png|'''Figure 11. Principle of photodiode driving circuit'''
File:Schematic photodiode driving circuit bolck.jpeg|'''Figure 12. Schematic photodiode driving circuit block'''
</gallery>

:We used an S5972 high-speed Si PIN photodiode to detect the light, which is designed for visible to near-infrared light detection. These photodiodes provide wideband characteristics at a low bias, making them suitable for optical communications and other high-speed photometry.

:We soldered all the components on the circuit chip as Figure 11 shows. After that, we tested its performance using a laser, it was approved that the optical signal was converted into the electrical signal and was measured by the oscilloscope.
* '''26 March 2022:'''
* Build up the whole system
* Tune the bias of two photodiodes
<gallery widths=300px heights=200px>
File:Whole setup.jpeg|'''Figure 13. The whole system setup'''
</gallery>
:We built up the whole setup on the optical platform. Then we tuned the bias of two photodiodes to make sure that the intensity of the laser hitting on both photodiodes is the same by adjusting the multimeter's voltage to around 0.
* '''2 April 2022:'''
* Focus the laser output
* Maximize the laser power output
* Characterize varaiation by varying optical power
<gallery widths=300px heights=200px>
File:Maximize the laser power output.jpeg|'''Figure 14. Maximize the laser power output'''
File:The detector noise power by varying the incident optical power.jpg|'''Figure 15. The plot of the detector noise power by varying the incident optical power'''
</gallery>
:We found that the laser output power in front of the polarizer was about 20 mW, but the power detected by each photodiode was only 0.4 mW. That is because the spot size of the laser was relatively large compared with the detection area of the photodiode. Therefore we needed to focus the lens in the laser block to maximize the detected laser power. To do this, we blocked one photodiode and used a multimeter to monitor the light power detected by another photodiode. After trials, we got a maximum value of voltage drop of 9.17 V, which corresponds to an optical power of 2.08 mW on each photodiode.

:Then, we characterized the change of noise level while rising incident optical power. And then we plotted a graph as shown in Figure 15, it is easy to find when the optical power is in a relatively low range, the noise level is flat which corresponds to the horizontal red line. While the optical power rises, the noise level increases with the optical power in a proportional manner. Therefore, we have enough reasons to believe that the overall noise is dominated by electronic noise in the low optical power range, while the noise level is dominated by shot noise in the high optical power range.
* '''9 April 2022:'''
* Soldered high pass filter
* Test its feasibility
<gallery widths=300px heights=200px>
File:Highpass filter principle circuit.png|'''Figure 16. Schematic of high pass filter circuit'''
File:Graph of theoretical high pass filter frequency response.jpg.png|'''Figure 17. Graph of theoretical high pass filter frequency response'''
File:Frequency of HPF.png|'''Figure 18. Graph of measured high pass filter frequency response'''
File:Schematic of high pass filter.jpeg|'''Figure 19. Setup of high pass filter'''
File:Setup of gain block and high pass filter.jpeg|'''Figure 20. Setup of gain block and high pass filter'''
</gallery>
:The measured total noise has a lot of low-frequency noise and is relatively flat power density in the range of 60-200 MHz. With a low pass filter of 200 MHz in the oscilloscope, we just needed a high pass filter of 60 MHz which compresses the low-frequency fluctuations. So we designed a high pass filter of 60 MHz and soldered the high pass filter.

:After that, we tested its performance. By comparing with the theoretical high pass filter graph, the measured high pass filter frequency response showed a high correspondence with it, which means it is feasible to apply it to the whole system to suppress the low-frequency fluctuations.
* '''16 April 2022:'''
* Apply the high pass filter to the circuit and test
* Record data and draw some graphs analysis
: In order to verify that the signals we obtained were quantum random numbers, we recorded the data at different sampling rates and performed autocorrelation calculations. These can be found in the "Result"-"Autocorrelation" part.

* '''23 April 2022:'''
* Processing experimental data
* Draw autocorrelation images
* Summarize and upload the experimental results

== '''Results''' ==
==='''Quantum noise'''===
*To ensure that the fluctuations at the amplifier output are dominated by quantum noise, the spectral power density is measured (in Figure 21. ).

[[File:Ampliﬁed noise levels measured into a resolution bandwidth B = 3 MHz..jpg|thumb|600px|center|'''Figure 21. Schematic of branching path quantum random number generators''']]

:Amplified noise levels measured into a resolution bandwidth B = 3 MHz. The total noise is measured from the photocurrent difference <math>i_1-i_2</math> with equal optical power impinging on both photodiodes. The current <math>i_1</math> of a single photodiode reveals colored classical noise. The electronic noise is measured without any optical input.
:In an alternative view, the laser beam can be seen as generating photocurrents <math>i_1</math> and <math>i_2</math> with a shot noise power proportional to the average optical power. The shot noise currents from the diodes add up as they are uncorrelated, while amplitude fluctuations in the laser intensity (referred to as classical noise) do not affect the photocurrent difference.

=== '''Autocorrelation'''===
*:Autocorrelation, sometimes known as serial correlation in the discrete-time case, is the correlation of a signal with a delayed copy of itself as a function of delay. Informally, it is the similarity between observations as a function of the time lag between them. In our experiment, if we obtain an ideal '''quantum random number generator''', the autocorrelation will be 1 when the time lag is 0, while the autocorrelation will be close to 0 when the time lag is not 0.

*:Given a signal <math>f(t)</math>, the continuous autocorrelation <math>R_{ff}(\tau)</math> is most often defined as the continuous cross-correlation integral of <math>f(t)</math> with itself, at lag <math>\tau</math>.

::::::::::::::::<math>R_{ff}(\tau) = \int_{-\infty}^\infty f(t+\tau)\overline{f(t)}\, {\rm d}t = \int_{-\infty}^\infty f(t) \overline{f(t-\tau)}\, {\rm d}t</math>

::where <math>\overline{f(t)}</math> represents the complex conjugate of <math>f(t)</math>. Note that the parameter <math>t</math> in the integral is a dummy variable and is only necessary to calculate the integral. It has no specific meaning.

*:'''Experimental result'''
:<gallery widths=500px heights=300px>
File:2.5 GHz (-20,20) After Highpass1.png|'''Figure 22. Autocorrelation of the total noise signal sampled at 2.5 GHz'''
File:500 kHz (-20,20) After Highpass1.png|'''Figure 23. Autocorrelation of the total noise signal sampled at 500 KHz'''
:</gallery>

:We recorded several sets of data with different sampling frequencies ( 2.5 GHz to 500 kHz) and obtained autocorrelation for each group. A very high correlation between any two adjacent points was observed when we use a 2.5 GHz sampling rate. This is simply because of an extremely high sampling rate which results in every two adjacent points being almost at the same position. We can get a better correlation by reducing the sampling frequency to such as 10 MHz or even lower.

:But the autocorrelation with a 500 kHz sampling rate is still not ideal. This is limited by our experimental setup. We caught up with too much electronic interference. A well-designed experimental setup with integrated photodiodes, amplifier, and high pass filter will stimulate a better result.

=== '''Randomness Extraction'''===
The amplified total noise is digitized into 16-bit words at a sampling rate of 10 MHz (because we get the best atuocorrelation result at this sampling rate) and recorded by an oscilloscope. All data are discrete values between <math>-2^{15}</math> and <math>2^{15}-1</math>. Figure 24 below shows the distribution of our raw data, which fits to a Gaussian distribution with a standard deviation <math>\sigma = 5240</math>.
[[File:Raw_data.png|thumb|600px|center|'''Figure 24 765876486''']]

In many applications, however, random numbers are required to be not only unpredictable but also uniformly distributed. Therefore the raw data collected by the oscilloscope cannot be used directly. Various randomness extractors, such as Trevisan's extractor and Linear Feedback Shift Register, have been used to convert non-uniformly distributed raw data in to a uniformly distributed binary stream. For simplicity, here we used random matrix multiplications to extract uniformly distributed random numbers.

[[File:Extracted.png|thumb|600px|center|'''Figure 25''']]
[[File:Contrast.png||thumb|600px|center|'''Figure 26''']]

=== '''Randomness Test'''===
*:To verify the randomness of the experimental results we obtained, we used two compression protocols(rar and zip) to compress the random numbers we generated. The compressed file size does not change significantly compared with the original file(from 58k to 55k), which, to some extent, illustrates the randomness of our results.

== '''References''' ==
[1] Miguel Herrero-Collantes and Juan Carlos Garcia-Escartin, Quantum random number generators, Rev. Mod. Phys, 89, 015004.

[2] Shi, Yicheng, Brenda Chng, and Christian Kurtsiefer, Random numbers from vacuum fluctuations, Applied Physics Letters, 109.4 (2016): 041101.

[3] https://www.digchip.com/datasheets/parts/datasheet/625/HL6501MG-pdf.php

[4] https://www.farnell.com/datasheets/3171163.pdf

Quantum Random Number Generator

2022-04-29T14:40:06Z

Zhang Munan: /* Setup */

== '''Team Members''' ==
Wang Yang A0228753X

Xiao Yucan A0236278W

Zhang Munan A0236273E

== '''Idea''' ==
We live in an increasingly connected world, where a superior source of entropy is the key to data security. The effectiveness of any cryptographic system is determined by the strength of the keys it used. In turn, the strength of the key is determined by the degree of randomness used in its generation. Besides, large amount of random numbers are at the core of Monte Carlo simulations, which are widely used in scientific research. Methods produce random numbers from any algorithm are called pseudo-random number generator(PRNG). And random numbers generated by PRNG are deterministic by definition and therefore unsuitable for cryptographic purposes.

In order to generate unpredictable random numbers, hardware random number generators have been widely used. These physically generated random numbers are considered "truly" random because it is either practically or fundamentally impossible to predict the outcome of such a device. Quantum Random Number Generators (QRNGs) belong to a class of hardware random number generators and leverage the random properties of quantum physics to generate a true source of entropy, improving the quality of seed content for key generation.

Early QRNGs were based on radioactive decay. And more recently, QRNGs based on Poisson statistics of photons have been developed. The core idea is shown in the figure below. Single photons generated by a laser source are incident on a semi-transparent mirror and the mutually exclusive events (reflection/transmission) are detected and associated with ‘0’ or ‘1’ bit values respectively. The unpredictability of generated numbers is ensured by the quantum nature of the process. However, such a scheme needs a reliable single photon source as well as single photon detectors and it's not possible for our project. Here, we decided to build a QRNG based on measuring vacuum fluctuations of a light field as a random source. More details will be discussed in the principle part.
[[File:Principle schematic of QRNG.png|thumb|300px|'''Figure 1. Schematic of branching path quantum random number generators''']]

=== Benefits of having a quantum random number generator ===
* The source of randomness is unpredictable and controlled by quantum process.
* Live/real-time monitoring of entropy source is possible and highly effective as well.
* All attacks on the entropy source are detectable.

=== Application of quantum random number generator ===
* Securing data at rest in data centres
* Securing any kind of sensitive data
* Securing data in the cloud
* One-time pad for authentication in banking and other transactions
* Gaming applications and lottery
* Block-chain network
* Numerical simulations, statistical research
* IoT devices
* E-commerce and banking applications
* Cryptographic applications
* Telecom and 5G
* Monte Carlo Simulation

== '''Principles''' ==
[[File:Schematic of setup 2.png|thumb|300px|'''Figure 2. Schematic of setup''']]
Figure 2 schematically shows our setup. Such a setup is known as balanced homodyne detection and can extract the information of the electrical field in the second mode entering the polarizing beam-splitter (PBS) by measuring the photocurrent difference <math>i_1-i_2</math>. A continuous wave laser (wavelength 658 nm) is incident on one input port of the PBS and used as the local oscillator (LO), while another input port is empty. So the homodyne detection is trying to measure the vacuum state of the electromagnetic field. The randomness source in our setup is the fluctuations of the vacuum field. Here we tried to balance the optical power impinging on the two photodiodes, therefore any power fluctuation coming from the laser diode will be detected simultaneously and canceled in the photocurrent difference.

Alternatively, the randomness can be seen as coming from the shot noise of the photocurrents <math>i_1</math> and <math>i_2</math> with a power proportional to the average optical power. Since the shot noise currents from the diodes are uncorrelated, the y add up. And the amplitude fluctuations in the laser intensity (referred to as classical noise) can be eliminated by measuring the photocurrent difference.

== '''Setup''' ==
The practical setup (shown in Figure 3) was built with as few components as possible to create a baseline performance that we can compare.

[[File:Experimental setup.png|thumb|300px|'''Figure 3. Experimental setup''']]

==='''Tool list'''===
① Laser Diode
: Laser Diode is powered by a laser driving unit. The light intensity can be changed by changing the laser current.
② Focal Lens
: By adjusting the focal lens, the intensity of light that finally hits the photodiodes is adjusted.
③ RP: Rotatable Polarizer
: The polarization state of the light is adjusted by rotating the polarizer.
④ Mirror 1
: By adjusting mirror 1, the position of transmitted and reflected light spots hitting on PD1 and PD2 can be adjusted simultaneously.
⑤ PBS: Polarizing Beam Splitter
: The laser beam incident on the PBS can pass through or be reflected depending on the polarization state. If the incident beam is diagonal polarized (45°), the intensity of reflected and transmitted light is equal.
⑥ Mirror 2
: By adjusting mirror 2, the position of transmitted light spots hitting on PD2 can be tuned.
⑦&⑧ Photodiodes
: Detect the intensity of incident light.
⑩ Gain block
:A ready-made 60 dB gain Block from quantum optic lab.
⑪ High pass filter
:Designed cutoff frequency = 60 MHz.

==='''Description'''===
The total light power is changed by changing the laser current and adjusting the focal lens, while the power of the two output ports of the PBS is balanced by rotating the polarizer in front of the laser diode. Light leaving the PBS is detected by a pair of reverse-biased photodiodes connected in series to perform the current subtraction. By adjusting the orientation of M1 and M2, the light intensity incident on PD1 and PD2 can be adjusted and balanced. The balancing of the photocurrents is monitored by observing the voltage drop across a resister <math>R_{DC}</math> (DC port). Here we use a multimeter to measure the voltage. The fluctuations <math>\Delta(i_1-i_2)</math> are amplified by a 60 dB ready-made Gain block. And after that, a high pass filter (HPF) with a cutoff frequency of 60 MHz is used to filter out low frequency noise.

==='''Characterization list'''===
① Oscilloscope: Used to monitor the AC port and collect data.

② Spectrum Analyzer: Used to analyze the spectrum of total noise.

③ Multimeter
:Used to monitor the DC port and balance two photodiodes.

== '''Process''' ==
* '''26 February 2022:'''
* Did a basic characterization of photodiode
* Inputted a sine wave signal and a laser pointer light, observed the waveform of the photodiode
<gallery widths=300px heights=200px>
File:Basic characterization of photodiode test.jpeg|'''Figure 4. Basic characterization of photodiode'''
File:Schematic of basic characterization of photodiode test.png|'''Figure 5. Schematic of basic characterization of photodiode'''
</gallery>

:To understand the frequency response of the circuit shown in figure 5, we use a function generator to generate a sinusoidal signal to drive the LED, and use this circuit to measure the light output. When the frequency of the signal is low, we can see a relatively complete sine waveform on the oscilloscope. But when the frequency exceeds 1GHz, we could not observe a regular and stable waveform.
* '''5 March 2022:'''
* Used different resistors to test the frequency response of photodiode
<gallery widths=300px heights=200px>
File:Frequency of PD.png|'''Figure 6. Graph of the frequency response of photodiode'''
</gallery>
:We changed the resistors in Figure 6, from 1 kΩ to 11 kΩ and then 20 kΩ. We found that the higher the resistance of the resistor, the larger the output voltage but less sensitive to the high frequency. That is because a reverse-biased photodiode has a certain capacitance and forms an RC series circuit with the resistor. The larger the resistor, the larger the time constant <math>\tau=RC</math> of the RC circuit, and the slower the charge and discharge, which leads to a worse response to high frequency signals.
* '''12 March 2022:'''
* Build up the laser system and ensured the laser output
<gallery widths=300px heights=200px>
File:Laser diode.png|'''Figure 7. HL6501MG laser diode and schematic of internal circuit'''
File:Schematic of electronics laserconnector circuit.jpeg|'''Figure 8. Schematic of electronics laser connector circuit'''
File:Laser source setup.png|'''Figure 9. Laser source setup'''
</gallery>
:We used an HL6501MG laser diode, which is a 0.65 μm band AlGaInP laser diode (LD) with a multi-quantum well (MQW) structure. It is suitable as a light source for large-capacity optical disc memories and various other types of optical equipment. Hermetic sealing of the small package (φ=5.6 mm) assures high reliability.

:The Laser source consists of ① Laser diode; ② Thermostat; ③ Supply circuit for Laser diode and Thermostat; ④ Shell; ⑤ Focal lens; ⑥ Radiator. The Laser Diode is in the thermostat which is connected to the Radiator. We can set the temperature on the Laser power supply. The Thermostat and Radiator will keep the temperature of the laser diode as same as that set on the laser power supply. There is a focal lens in front of the laser diode. We can use it to change the focal length the enlarge the laser intensity hitting on the photodiodes. And a shell made of acrylic sheet and 4 balance posts.
* '''19 March 2022:'''
* Soldered photodiode driving circuit
* Test the feasibility
<gallery widths=300px heights=200px>
File:Photo diode outlines.png|'''Figure 10. S5972 Si PIN photodiode and schematic of internal circuit'''
File:Principle of photodiode driving circuit.png|'''Figure 11. Principle of photodiode driving circuit'''
File:Schematic photodiode driving circuit bolck.jpeg|'''Figure 12. Schematic photodiode driving circuit block'''
</gallery>

:We used an S5972 high-speed Si PIN photodiode to detect the light, which is designed for visible to near-infrared light detection. These photodiodes provide wideband characteristics at a low bias, making them suitable for optical communications and other high-speed photometry.

:We soldered all the components on the circuit chip as Figure 11 shows. After that, we tested its performance using a laser, it was approved that the optical signal was converted into the electrical signal and was measured by the oscilloscope.
* '''26 March 2022:'''
* Build up the whole system
* Tune the bias of two photodiodes
<gallery widths=300px heights=200px>
File:Whole setup.jpeg|'''Figure 13. The whole system setup'''
</gallery>
:We built up the whole setup on the optical platform. Then we tuned the bias of two photodiodes to make sure that the intensity of the laser hitting on both photodiodes is the same by adjusting the multimeter's voltage to around 0.
* '''2 April 2022:'''
* Focus the laser output
* Maximize the laser power output
* Characterize varaiation by varying optical power
<gallery widths=300px heights=200px>
File:Maximize the laser power output.jpeg|'''Figure 14. Maximize the laser power output'''
File:The detector noise power by varying the incident optical power.jpg|'''Figure 15. The plot of the detector noise power by varying the incident optical power'''
</gallery>
:We found that the laser output power in front of the polarizer was about 20 mW, but the power detected by each photodiode was only 0.4 mW. That is because the spot size of the laser was relatively large compared with the detection area of the photodiode. Therefore we needed to focus the lens in the laser block to maximize the detected laser power. To do this, we blocked one photodiode and used a multimeter to monitor the light power detected by another photodiode. After trials, we got a maximum value of voltage drop of 9.17 V, which corresponds to an optical power of 2.08 mW on each photodiode.

:Then, we characterized the change of noise level while rising incident optical power. And then we plotted a graph as shown in Figure 15, it is easy to find when the optical power is in a relatively low range, the noise level is flat which corresponds to the horizontal red line. While the optical power rises, the noise level increases with the optical power in a proportional manner. Therefore, we have enough reasons to believe that the overall noise is dominated by electronic noise in the low optical power range, while the noise level is dominated by shot noise in the high optical power range.
* '''9 April 2022:'''
* Soldered high pass filter
* Test its feasibility
<gallery widths=300px heights=200px>
File:Highpass filter principle circuit.png|'''Figure 16. Schematic of high pass filter circuit'''
File:Graph of theoretical high pass filter frequency response.jpg.png|'''Figure 17. Graph of theoretical high pass filter frequency response'''
File:Frequency of HPF.png|'''Figure 18. Graph of measured high pass filter frequency response'''
File:Schematic of high pass filter.jpeg|'''Figure 19. Setup of high pass filter'''
File:Setup of gain block and high pass filter.jpeg|'''Figure 20. Setup of gain block and high pass filter'''
</gallery>
:The measured total noise has a lot of low-frequency noise and is relatively flat power density in the range of 60-200 MHz. With a low pass filter of 200 MHz in the oscilloscope, we just needed a high pass filter of 60 MHz which compresses the low-frequency fluctuations. So we designed a high pass filter of 60 MHz and soldered the high pass filter.

:After that, we tested its performance. By comparing with the theoretical high pass filter graph, the measured high pass filter frequency response showed a high correspondence with it, which means it is feasible to apply it to the whole system to suppress the low-frequency fluctuations.
* '''16 April 2022:'''
* Apply the high pass filter to the circuit and test
* Record data and draw some graphs analysis
: In order to verify that the signals we obtained were quantum random numbers, we recorded the data at different sampling rates and performed autocorrelation calculations. These can be found in the "Result"-"Autocorrelation" part.

* '''23 April 2022:'''
* Processing experimental data
* Draw autocorrelation images
* Summarize and upload the experimental results

== '''Results''' ==
==='''Quantum noise'''===
*To ensure that the fluctuations at the amplifier output are dominated by quantum noise, the spectral power density is measured (in Figure 21. ).

[[File:Ampliﬁed noise levels measured into a resolution bandwidth B = 3 MHz..jpg|thumb|600px|center|'''Figure 21. Schematic of branching path quantum random number generators''']]

:Amplified noise levels measured into a resolution bandwidth B = 3 MHz. The total noise is measured from the photocurrent difference <math>i_1-i_2</math> with equal optical power impinging on both photodiodes. The current <math>i_1</math> of a single photodiode reveals colored classical noise. The electronic noise is measured without any optical input.
:In an alternative view, the laser beam can be seen as generating photocurrents <math>i_1</math> and <math>i_2</math> with a shot noise power proportional to the average optical power. The shot noise currents from the diodes add up as they are uncorrelated, while amplitude fluctuations in the laser intensity (referred to as classical noise) do not affect the photocurrent difference.

=== '''Autocorrelation'''===
*:Autocorrelation, sometimes known as serial correlation in the discrete-time case, is the correlation of a signal with a delayed copy of itself as a function of delay. Informally, it is the similarity between observations as a function of the time lag between them. In our experiment, if we obtain an ideal '''quantum random number generator''', the autocorrelation will be 1 when the time lag is 0, while the autocorrelation will be close to 0 when the time lag is not 0.

*:Given a signal <math>f(t)</math>, the continuous autocorrelation <math>R_{ff}(\tau)</math> is most often defined as the continuous cross-correlation integral of <math>f(t)</math> with itself, at lag <math>\tau</math>.

::::::::::::::::<math>R_{ff}(\tau) = \int_{-\infty}^\infty f(t+\tau)\overline{f(t)}\, {\rm d}t = \int_{-\infty}^\infty f(t) \overline{f(t-\tau)}\, {\rm d}t</math>

::where <math>\overline{f(t)}</math> represents the complex conjugate of <math>f(t)</math>. Note that the parameter <math>t</math> in the integral is a dummy variable and is only necessary to calculate the integral. It has no specific meaning.

*:'''Experimental result'''
:<gallery widths=500px heights=300px>
File:2.5 GHz (-20,20) After Highpass1.png|'''Figure 22. Autocorrelation of the total noise signal sampled at 2.5 GHz'''
File:500 kHz (-20,20) After Highpass1.png|'''Figure 23. Autocorrelation of the total noise signal sampled at 500 KHz'''
:</gallery>

:We recorded several sets of data with different sampling frequencies ( 2.5 GHz to 500 kHz) and obtained autocorrelation for each group. A very high correlation between any two adjacent points was observed when we use a 2.5 GHz sampling rate. This is simply because of an extremely high sampling rate which results in every two adjacent points being almost at the same position. We can get a better correlation by reducing the sampling frequency to such as 10 MHz or even lower.

:But the autocorrelation with a 500 kHz sampling rate is still not ideal. This is limited by our experimental setup. We caught up with too much electronic interference. A well-designed experimental setup with integrated photodiodes, amplifier, and high pass filter will stimulate a better result.

=== '''Randomness Extraction'''===
123125125125
[[File:Raw_data.png|thumb|600px|center|'''Figure 24 765876486''']]

[[File:Extracted.png|thumb|600px|center|'''Figure 25''']]
[[File:Contrast.png||thumb|600px|center|'''Figure 26''']]

=== '''Randomness Test'''===
*:To verify the randomness of the experimental results we obtained, we used two compression protocols(rar and zip) to compress the random numbers we generated. The compressed file size does not change significantly compared with the original file(from 58k to 55k), which, to some extent, illustrates the randomness of our results.

== '''References''' ==
[1] Miguel Herrero-Collantes and Juan Carlos Garcia-Escartin, Quantum random number generators, Rev. Mod. Phys, 89, 015004.

[2] Shi, Yicheng, Brenda Chng, and Christian Kurtsiefer, Random numbers from vacuum fluctuations, Applied Physics Letters, 109.4 (2016): 041101.

[3] https://www.digchip.com/datasheets/parts/datasheet/625/HL6501MG-pdf.php

[4] https://www.farnell.com/datasheets/3171163.pdf

Quantum Random Number Generator

2022-04-29T14:19:22Z

Zhang Munan: /* Principles */

== '''Team Members''' ==
Wang Yang A0228753X

Xiao Yucan A0236278W

Zhang Munan A0236273E

== '''Idea''' ==
We live in an increasingly connected world, where a superior source of entropy is the key to data security. The effectiveness of any cryptographic system is determined by the strength of the keys it used. In turn, the strength of the key is determined by the degree of randomness used in its generation. Besides, large amount of random numbers are at the core of Monte Carlo simulations, which are widely used in scientific research. Methods produce random numbers from any algorithm are called pseudo-random number generator(PRNG). And random numbers generated by PRNG are deterministic by definition and therefore unsuitable for cryptographic purposes.

In order to generate unpredictable random numbers, hardware random number generators have been widely used. These physically generated random numbers are considered "truly" random because it is either practically or fundamentally impossible to predict the outcome of such a device. Quantum Random Number Generators (QRNGs) belong to a class of hardware random number generators and leverage the random properties of quantum physics to generate a true source of entropy, improving the quality of seed content for key generation.

Early QRNGs were based on radioactive decay. And more recently, QRNGs based on Poisson statistics of photons have been developed. The core idea is shown in the figure below. Single photons generated by a laser source are incident on a semi-transparent mirror and the mutually exclusive events (reflection/transmission) are detected and associated with ‘0’ or ‘1’ bit values respectively. The unpredictability of generated numbers is ensured by the quantum nature of the process. However, such a scheme needs a reliable single photon source as well as single photon detectors and it's not possible for our project. Here, we decided to build a QRNG based on measuring vacuum fluctuations of a light field as a random source. More details will be discussed in the principle part.
[[File:Principle schematic of QRNG.png|thumb|300px|'''Figure 1. Schematic of branching path quantum random number generators''']]

=== Benefits of having a quantum random number generator ===
* The source of randomness is unpredictable and controlled by quantum process.
* Live/real-time monitoring of entropy source is possible and highly effective as well.
* All attacks on the entropy source are detectable.

=== Application of quantum random number generator ===
* Securing data at rest in data centres
* Securing any kind of sensitive data
* Securing data in the cloud
* One-time pad for authentication in banking and other transactions
* Gaming applications and lottery
* Block-chain network
* Numerical simulations, statistical research
* IoT devices
* E-commerce and banking applications
* Cryptographic applications
* Telecom and 5G
* Monte Carlo Simulation

== '''Principles''' ==
[[File:Schematic of setup 2.png|thumb|300px|'''Figure 2. Schematic of setup''']]
Figure 2 schematically shows our setup. Such a setup is known as balanced homodyne detection and can extract the information of the electrical field in the second mode entering the polarizing beam-splitter (PBS) by measuring the photocurrent difference <math>i_1-i_2</math>. A continuous wave laser (wavelength 658 nm) is incident on one input port of the PBS and used as the local oscillator (LO), while another input port is empty. So the homodyne detection is trying to measure the vacuum state of the electromagnetic field. The randomness source in our setup is the fluctuations of the vacuum field. Here we tried to balance the optical power impinging on the two photodiodes, therefore any power fluctuation coming from the laser diode will be detected simultaneously and canceled in the photocurrent difference.

Alternatively, the randomness can be seen as coming from the shot noise of the photocurrents <math>i_1</math> and <math>i_2</math> with a power proportional to the average optical power. Since the shot noise currents from the diodes are uncorrelated, the y add up. And the amplitude fluctuations in the laser intensity (referred to as classical noise) can be eliminated by measuring the photocurrent difference.

== '''Setup''' ==
The practical setup was built with as few components as possible to create a baseline performance that we can compare. A schematic of the setup is shown in Figure 3.

[[File:Experimental setup.png|thumb|300px|'''Figure 3. Experimental setup''']]

==='''Tool list'''===
① Laser Diode
: Laser Diode is powered by a laser driving unit. The light intensity can be changed by changing the laser current.
② Focal Lens
: By adjusting the focal length, the intensity of light that finally hits the photodiodes is adjusted.
③ RP: Rotatable Polarizer
: The polarization state of the light is adjusted by rotating the polarizer.
④ Mirror 1
: By adjusting mirror 1, the position of transmitted and reflected light spots hitting on PD1 and PD2 can be adjusted simultaneously.
⑤ PBS: Polarizing Beam Splitter
: The laser beam incident on the PBS can pass through or be reflected depending on the polarization state. If the incident beam is diagonal polarized (45°), the intensity of reflected and transmitted light is equal.
⑥ Mirror 2
: By adjusting mirror 2, the position of transmitted light spots hitting on PD2 can be tuned.
⑦&⑧: Photodiodes
: Detect the intensity of incident light.

==='''Description'''===
The total light power is changed by changing the laser current and adjusting the focal lens, while the power of the two output ports of the PBS is balanced by rotating the polarizer in front of the laser diode. Light leaving the PBS is detected by a pair of reverse-biased photodiodes connected in series to perform the current subtraction. By adjusting the orientation of M1 and M2, the light intensity incident on PD1 and PD2 can be adjusted and balanced. The balancing of the photocurrents is monitored by observing the voltage drop across a resister <math>R_{DC}</math> (DC port). Here we use a multimeter to measure the voltage. The fluctuations <math>\Delta(i_1-i_2)</math>

==='''Characterization list'''===
① Oscilloscope

② Spectrum Analyzer

== '''Process''' ==
* '''26 February 2022:'''
* Did a basic characterization of photodiode
* Inputted a sine wave signal and a laser pointer light, observed the waveform of the photodiode
<gallery widths=300px heights=200px>
File:Basic characterization of photodiode test.jpeg|'''Figure 4. Basic characterization of photodiode'''
File:Schematic of basic characterization of photodiode test.png|'''Figure 5. Schematic of basic characterization of photodiode'''
</gallery>

:To understand the frequency response of the circuit shown in figure 5, we use a function generator to generate a sinusoidal signal to drive the LED, and use this circuit to measure the light output. When the frequency of the signal is low, we can see a relatively complete sine waveform on the oscilloscope. But when the frequency exceeds 1GHz, we could not observe a regular and stable waveform.
* '''5 March 2022:'''
* Used different resistors to test the frequency response of photodiode
<gallery widths=300px heights=200px>
File:Frequency of PD.png|'''Figure 6. Graph of the frequency response of photodiode'''
</gallery>
:We changed the resistors in Figure 6, from 1 kΩ to 11 kΩ and then 20 kΩ. We found that the higher the resistance of the resistor, the larger the output voltage but less sensitive to the high frequency. That is because a reverse-biased photodiode has a certain capacitance and forms an RC series circuit with the resistor. The larger the resistor, the larger the time constant <math>\tau=RC</math> of the RC circuit, and the slower the charge and discharge, which leads to a worse response to high frequency signals.
* '''12 March 2022:'''
* Build up the laser system and ensured the laser output
<gallery widths=300px heights=200px>
File:Laser diode.png|'''Figure 7. HL6501MG laser diode and schematic of internal circuit'''
File:Schematic of electronics laserconnector circuit.jpeg|'''Figure 8. Schematic of electronics laser connector circuit'''
File:Laser source setup.png|'''Figure 9. Laser source setup'''
</gallery>
:We used an HL6501MG laser diode, which is a 0.65 μm band AlGaInP laser diode (LD) with a multi-quantum well (MQW) structure. It is suitable as a light source for large-capacity optical disc memories and various other types of optical equipment. Hermetic sealing of the small package (φ=5.6 mm) assures high reliability.

:The Laser source consists of ① Laser diode; ② Thermostat; ③ Supply circuit for Laser diode and Thermostat; ④ Shell; ⑤ Focal lens; ⑥ Radiator. The Laser Diode is in the thermostat which is connected to the Radiator. We can set the temperature on the Laser power supply. The Thermostat and Radiator will keep the temperature of the laser diode as same as that set on the laser power supply. There is a focal lens in front of the laser diode. We can use it to change the focal length the enlarge the laser intensity hitting on the photodiodes. And a shell made of acrylic sheet and 4 balance posts.
* '''19 March 2022:'''
* Soldered photodiode driving circuit
* Test the feasibility
<gallery widths=300px heights=200px>
File:Photo diode outlines.png|'''Figure 10. S5972 Si PIN photodiode and schematic of internal circuit'''
File:Principle of photodiode driving circuit.png|'''Figure 11. Principle of photodiode driving circuit'''
File:Schematic photodiode driving circuit bolck.jpeg|'''Figure 12. Schematic photodiode driving circuit block'''
</gallery>

:We used an S5972 high-speed Si PIN photodiode to detect the light, which is designed for visible to near-infrared light detection. These photodiodes provide wideband characteristics at a low bias, making them suitable for optical communications and other high-speed photometry.

:We soldered all the components on the circuit chip as Figure 11 shows. After that, we tested its performance using a laser, it was approved that the optical signal was converted into the electrical signal and was measured by the oscilloscope.
* '''26 March 2022:'''
* Build up the whole system
* Tune the bias of two photodiodes
<gallery widths=300px heights=200px>
File:Whole setup.jpeg|'''Figure 13. The whole system setup'''
</gallery>
:We built up the whole setup on the optical platform. Then we tuned the bias of two photodiodes to make sure that the intensity of the laser hitting on both photodiodes is the same by adjusting the multimeter's voltage to around 0.
* '''2 April 2022:'''
* Focus the laser output
* Maximize the laser power output
* Characterize varaiation by varying optical power
<gallery widths=300px heights=200px>
File:Maximize the laser power output.jpeg|'''Figure 14. Maximize the laser power output'''
File:The detector noise power by varying the incident optical power.jpg|'''Figure 15. The plot of the detector noise power by varying the incident optical power'''
</gallery>
:We found that the laser output power in front of the polarizer was about 20 mW, but the power detected by each photodiode was only 0.4 mW. That is because the spot size of the laser was relatively large compared with the detection area of the photodiode. Therefore we needed to focus the lens in the laser block to maximize the detected laser power. To do this, we blocked one photodiode and used a multimeter to monitor the light power detected by another photodiode. After trials, we got a maximum value of voltage drop of 9.17 V, which corresponds to an optical power of 2.08 mW on each photodiode.

:Then, we characterized the change of noise level while rising incident optical power. And then we plotted a graph as shown in Figure 15, it is easy to find when the optical power is in a relatively low range, the noise level is flat which corresponds to the horizontal red line. While the optical power rises, the noise level increases with the optical power in a proportional manner. Therefore, we have enough reasons to believe that the overall noise is dominated by electronic noise in the low optical power range, while the noise level is dominated by shot noise in the high optical power range.
* '''9 April 2022:'''
* Soldered high pass filter
* Test its feasibility
<gallery widths=300px heights=200px>
File:Highpass filter principle circuit.png|'''Figure 16. Schematic of high pass filter circuit'''
File:Graph of theoretical high pass filter frequency response.jpg.png|'''Figure 17. Graph of theoretical high pass filter frequency response'''
File:Frequency of HPF.png|'''Figure 18. Graph of measured high pass filter frequency response'''
File:Schematic of high pass filter.jpeg|'''Figure 19. Setup of high pass filter'''
File:Setup of gain block and high pass filter.jpeg|'''Figure 20. Setup of gain block and high pass filter'''
</gallery>
:The measured total noise has a lot of low-frequency noise and is relatively flat power density in the range of 60-200 MHz. With a low pass filter of 200 MHz in the oscilloscope, we just needed a high pass filter of 60 MHz which compresses the low-frequency fluctuations. So we designed a high pass filter of 60 MHz and soldered the high pass filter.

:After that, we tested its performance. By comparing with the theoretical high pass filter graph, the measured high pass filter frequency response showed a high correspondence with it, which means it is feasible to apply it to the whole system to suppress the low-frequency fluctuations.
* '''16 April 2022:'''
* Apply the high pass filter to the circuit and test
* Record data and draw some graphs analysis
: In order to verify that the signals we obtained were quantum random numbers, we recorded the data at different sampling rates and performed autocorrelation calculations. These can be found in the "Result"-"Autocorrelation" part.

* '''23 April 2022:'''
* Processing experimental data
* Draw autocorrelation images
* Summarize and upload the experimental results

== '''Results''' ==
==='''Quantum noise'''===
*To ensure that the fluctuations at the amplifier output are dominated by quantum noise, the spectral power density is measured (in Figure 21. ).

[[File:Ampliﬁed noise levels measured into a resolution bandwidth B = 3 MHz..jpg|thumb|600px|center|'''Figure 21. Schematic of branching path quantum random number generators''']]

:Amplified noise levels measured into a resolution bandwidth B = 3 MHz. The total noise is measured from the photocurrent difference <math>i_1-i_2</math> with equal optical power impinging on both photodiodes. The current <math>i_1</math> of a single photodiode reveals colored classical noise. The electronic noise is measured without any optical input.
:In an alternative view, the laser beam can be seen as generating photocurrents <math>i_1</math> and <math>i_2</math> with a shot noise power proportional to the average optical power. The shot noise currents from the diodes add up as they are uncorrelated, while amplitude fluctuations in the laser intensity (referred to as classical noise) do not affect the photocurrent difference.

=== '''Autocorrelation'''===
*:Autocorrelation, sometimes known as serial correlation in the discrete-time case, is the correlation of a signal with a delayed copy of itself as a function of delay. Informally, it is the similarity between observations as a function of the time lag between them. In our experiment, if we obtain an ideal '''quantum random number generator''', the autocorrelation will be 1 when the time lag is 0, while the autocorrelation will be close to 0 when the time lag is not 0.

*:Given a signal <math>f(t)</math>, the continuous autocorrelation <math>R_{ff}(\tau)</math> is most often defined as the continuous cross-correlation integral of <math>f(t)</math> with itself, at lag <math>\tau</math>.

::::::::::::::::<math>R_{ff}(\tau) = \int_{-\infty}^\infty f(t+\tau)\overline{f(t)}\, {\rm d}t = \int_{-\infty}^\infty f(t) \overline{f(t-\tau)}\, {\rm d}t</math>

::where <math>\overline{f(t)}</math> represents the complex conjugate of <math>f(t)</math>. Note that the parameter <math>t</math> in the integral is a dummy variable and is only necessary to calculate the integral. It has no specific meaning.

*:'''Experimental result'''
:<gallery widths=500px heights=300px>
File:2.5 GHz (-20,20) After Highpass1.png|'''Figure 22. Autocorrelation of the total noise signal sampled at 2.5 GHz'''
File:500 kHz (-20,20) After Highpass1.png|'''Figure 23. Autocorrelation of the total noise signal sampled at 500 KHz'''
:</gallery>

:We recorded several sets of data with different sampling frequencies ( 2.5 GHz to 500 kHz) and obtained autocorrelation for each group. A very high correlation between any two adjacent points was observed when we use a 2.5 GHz sampling rate. This is simply because of an extremely high sampling rate which results in every two adjacent points being almost at the same position. We can get a better correlation by reducing the sampling frequency to such as 10 MHz or even lower.

:But the autocorrelation with a 500 kHz sampling rate is still not ideal. This is limited by our experimental setup. We caught up with too much electronic interference. A well-designed experimental setup with integrated photodiodes, amplifier, and high pass filter will stimulate a better result.

=== '''Randomness Extraction'''===
123125125125
[[File:Raw_data.png|thumb|600px|center|'''Figure 24 765876486''']]

[[File:Extracted.png|thumb|600px|center|'''Figure 25''']]
[[File:Contrast.png||thumb|600px|center|'''Figure 26''']]

=== '''Randomness Test'''===
*:To verify the randomness of the experimental results we obtained, we used two compression protocols(rar and zip) to compress the random numbers we generated. The compressed file size does not change significantly compared with the original file(from 58k to 55k), which, to some extent, illustrates the randomness of our results.

== '''References''' ==
[1] Miguel Herrero-Collantes and Juan Carlos Garcia-Escartin, Quantum random number generators, Rev. Mod. Phys, 89, 015004.

[2] Shi, Yicheng, Brenda Chng, and Christian Kurtsiefer, Random numbers from vacuum fluctuations, Applied Physics Letters, 109.4 (2016): 041101.

[3] https://www.digchip.com/datasheets/parts/datasheet/625/HL6501MG-pdf.php

[4] https://www.farnell.com/datasheets/3171163.pdf

Quantum Random Number Generator

2022-04-29T09:24:54Z

Zhang Munan: /* Process */

== '''Team Members''' ==
Wang Yang A0228753X

Xiao Yucan A0236278W

Zhang Munan A0236273E

== '''Idea''' ==
We live in an increasingly connected world, where a superior source of entropy is the key to data security. The effectiveness of any cryptographic system is determined by the strength of the keys it used. In turn, the strength of the key is determined by the degree of randomness used in its generation. Besides, large amount of random numbers are at the core of Monte Carlo simulations, which are widely used in scientific research. Methods produce random numbers from any algorithm are called pseudo-random number generator(PRNG). And random numbers generated by PRNG are deterministic by definition and therefore unsuitable for cryptographic purposes.

In order to generate unpredictable random numbers, hardware random number generators have been widely used. These physically generated random numbers are considered "truly" random because it is either practically or fundamentally impossible to predict the outcome of such a device. Quantum Random Number Generators (QRNGs) belong to a class of hardware random number generators and leverage the random properties of quantum physics to generate a true source of entropy, improving the quality of seed content for key generation.

Early QRNGs were based on radioactive decay. And more recently, QRNGs based on Poisson statistics of photons have been developed. The core idea is shown in the figure below. Single photons generated by a laser source are incident on a semi-transparent mirror and the mutually exclusive events (reflection/transmission) are detected and associated with ‘0’ or ‘1’ bit values respectively. The unpredictability of generated numbers is ensured by the quantum nature of the process. However, such a scheme needs a reliable single photon source as well as single photon detectors and it's not possible for our project. Here, we decided to build a QRNG based on measuring vacuum fluctuations of a light field as a random source. More details will be discussed in the principle part.
[[File:Principle schematic of QRNG.png|thumb|300px|'''Figure 1. Schematic of branching path quantum random number generators''']]

=== Benefits of having a quantum random number generator ===
* The source of randomness is unpredictable and controlled by quantum process.
* Live/real-time monitoring of entropy source is possible and highly effective as well.
* All attacks on the entropy source are detectable.

=== Application of quantum random number generator ===
* Securing data at rest in data centres
* Securing any kind of sensitive data
* Securing data in the cloud
* One-time pad for authentication in banking and other transactions
* Gaming applications and lottery
* Block-chain network
* Numerical simulations, statistical research
* IoT devices
* E-commerce and banking applications
* Cryptographic applications
* Telecom and 5G
* Monte Carlo Simulation

== '''Principles''' ==
[[File:Schematic of setup 2.png|thumb|300px|'''Figure 2. Schematic of setup''']]
Figure 2 schematically shows our setup. Such a setup is known as balanced homodyne detection and can extract the information of the electrical field in the second mode entering the polarizing beam-splitter (PBS) by measuring the photocurrent difference <math>i_1-i_2</math>. A continuous wave laser (wavelength 658 nm) is incident on one input port of the PBS and used as the local oscillator (LO), while another input port is empty. So the homodyne detection is trying to measure the vacuum state of the electromagnetic field. The randomness source in our setup is the fluctuations of the vacuum field. Here we tried to balance the optical power impinging on the two photodiodes, therefore any power fluctuation coming from the laser diode will be detected simultaneously and canceled in the photocurrent difference.

Alternatively, the randomness can be seen as coming from the shot noise of the photocurrents <math>i_1</math> and <math>i_2</math> with a power proportional to the average optical power. Since the shot noise currents from the diodes are uncorrelated, the noise adds up. And the amplitude fluctuations in the laser intensity (referred to as classical noise) can be eliminated by measuring the photocurrent difference.

== '''Setup''' ==
The practical setup was built with as few components as possible to create a baseline performance that we can compare. A schematic of the setup is shown in Figure 3.

[[File:Experimental setup.png|thumb|300px|'''Figure 3. Experimental setup''']]

==='''Tool list'''===
① Laser Diode
: Laser Diode is powered by a laser driving unit. The light intensity can be changed by changing the laser current.
② Focal Lens
: By adjusting the focal length, the intensity of light that finally hits the photodiodes is adjusted.
③ RP: Rotatable Polarizer
: The polarization state of the light is adjusted by rotating the polarizer.
④ Mirror 1
: By adjusting mirror 1, the position of transmitted and reflected light spots hitting on PD1 and PD2 can be adjusted simultaneously.
⑤ PBS: Polarizing Beam Splitter
: The laser beam incident on the PBS can pass through or be reflected depending on the polarization state. If the incident beam is diagonal polarized (45°), the intensity of reflected and transmitted light is equal.
⑥ Mirror 2
: By adjusting mirror 2, the position of transmitted light spots hitting on PD2 can be tuned.
⑦&⑧: Photodiodes
: Detect the intensity of incident light.

==='''Description'''===
The total light power is changed by changing the laser current and adjusting the focal lens, while the power of the two output ports of the PBS is balanced by rotating the polarizer in front of the laser diode. Light leaving the PBS is detected by a pair of reverse-biased photodiodes connected in series to perform the current subtraction. By adjusting the orientation of M1 and M2, the light intensity incident on PD1 and PD2 can be adjusted and balanced. The balancing of the photocurrents is monitored by observing the voltage drop across a resister <math>R_{DC}</math> (DC port). Here we use a multimeter to measure the voltage. The fluctuations <math>\Delta(i_1-i_2)</math>

==='''Characterization list'''===
① Oscilloscope

② Spectrum Analyzer

== '''Process''' ==
* '''26 February 2022:'''
* Did a basic characterization of photodiode
* Inputted a sine wave signal and a laser pointer light, observed the waveform of the photodiode
<gallery widths=300px heights=200px>
File:Basic characterization of photodiode test.jpeg|'''Figure 4. Basic characterization of photodiode'''
File:Schematic of basic characterization of photodiode test.png|'''Figure 5. Schematic of basic characterization of photodiode'''
</gallery>

:To understand the frequency response of the circuit shown in figure 5, we use a function generator to generate a sinusoidal signal to drive the LED, and use this circuit to measure the light output. When the frequency of the signal is low, we can see a relatively complete sine waveform on the oscilloscope. But when the frequency exceeds 1GHz, we could not observe a regular and stable waveform.
* '''5 March 2022:'''
* Used different resistors to test the frequency response of photodiode
<gallery widths=300px heights=200px>
File:Frequency of PD.png|'''Figure 6. Graph of the frequency response of photodiode'''
</gallery>
:We changed the resistors in Figure 6, from 1 kΩ to 11 kΩ and then 20 kΩ. We found that the higher the resistance of the resistor, the larger the output voltage but less sensitive to the high frequency. That is because a reverse-biased photodiode has a certain capacitance and forms an RC series circuit with the resistor. The larger the resistor, the larger the time constant <math>\tau=RC</math> of the RC circuit, and the slower the charge and discharge, which leads to a worse response to high frequency signals.
* '''12 March 2022:'''
* Build up the laser system and ensured the laser output
<gallery widths=300px heights=200px>
File:Laser diode.png|'''Figure 7. HL6501MG laser diode and schematic of internal circuit'''
File:Schematic of electronics laserconnector circuit.jpeg|'''Figure 8. Schematic of electronics laser connector circuit'''
File:Laser source setup.png|'''Figure 9. Laser source setup'''
</gallery>
:We used an HL6501MG laser diode, which is a 0.65 μm band AlGaInP laser diode (LD) with a multi-quantum well (MQW) structure. It is suitable as a light source for large-capacity optical disc memories and various other types of optical equipment. Hermetic sealing of the small package (φ=5.6 mm) assures high reliability.

:The Laser source consists of ① Laser diode; ② Thermostat; ③ Supply circuit for Laser diode and Thermostat; ④ Shell; ⑤ Focal lens; ⑥ Radiator. The Laser Diode is in the thermostat which is connected to the Radiator. We can set the temperature on the Laser power supply. The Thermostat and Radiator will keep the temperature of the laser diode as same as that set on the laser power supply. There is a focal lens in front of the laser diode. We can use it to change the focal length the enlarge the laser intensity hitting on the photodiodes. And a shell made of acrylic sheet and 4 balance posts.
* '''19 March 2022:'''
* Soldered photodiode driving circuit
* Test the feasibility
<gallery widths=300px heights=200px>
File:Photo diode outlines.png|'''Figure 10. S5972 Si PIN photodiode and schematic of internal circuit'''
File:Principle of photodiode driving circuit.png|'''Figure 11. Principle of photodiode driving circuit'''
File:Schematic photodiode driving circuit bolck.jpeg|'''Figure 12. Schematic photodiode driving circuit block'''
</gallery>

:We used an S5972 high-speed Si PIN photodiode to detect the light, which is designed for visible to near-infrared light detection. These photodiodes provide wideband characteristics at a low bias, making them suitable for optical communications and other high-speed photometry.

:We soldered all the components on the circuit chip as Figure 11 shows. After that, we tested its performance using a laser, it was approved that the optical signal was converted into the electrical signal and was measured by the oscilloscope.
* '''26 March 2022:'''
* Build up the whole system
* Tune the bias of two photodiodes
<gallery widths=300px heights=200px>
File:Whole setup.jpeg|'''Figure 13. The whole system setup'''
</gallery>
:We built up the whole setup on the optical platform. Then we tuned the bias of two photodiodes to make sure that the intensity of the laser hitting on both photodiodes is the same by adjusting the multimeter's voltage to around 0.
* '''2 April 2022:'''
* Focus the laser output
* Maximize the laser power output
* Characterize varaiation by varying optical power
<gallery widths=300px heights=200px>
File:Maximize the laser power output.jpeg|'''Figure 14. Maximize the laser power output'''
File:The detector noise power by varying the incident optical power.jpg|'''Figure 15. The plot of the detector noise power by varying the incident optical power'''
</gallery>
:We found that the laser output power in front of the polarizer was about 20 mW, but the power detected by each photodiode was only 0.4 mW. That is because the spot size of the laser was relatively large compared with the detection area of the photodiode. Therefore we needed to focus the lens in the laser block to maximize the detected laser power. To do this, we blocked one photodiode and used a multimeter to monitor the light power detected by another photodiode. After trials, we got a maximum value of voltage drop of 9.17 V, which corresponds to an optical power of 2.08 mW on each photodiode.

:Then, we characterized the change of noise level while rising incident optical power. And then we plotted a graph as shown in Figure 15, it is easy to find when the optical power is in a relatively low range, the noise level is flat which corresponds to the horizontal red line. While the optical power rises, the noise level increases with the optical power in a proportional manner. Therefore, we have enough reasons to believe that the overall noise is dominated by electronic noise in the low optical power range, while the noise level is dominated by shot noise in the high optical power range.
* '''9 April 2022:'''
* Soldered high pass filter
* Test its feasibility
<gallery widths=300px heights=200px>
File:Highpass filter principle circuit.png|'''Figure 16. Schematic of high pass filter circuit'''
File:Graph of theoretical high pass filter frequency response.jpg.png|'''Figure 17. Graph of theoretical high pass filter frequency response'''
File:Frequency of HPF.png|'''Figure 18. Graph of measured high pass filter frequency response'''
File:Schematic of high pass filter.jpeg|'''Figure 19. Setup of high pass filter'''
File:Setup of gain block and high pass filter.jpeg|'''Figure 20. Setup of gain block and high pass filter'''
</gallery>
:The measured total noise has a lot of low-frequency noise and is relatively flat power density in the range of 60-200 MHz. With a low pass filter of 200 MHz in the oscilloscope, we just needed a high pass filter of 60 MHz which compresses the low-frequency fluctuations. So we designed a high pass filter of 60 MHz and soldered the high pass filter.

:After that, we tested its performance. By comparing with the theoretical high pass filter graph, the measured high pass filter frequency response showed a high correspondence with it, which means it is feasible to apply it to the whole system to suppress the low-frequency fluctuations.
* '''16 April 2022:'''
* Apply the high pass filter to the circuit and test
* Record data and draw some graphs analysis
: In order to verify that the signals we obtained were quantum random numbers, we recorded the data at different sampling rates and performed autocorrelation calculations. These can be found in the "Result"-"Autocorrelation" part.

* '''23 April 2022:'''
* Processing experimental data
* Draw autocorrelation images
* Summarize and upload the experimental results

== '''Results''' ==
==='''Quantum noise'''===
*To ensure that the fluctuations at the amplifier output are dominated by quantum noise, the spectral power density is measured (in Figure 21. ).

[[File:Ampliﬁed noise levels measured into a resolution bandwidth B = 3 MHz..jpg|thumb|600px|center|'''Figure 21. Schematic of branching path quantum random number generators''']]

:Amplified noise levels measured into a resolution bandwidth B = 3 MHz. The total noise is measured from the photocurrent difference <math>i_1-i_2</math> with equal optical power impinging on both photodiodes. The current <math>i_1</math> of a single photodiode reveals colored classical noise. The electronic noise is measured without any optical input.
:In an alternative view, the laser beam can be seen as generating photocurrents <math>i_1</math> and <math>i_2</math> with a shot noise power proportional to the average optical power. The shot noise currents from the diodes add up as they are uncorrelated, while amplitude fluctuations in the laser intensity (referred to as classical noise) do not affect the photocurrent difference.

=== '''Autocorrelation'''===
*:Autocorrelation, sometimes known as serial correlation in the discrete-time case, is the correlation of a signal with a delayed copy of itself as a function of delay. Informally, it is the similarity between observations as a function of the time lag between them. In our experiment, if we obtain an ideal '''quantum random number generator''', the autocorrelation will be 1 when the time lag is 0, while the autocorrelation will be close to 0 when the time lag is not 0.

*:Given a signal <math>f(t)</math>, the continuous autocorrelation <math>R_{ff}(\tau)</math> is most often defined as the continuous cross-correlation integral of <math>f(t)</math> with itself, at lag <math>\tau</math>.

::::::::::::::::<math>R_{ff}(\tau) = \int_{-\infty}^\infty f(t+\tau)\overline{f(t)}\, {\rm d}t = \int_{-\infty}^\infty f(t) \overline{f(t-\tau)}\, {\rm d}t</math>

::where <math>\overline{f(t)}</math> represents the complex conjugate of <math>f(t)</math>. Note that the parameter <math>t</math> in the integral is a dummy variable and is only necessary to calculate the integral. It has no specific meaning.

*:'''Experimental result'''
:<gallery widths=500px heights=300px>
File:2.5 GHz (-20,20) After Highpass1.png|'''Figure 22. Autocorrelation of the total noise signal sampled at 2.5 GHz'''
File:500 kHz (-20,20) After Highpass1.png|'''Figure 23. Autocorrelation of the total noise signal sampled at 500 KHz'''
:</gallery>

:We recorded several sets of data with different sampling frequencies ( 2.5 GHz to 500 kHz) and obtained autocorrelation for each group. A very high correlation between any two adjacent points was observed when we use a 2.5 GHz sampling rate. This is simply because of an extremely high sampling rate which results in every two adjacent points being almost at the same position. We can get a better correlation by reducing the sampling frequency to such as 10 MHz or even lower.

:But the autocorrelation with a 500 kHz sampling rate is still not ideal. This is limited by our experimental setup. We caught up with too much electronic interference. A well-designed experimental setup with integrated photodiodes, amplifier, and high pass filter will stimulate a better result.

=== '''Randomness Extraction'''===
:<gallery widths=350px heights=200px>
File:Raw_data.png|'''Figure 24. '''
File:Contrast.png|'''Figure 25. '''
File:Extracted.png|'''Figure 26. '''
:</gallery>

=== '''Randomness Test'''===

== '''References''' ==
[1] Miguel Herrero-Collantes and Juan Carlos Garcia-Escartin, Quantum random number generators, Rev. Mod. Phys, 89, 015004.

[2] Shi, Yicheng, Brenda Chng, and Christian Kurtsiefer, Random numbers from vacuum fluctuations, Applied Physics Letters, 109.4 (2016): 041101.

[3] https://www.digchip.com/datasheets/parts/datasheet/625/HL6501MG-pdf.php

[4] https://www.farnell.com/datasheets/3171163.pdf

Quantum Random Number Generator

2022-04-29T09:18:42Z

Zhang Munan: /* Process */

== '''Team Members''' ==
Wang Yang A0228753X

Xiao Yucan A0236278W

Zhang Munan A0236273E

== '''Idea''' ==
We live in an increasingly connected world, where a superior source of entropy is the key to data security. The effectiveness of any cryptographic system is determined by the strength of the keys it used. In turn, the strength of the key is determined by the degree of randomness used in its generation. Besides, large amount of random numbers are at the core of Monte Carlo simulations, which are widely used in scientific research. Methods produce random numbers from any algorithm are called pseudo-random number generator(PRNG). And random numbers generated by PRNG are deterministic by definition and therefore unsuitable for cryptographic purposes.

In order to generate unpredictable random numbers, hardware random number generators have been widely used. These physically generated random numbers are considered "truly" random because it is either practically or fundamentally impossible to predict the outcome of such a device. Quantum Random Number Generators (QRNGs) belong to a class of hardware random number generators and leverage the random properties of quantum physics to generate a true source of entropy, improving the quality of seed content for key generation.

Early QRNGs were based on radioactive decay. And more recently, QRNGs based on Poisson statistics of photons have been developed. The core idea is shown in the figure below. Single photons generated by a laser source are incident on a semi-transparent mirror and the mutually exclusive events (reflection/transmission) are detected and associated with ‘0’ or ‘1’ bit values respectively. The unpredictability of generated numbers is ensured by the quantum nature of the process. However, such a scheme needs a reliable single photon source as well as single photon detectors and it's not possible for our project. Here, we decided to build a QRNG based on measuring vacuum fluctuations of a light field as a random source. More details will be discussed in the principle part.
[[File:Principle schematic of QRNG.png|thumb|300px|'''Figure 1. Schematic of branching path quantum random number generators''']]

=== Benefits of having a quantum random number generator ===
* The source of randomness is unpredictable and controlled by quantum process.
* Live/real-time monitoring of entropy source is possible and highly effective as well.
* All attacks on the entropy source are detectable.

=== Application of quantum random number generator ===
* Securing data at rest in data centres
* Securing any kind of sensitive data
* Securing data in the cloud
* One-time pad for authentication in banking and other transactions
* Gaming applications and lottery
* Block-chain network
* Numerical simulations, statistical research
* IoT devices
* E-commerce and banking applications
* Cryptographic applications
* Telecom and 5G
* Monte Carlo Simulation

== '''Principles''' ==
[[File:Schematic of setup 2.png|thumb|300px|'''Figure 2. Schematic of setup''']]
Figure 2 schematically shows our setup. Such a setup is known as balanced homodyne detection and can extract the information of the electrical field in the second mode entering the polarizing beam-splitter (PBS) by measuring the photocurrent difference <math>i_1-i_2</math>. A continuous wave laser (wavelength 658 nm) is incident on one input port of the PBS and used as the local oscillator (LO), while another input port is empty. So the homodyne detection is trying to measure the vacuum state of the electromagnetic field. The randomness source in our setup is the fluctuations of the vacuum field. Here we tried to balance the optical power impinging on the two photodiodes, therefore any power fluctuation coming from the laser diode will be detected simultaneously and canceled in the photocurrent difference.

Alternatively, the randomness can be seen as coming from the shot noise of the photocurrents <math>i_1</math> and <math>i_2</math> with a power proportional to the average optical power. Since the shot noise currents from the diodes are uncorrelated, the noise adds up. And the amplitude fluctuations in the laser intensity (referred to as classical noise) can be eliminated by measuring the photocurrent difference.

== '''Setup''' ==
The practical setup was built with as few components as possible to create a baseline performance that we can compare. A schematic of the setup is shown in Figure 3.

[[File:Experimental setup.png|thumb|300px|'''Figure 3. Experimental setup''']]

==='''Tool list'''===
① Laser Diode
: Laser Diode is powered by a laser driving unit. The light intensity can be changed by changing the laser current.
② Focal Lens
: By adjusting the focal length, the intensity of light that finally hits the photodiodes is adjusted.
③ RP: Rotatable Polarizer
: The polarization state of the light is adjusted by rotating the polarizer.
④ Mirror 1
: By adjusting mirror 1, the position of transmitted and reflected light spots hitting on PD1 and PD2 can be adjusted simultaneously.
⑤ PBS: Polarizing Beam Splitter
: The laser beam incident on the PBS can pass through or be reflected depending on the polarization state. If the incident beam is diagonal polarized (45°), the intensity of reflected and transmitted light is equal.
⑥ Mirror 2
: By adjusting mirror 2, the position of transmitted light spots hitting on PD2 can be tuned.
⑦&⑧: Photodiodes
: Detect the intensity of incident light.

==='''Description'''===
The total light power is changed by changing the laser current and adjusting the focal lens, while the power of the two output ports of the PBS is balanced by rotating the polarizer in front of the laser diode. Light leaving the PBS is detected by a pair of reverse-biased photodiodes connected in series to perform the current subtraction. By adjusting the orientation of M1 and M2, the light intensity incident on PD1 and PD2 can be adjusted and balanced. The balancing of the photocurrents is monitored by observing the voltage drop across a resister <math>R_{DC}</math> (DC port). Here we use a multimeter to measure the voltage. The fluctuations <math>\Delta(i_1-i_2)</math>

==='''Characterization list'''===
① Oscilloscope

② Spectrum Analyzer

== '''Process''' ==
* '''26 February 2022:'''
* Did a basic characterization of photodiode
* Inputted a sine wave signal and a laser pointer light, observed the waveform of the photodiode
<gallery widths=300px heights=200px>
File:Basic characterization of photodiode test.jpeg|'''Figure 4. Basic characterization of photodiode'''
File:Schematic of basic characterization of photodiode test.png|'''Figure 5. Schematic of basic characterization of photodiode'''
</gallery>

:To understand the frequency response of the circuit shown in figure 5, we use a function generator to generate a sinusoidal signal to drive the LED, and use this circuit to measure the light output. When the frequency of the signal is low, we can see a relatively complete sine waveform on the oscilloscope. But when the frequency exceeds 1GHz, we could not observe a regular and stable waveform.
* '''5 March 2022:'''
* Used different resistors to test the frequency response of photodiode
<gallery widths=300px heights=200px>
File:Frequency of PD.png|'''Figure 6. Graph of the frequency response of photodiode'''
</gallery>
:We changed the resistors in Figure 6, from 1 kΩ to 11 kΩ and then 20 kΩ. We found that the higher the resistance of the resistor, the larger the output voltage but less sensitive to the high frequency. That is because a reverse-biased photodiode has a certain capacitance and forms an RC series circuit with the resistor. The larger the resistor, the larger the time constant <math>\tau=RC</math> of the RC circuit, and the slower the charge and discharge, which leads to a worse response to high frequency signals.
* '''12 March 2022:'''
* Build up the laser system and ensured the laser output
<gallery widths=300px heights=200px>
File:Laser diode.png|'''Figure 7. HL6501MG laser diode and schematic of internal circuit'''
File:Schematic of electronics laserconnector circuit.jpeg|'''Figure 8. Schematic of electronics laser connector circuit'''
File:Laser source setup.png|'''Figure 9. Laser source setup'''
</gallery>
:We used an HL6501MG laser diode, which is a 0.65 μm band AlGaInP laser diode (LD) with a multi-quantum well (MQW) structure. It is suitable as a light source for large-capacity optical disc memories and various other types of optical equipment. Hermetic sealing of the small package (φ=5.6 mm) assures high reliability.

:The Laser source consists of ① Laser diode; ② Thermostat; ③ Supply circuit for Laser diode and Thermostat; ④ Shell; ⑤ Focal lens; ⑥ Radiator. The Laser Diode is in the thermostat which is connected to the Radiator. We can set the temperature on the Laser power supply. The Thermostat and Radiator will keep the temperature of the laser diode as same as that set on the laser power supply. There is a focal lens in front of the laser diode. We can use it to change the focal length the enlarge the laser intensity hitting on the photodiodes. And a shell made of acrylic sheet and 4 balance posts.
* '''19 March 2022:'''
* Soldered photodiode driving circuit
* Test the feasibility
<gallery widths=300px heights=200px>
File:Photo diode outlines.png|'''Figure 10. S5972 Si PIN photodiode and schematic of internal circuit'''
File:Principle of photodiode driving circuit.png|'''Figure 11. Principle of photodiode driving circuit'''
File:Schematic photodiode driving circuit bolck.jpeg|'''Figure 12. Schematic photodiode driving circuit block'''
</gallery>

:We applied an S5972 high-speed Si PIN photodiode for detecting the light, it is designed for visible to near-infrared light detection. These photodiodes provide wideband characteristics at a low bias, making them suitable for optical communications and other high-speed photometry.

:We combined two photodiodes in the circuit and soldered them in the circuit chip as Figure 11 shows. After that, we tested its performance by the laser source, it was approved that the optical signal was converted into the electrical signal and was observed by oscilloscope.
* '''26 March 2022:'''
* Build up the whole system
* Tune the bias of two photodiodes
<gallery widths=300px heights=200px>
File:Whole setup.jpeg|'''Figure 13. The whole system setup'''
</gallery>
:We built up the whole setup on the optical platform. Then we tuned the bias of two photodiodes to make sure that the intensity of the laser hitting on both photodiodes is the same by adjusting the multimeter's voltage to around 0.
* '''2 April 2022:'''
* Focus the laser output
* Maximize the laser power output
* Characterize varaiation by varying optical power
<gallery widths=300px heights=200px>
File:Maximize the laser power output.jpeg|'''Figure 14. Maximize the laser power output'''
File:The detector noise power by varying the incident optical power.jpg|'''Figure 15. The plot of the detector noise power by varying the incident optical power'''
</gallery>
:We found that the laser output power in front of the polarizer was about 20 mW, but the power detected by each photodiode was only 0.4 mW. That is because the spot size of the laser was relatively large compared with the detection area of the photodiode. Therefore we needed to focus the lens in the laser block to maximize the detected laser power. To do this, we blocked one photodiode and used a multimeter to monitor the light power detected by another photodiode. After trials, we got a maximum value of voltage drop of 9.17 V, which corresponds to an optical power of 2.08 mW on each photodiode.

:Then, we characterized the change of noise level while rising incident optical power. And then we plotted a graph as shown in Figure 15, it is easy to find when the optical power is in a relatively low range, the noise level is flat which corresponds to the horizontal red line. While the optical power rises, the noise level increases with the optical power in a proportional manner. Therefore, we have enough reasons to believe that the overall noise is dominated by electronic noise in the low optical power range, while the noise level is dominated by shot noise in the high optical power range.
* '''9 April 2022:'''
* Soldered high pass filter
* Test its feasibility
<gallery widths=300px heights=200px>
File:Highpass filter principle circuit.png|'''Figure 16. Schematic of high pass filter circuit'''
File:Graph of theoretical high pass filter frequency response.jpg.png|'''Figure 17. Graph of theoretical high pass filter frequency response'''
File:Frequency of HPF.png|'''Figure 18. Graph of measured high pass filter frequency response'''
File:Schematic of high pass filter.jpeg|'''Figure 19. Setup of high pass filter'''
File:Setup of gain block and high pass filter.jpeg|'''Figure 20. Setup of gain block and high pass filter'''
</gallery>
:The measured total noise has a lot of low-frequency noise and is relatively flat power density in the range of 60-200 MHz. With a low pass filter of 200 MHz in the oscilloscope, we just needed a high pass filter of 60 MHz which compresses the low-frequency fluctuations. So we designed a high pass filter of 60 MHz and soldered the high pass filter.

:After that, we tested its performance. By comparing with the theoretical high pass filter graph, the measured high pass filter frequency response showed a high correspondence with it, which means it is feasible to apply it to the whole system to suppress the low-frequency fluctuations.
* '''16 April 2022:'''
* Apply the high pass filter to the circuit and test
* Record data and draw some graphs analysis
: In order to verify that the signals we obtained were quantum random numbers, we recorded the data at different sampling rates and performed autocorrelation calculations. These can be found in the "Result"-"Autocorrelation" part.

* '''23 April 2022:'''
* Processing experimental data
* Draw autocorrelation images
* Summarize and upload the experimental results

== '''Results''' ==
==='''Quantum noise'''===
*To ensure that the fluctuations at the amplifier output are dominated by quantum noise, the spectral power density is measured (in Figure 21. ).

[[File:Ampliﬁed noise levels measured into a resolution bandwidth B = 3 MHz..jpg|thumb|600px|center|'''Figure 21. Schematic of branching path quantum random number generators''']]

:Amplified noise levels measured into a resolution bandwidth B = 3 MHz. The total noise is measured from the photocurrent difference <math>i_1-i_2</math> with equal optical power impinging on both photodiodes. The current <math>i_1</math> of a single photodiode reveals colored classical noise. The electronic noise is measured without any optical input.
:In an alternative view, the laser beam can be seen as generating photocurrents <math>i_1</math> and <math>i_2</math> with a shot noise power proportional to the average optical power. The shot noise currents from the diodes add up as they are uncorrelated, while amplitude fluctuations in the laser intensity (referred to as classical noise) do not affect the photocurrent difference.

=== '''Autocorrelation'''===
*:Autocorrelation, sometimes known as serial correlation in the discrete-time case, is the correlation of a signal with a delayed copy of itself as a function of delay. Informally, it is the similarity between observations as a function of the time lag between them. In our experiment, if we obtain an ideal '''quantum random number generator''', the autocorrelation will be 1 when the time lag is 0, while the autocorrelation will be close to 0 when the time lag is not 0.

*:Given a signal <math>f(t)</math>, the continuous autocorrelation <math>R_{ff}(\tau)</math> is most often defined as the continuous cross-correlation integral of <math>f(t)</math> with itself, at lag <math>\tau</math>.

::::::::::::::::<math>R_{ff}(\tau) = \int_{-\infty}^\infty f(t+\tau)\overline{f(t)}\, {\rm d}t = \int_{-\infty}^\infty f(t) \overline{f(t-\tau)}\, {\rm d}t</math>

::where <math>\overline{f(t)}</math> represents the complex conjugate of <math>f(t)</math>. Note that the parameter <math>t</math> in the integral is a dummy variable and is only necessary to calculate the integral. It has no specific meaning.

*:'''Experimental result'''
:<gallery widths=500px heights=300px>
File:2.5 GHz (-20,20) After Highpass1.png|'''Figure 22. Autocorrelation of the total noise signal sampled at 2.5 GHz'''
File:500 kHz (-20,20) After Highpass1.png|'''Figure 23. Autocorrelation of the total noise signal sampled at 500 KHz'''
:</gallery>

:We recorded several sets of data with different sampling frequencies ( 2.5 GHz to 500 kHz) and obtained autocorrelation for each group. A very high correlation between any two adjacent points was observed when we use a 2.5 GHz sampling rate. This is simply because of an extremely high sampling rate which results in every two adjacent points being almost at the same position. We can get a better correlation by reducing the sampling frequency to such as 10 MHz or even lower.

:But the autocorrelation with a 500 kHz sampling rate is still not ideal. This is limited by our experimental setup. We caught up with too much electronic interference. A well-designed experimental setup with integrated photodiodes, amplifier, and high pass filter will stimulate a better result.

=== '''Histogram'''===
:<gallery widths=350px heights=200px>
File:Raw_data.png|'''Figure 24. '''
File:Contrast.png|'''Figure 25. '''
File:Extracted.png|'''Figure 26. '''
:</gallery>

== '''References''' ==
[1] Miguel Herrero-Collantes and Juan Carlos Garcia-Escartin, Quantum random number generators, Rev. Mod. Phys, 89, 015004.

[2] Shi, Yicheng, Brenda Chng, and Christian Kurtsiefer, Random numbers from vacuum fluctuations, Applied Physics Letters, 109.4 (2016): 041101.

[3] https://www.digchip.com/datasheets/parts/datasheet/625/HL6501MG-pdf.php

[4] https://www.farnell.com/datasheets/3171163.pdf

Quantum Random Number Generator

2022-04-27T05:33:46Z

Zhang Munan: /* Setup */

== '''Team Members''' ==
Wang Yang A0228753X

Xiao Yucan A0236278W

Zhang Munan A0236273E

== '''Idea''' ==
We live in an increasingly connected world, where a superior source of entropy is the key to data security. The effectiveness of any cryptographic system is determined by the strength of the keys it used. In turn, the strength of the key is determined by the degree of randomness used in its generation. Besides, large amount of random numbers are at the core of Monte Carlo simulations, which are widely used in scientific research. Methods produce random numbers from any algorithm are called pseudo-random number generator(PRNG). And random numbers generated by PRNG are deterministic by definition and therefore unsuitable for cryptographic purposes.

In order to generate unpredictable random numbers, hardware random number generators have been widely used. These physically generated random numbers are considered "truly" random because it is either practically or fundamentally impossible to predict the outcome of such a device. Quantum Random Number Generators (QRNGs) belong to a class of hardware random number generators and leverage the random properties of quantum physics to generate a true source of entropy, improving the quality of seed content for key generation.

Early QRNGs were based on radioactive decay. And more recently, QRNGs based on Poisson statistics of photons have been developed. The core idea is shown in the figure below. Single photons generated by a laser source are incident on a semi-transparent mirror and the mutually exclusive events (reflection/transmission) are detected and associated with ‘0’ or ‘1’ bit values respectively. The unpredictability of generated numbers is ensured by the quantum nature of the process. However, such a scheme needs a reliable single photon source as well as single photon detectors and it's not possible for our project. Here, we decided to build a QRNG based on measuring vacuum fluctuations of a light field as a random source. More details will be discussed in the principle part.
[[File:Principle schematic of QRNG.png|thumb|300px|'''Figure 1. Schematic of branching path quantum random number generators''']]

=== Benefits of having a quantum random number generator: ===
* The source of randomness is unpredictable and controlled by quantum process.
* Live/real-time monitoring of entropy source is possible and highly effective as well.
* All attacks on the entropy source are detectable.

=== Application of quantum random number generator:===
* Securing data at rest in data centres
* Securing any kind of sensitive data
* Securing data in the cloud
* One-time pad for authentication in banking and other transactions
* Gaming applications and lottery
* Block-chain network
* Numerical simulations, statistical research
* IoT devices
* E-commerce and banking applications
* Cryptographic applications
* Telecom and 5G
* Monte Carlo Simulation

== '''Principles''' ==
[[File:WeChat7f083c000c217b276a91e43dbb2e62cf.png|thumb|300px|'''Figure 2. Schematic of quantum random number generator based on measuring vacuum fluctuations''']]
Figure 2 schematically shows our setup. Such a setup is known as balanced homodyne detection and can extract the information of the electrical field in the second mode entering the polarizing beam-splitter (PBS) by measuring the photocurrent difference <math>i_1-i_2</math>. A continuous wave laser (wavelength 658 nm) is incident on one input port of the PBS and used as the local oscillator (LO), while another input port is empty. So the homodyne detection is trying to measure the vacuum state of the electromagnetic field. The randomness source in our setup is the fluctuations of the vacuum field. Here we tried to balance the optical power impinging on the two photodiodes, therefore any power fluctuation coming from the laser diode will be detected simultaneously and canceled in the photocurrent difference.

Alternatively, the randomness can be seen as coming from the shot noise of the photocurrents <math>i_1</math> and <math>i_2</math> with a power proportional to the average optical power. Since the shot noise currents from the diodes are uncorrelated, the noise adds up. And the amplitude fluctuations in the laser intensity (referred to as classical noise) can be eliminated by measuring the photocurrent difference.

== '''Setup''' ==
[[File:Schematic of setup 2.png|thumb|300px|'''Figure 3. Schematic of setup''']]
The original setup was built with as few components as possible to create a baseline performance that we can compare. A schematic of setup is shown in Figure 3.

[[File:Experimental setup.png|thumb|300px|'''Figure 4. Experimental setup''']]

==='''Tool list'''===
① Laser Diode
: Laser Diode is powered by a laser driving unit. The light intensity can be changed by changing the laser current.
② Focal Lens
: By adjusting the focal length, the intensity of light that finally hits the photodiodes is adjusted.
③ RP: Rotatable Polarizer
: The polarization state of the light is adjusted by rotating the polarizer.
④ Mirror 1
: By adjusting mirror 1, the position of transmitted and reflected light spots hitting on PD1 and PD2 can be adjusted simultaneously.
⑤ PBS: Polarizing Beam Splitter
: The laser beam incident on the PBS can pass through or be reflected depending on the polarization state. If the incident beam is diagonal polarized (45°), the intensity of reflected and transmitted light is equal.
⑥ Mirror 2
: By adjusting mirror 2, the position of transmitted light spots hitting on PD2 can be tuned.
⑦&⑧: Photodiodes
: Detect the intensity of incident light.

==='''Description'''===
The total light power is changed by changing the laser current and adjusting the focal lens, while the power of the two output ports of the PBS is balanced by rotating the polarizer in front of the laser diode. Light leaving the PBS is detected by a pair of reverse biased photodiodes connected in series to perform the current subtraction. By adjusting the orientation of M1 and M2, the light intensity incident on PD1 and PD2 can be adjusted and balanced. The balancing of the photocurrents is monitored by observing the voltage drop across a resister <math>R_{DC}</math> (DC port). Here we use a multimeter to measure the voltage. The fluctuations <math>\Delta(i_1-i_2)</math>

==='''Characterization list'''===
① Oscilloscope

② Spectrum Analyzer

== '''Process''' ==
* '''26 February 2022:'''
* Did a basic characterization of photodiode
* Inputted a sine wave signal and a laser pointer light, observed the waveform of the photodiode
<gallery widths=300px heights=200px>
File:Basic characterization of photodiode test.jpeg|'''Figure 5. Basic characterization of photodiode test'''
File:Schematic of basic characterization of photodiode test.png|'''Figure 6. Schematic of basic characterization of photodiode test'''
</gallery>
:To understand the optical response of the photodiode, we used a laser pointer to test its output waveform, because the laser is not periodic, so the waveform is not regular, but there are signals from the oscilloscope.

:Then we inputted a periodic sine signal to excite the laser diode to output laser incidents on the photodiode, and it showed a periodic sine signal with a very regular sine waveform. When the frequency increased over 1 GHz, we could not observe a regular and stable waveform.
* '''5 March 2022:'''
* Used different resistors to test the frequency response of photodiode
<gallery widths=300px heights=200px>
File:Graph of frequency response of photodiode.jpg|'''Figure 7. Graph of frequency response of photodiode'''
</gallery>
:We changed the resistors in Figure 6, from 1 kΩ to 11 kΩ and then 20 kΩ. We found that higher the resistance of the resistor higher the output voltage but less sensitive to the high frequency.
* '''12 March 2022:'''
* Build up the laser system and ensured the laser output
<gallery widths=300px heights=200px>
File:Laser diode.png|'''Figure 8. HL6501MG laser diode and schematic of internal circuit'''
File:Schematic of electronics laserconnector circuit.jpeg|'''Figure 9. Schematic of electronics laser connector circuit'''
File:Laser source setup.png|'''Figure 10. Laser source setup'''
</gallery>
:We used a HL6501MG laser diode, it is a 0.65 μm band AlGaInP laser diode (LD) with a multi-quantum well (MQW) structure. It is suitable as a light source for large-capacity optical disc memories and various other types of optical equipment. Hermetic sealing of the small package (φ=5.6 mm) assures high reliability.

:The Laser source consist of ① Laser diode; ② Thermostat; ③ Supply circuit for Laser diode and Thermostat; ④ Shell; ⑤ Focal lens; ⑥ Radiator. The Laser Diode is in the thermostat which is connected to the Radiator. We can set the temperature on the Laser power supply. The Thermostat and Radiator will keep the temperature of the laser diode as same as that set on the laser power supply. There is a focal lens in front of the laser diode. We can use it to change the focal length the enlarge the laser intensity hitting on the photo diodes. And a shell made of acrylic sheet and 4 balance posts.
* '''19 March 2022:'''
* Soldered photodiode driving circuit
* Test the feasibility
<gallery widths=300px heights=200px>
File:Photo diode outlines.png|'''Figure 11. S5972 Si PIN photodiode and schematic of internal circuit'''
File:Principle of photodiode driving circuit.png|'''Figure 12. Principle of photodiode driving circuit'''
File:Schematic photodiode driving circuit bolck.jpeg|'''Figure 13. Schematic photodiode driving circuit bolck'''
</gallery>

:We applied an S5972 high-speed Si PIN photodiode for detecting the light, it is designed for visible to near-infrared light detection. These photodiodes provide wideband characteristics at a low bias, making them suitable for optical communications and other high-speed photometry.

:We combined two photodiodes in the circuit and soldered them in the circuit chip as Figure 12 shows. After that, we tested its performance by the laser source, it was approved that the optical signal was converted into the electrical signal and was observed by oscilloscope.
* '''26 March 2022:'''
* Build up the whole system
* Tune the bias of two photodiodes
<gallery widths=300px heights=200px>
File:Whole setup.jpeg|'''Figure 14. The whole system setup'''
</gallery>
:We built up the whole setup on the optical platform. Then we tuned the bias of two photodiodes to make sure that the intensity of the laser hitting on both photodiodes is the same by adjusting the multimeter's voltage around 0.
* '''2 April 2022:'''
* Focus the laser output
* Maximize the laser power output
<gallery widths=300px heights=200px>
File:Maximize the laser power output.jpeg|'''Figure 15. Maximize the laser power output'''
</gallery>
:We found that the Laser power output in front of the RP is 20 mW. But the power detected by the photodiodes was only 0.4 mW. So, we needed to change the focal length of the focal lens to maximize the laser power output. We blocked one photodiode and the used the output voltage to calculate the output laser power.After lots of test, we get the maximum value of out put voltage, 9.17 V, which means 8.85 mW. Almost half of that detected before the RP.
* '''9 April 2022:'''
* Soldered high pass filter
* Test its feasibility
<gallery widths=300px heights=200px>
File:Highpass filter principle circuit.png|'''Figure 16. Schematic of high pass filter circuit'''
File:Graph of theoretical high pass filter frequency response.jpg.png|'''Figure 17. Graph of theoretical high pass filter frequency response'''
File:Graph of measured high pass filter frequency response.jpg|'''Figure 18. Graph of measured high pass filter frequency response'''
File:Schematic of high pass filter.jpeg|'''Figure 19. Setup of high pass filter'''
File:Setup of gain block and high pass filter.jpeg|'''Figure 20. Setup of gain block and high pass filter'''
</gallery>
:The measured total noise has a relatively flat power density in the range of 60-200 MHz. With a low pass filter of 200 MHz in the oscilloscope, we just needed a high pass filter of 60 MHz which compresses the low-frequency fluctuations. So we designed a high pass filter of 60 MHz and soldered the high pass filter.

:After that, we tested its performance. By comparing with the theoretical high pass filter graph, the measured high pass filter frequency response showed a high correspondence with it, which means it is feasible to apply it to the whole system to suppress the low-frequency fluctuations.
* '''16 April 2022:'''
* Apply the high pass filter to the circuit and test
* Record data and draw some graphs analysis
<gallery widths=300px heights=200px>
File:Autocorrelation of the total noise signal sampled at 2.5 GHz.jpeg|'''Figure 21. Autocorrelation of the total noise signal sampled at 2.5 GHz'''
File:Autocorrelation of the total noise signal sampled at 1.25 GHz 2.jpeg|'''Figure 22. Autocorrelation of the total noise signal sampled at 1.25 GHz'''
File:Autocorrelation of the total noise signal sampled at 500 MHz.jpeg|'''Figure 23. Autocorrelation of the total noise signal sampled at 500 MHz'''
File:Autocorrelation of the total noise signal sampled at 250 MHz.jpeg|'''Figure 24. Autocorrelation of the total noise signal sampled at 250 MHz'''
File:Autocorrelation of the total noise signal sampled at 100 MHz.jpeg|'''Figure 25. Autocorrelation of the total noise signal sampled at 100 MHz'''
File:Autocorrelation of the total noise signal sampled at 50 MHz.jpeg|'''Figure 26. Autocorrelation of the total noise signal sampled at 50 MHz'''
File:Autocorrelation of the total noise signal sampled at 25 MHz.jpeg|'''Figure 27. Autocorrelation of the total noise signal sampled at 25 MHz'''
File:Autocorrelation of the total noise signal sampled at 10 MHz.jpeg|'''Figure 28. Autocorrelation of the total noise signal sampled at 10 MHz'''
File:Autocorrelation of the total noise signal sampled at 5 MHz.jpeg|'''Figure 29. Autocorrelation of the total noise signal sampled at 5 MHz'''
</gallery>
'''Codes:'''(Example of autocorrelation graph at 2.5 GHz)

VarName2 = TrigTime;
[ACF,lags] = xcorr(VarName2);
plot(lags,ACF./max(ACF),'LineWidth',1);
xlim([-100,100]);
xlabel('Delay \itd','FontSize',25);
ylabel('Autocorrelation |\itA(d)|','FontSize',25);
title('Autocorrelation of the total noise signal sampled at 2.5 GHz','FontSize',25);
set(gca,'FontSize',25);
* '''23 April 2022:'''
* Processing experimental data
* Draw autocorrelation images
* Summarize and upload the experimental results

== '''Results and analysis''' ==

=== '''Results'''===

=== '''Analysis'''===

== '''References''' ==
[1] Miguel Herrero-Collantes and Juan Carlos Garcia-Escartin, Quantum random number generators, Rev. Mod. Phys, 89, 015004.

[2] Shi, Yicheng, Brenda Chng, and Christian Kurtsiefer, Random numbers from vacuum fluctuations, Applied Physics Letters, 109.4 (2016): 041101.

[3] https://www.digchip.com/datasheets/parts/datasheet/625/HL6501MG-pdf.php

[4] https://www.farnell.com/datasheets/3171163.pdf

Quantum Random Number Generator

2022-04-27T05:30:39Z

Zhang Munan: /* Setup */

== '''Team Members''' ==
Wang Yang A0228753X

Xiao Yucan A0236278W

Zhang Munan A0236273E

== '''Idea''' ==
We live in an increasingly connected world, where a superior source of entropy is the key to data security. The effectiveness of any cryptographic system is determined by the strength of the keys it used. In turn, the strength of the key is determined by the degree of randomness used in its generation. Besides, large amount of random numbers are at the core of Monte Carlo simulations, which are widely used in scientific research. Methods produce random numbers from any algorithm are called pseudo-random number generator(PRNG). And random numbers generated by PRNG are deterministic by definition and therefore unsuitable for cryptographic purposes.

In order to generate unpredictable random numbers, hardware random number generators have been widely used. These physically generated random numbers are considered "truly" random because it is either practically or fundamentally impossible to predict the outcome of such a device. Quantum Random Number Generators (QRNGs) belong to a class of hardware random number generators and leverage the random properties of quantum physics to generate a true source of entropy, improving the quality of seed content for key generation.

Early QRNGs were based on radioactive decay. And more recently, QRNGs based on Poisson statistics of photons have been developed. The core idea is shown in the figure below. Single photons generated by a laser source are incident on a semi-transparent mirror and the mutually exclusive events (reflection/transmission) are detected and associated with ‘0’ or ‘1’ bit values respectively. The unpredictability of generated numbers is ensured by the quantum nature of the process. However, such a scheme needs a reliable single photon source as well as single photon detectors and it's not possible for our project. Here, we decided to build a QRNG based on measuring vacuum fluctuations of a light field as a random source. More details will be discussed in the principle part.
[[File:Principle schematic of QRN.png|thumb|300px|'''Figure 1. Schematic of branching path quantum random number generators''']]

=== Benefits of having a quantum random number generator: ===
* The source of randomness is unpredictable and controlled by quantum process.
* Live/real-time monitoring of entropy source is possible and highly effective as well.
* All attacks on the entropy source are detectable.

=== Application of quantum random number generator:===
* Securing data at rest in data centres
* Securing any kind of sensitive data
* Securing data in the cloud
* One-time pad for authentication in banking and other transactions
* Gaming applications and lottery
* Block-chain network
* Numerical simulations, statistical research
* IoT devices
* E-commerce and banking applications
* Cryptographic applications
* Telecom and 5G
* Monte Carlo Simulation

== '''Principles''' ==
[[File:WeChat7f083c000c217b276a91e43dbb2e62cf.png|thumb|300px|'''Figure 2. Schematic of quantum random number generator based on measuring vacuum fluctuations''']]
Figure 2 schematically shows our setup. Such a setup is known as balanced homodyne detection and can extract the information of the electrical field in the second mode entering the polarizing beam-splitter (PBS) by measuring the photocurrent difference <math>i_1-i_2</math>. A continuous wave laser (wavelength 658 nm) is incident on one input port of the PBS and used as the local oscillator (LO), while another input port is empty. So the homodyne detection is trying to measure the vacuum state of the electromagnetic field. The randomness source in our setup is the fluctuations of the vacuum field. Here we tried to balance the optical power impinging on the two photodiodes, therefore any power fluctuation coming from the laser diode will be detected simultaneously and canceled in the photocurrent difference.

Alternatively, the randomness can be seen as coming from the shot noise of the photocurrents <math>i_1</math> and <math>i_2</math> with a power proportional to the average optical power. Since the shot noise currents from the diodes are uncorrelated, the noise adds up. And the amplitude fluctuations in the laser intensity (referred to as classical noise) can be eliminated by measuring the photocurrent difference.

== '''Setup''' ==
[[File:Schematic of setup 2.png|thumb|300px|'''Figure 3. Schematic of setup''']]
The original setup was built with as few components as possible to create a baseline performance that we can compare. A schematic of setup is shown in Figure 3.

[[File:Experimental setup.png|thumb|300px|'''Figure 4. Experimental setup''']]

==='''Tool list'''===
① Laser Diode
: Laser Diode is powered by a laser driving unit. The light intensity can be changed by changing the laser current.
② Focal Lens
: By adjusting the focal length, the intensity of light that finally hits the photodiodes is adjusted.
③ RP: Rotatable Polarizer
: The polarization state of the light is adjusted by rotating the polarizer.
④ Mirror 1
: By adjusting mirror 1, the position of transmitted and reflected light spots hitting on PD1 and PD2 can be adjusted simultaneously.
⑤ PBS: Polarizing Beam Splitter
: The laser beam incident on the PBS can pass through or be reflected depending on the polarization state. If the incident beam is diagonal polarized (<math>45/degree</math>), the intensity of reflected and transmitted light is equal.
⑥ Mirror 2
: By adjusting mirror 2, the position of transmitted light spots hitting on PD2 can be tuned.
⑦&⑧: Photodiodes
: Detect the intensity of incident light.

==='''Description'''===
The total light power is changed by changing the laser current and adjusting the focal lens, while the power of the two output ports of the PBS is balanced by rotating the polarizer in front of the laser diode. Light leaving the PBS is detected by a pair of reverse biased photodiodes connected in series to perform the current subtraction. By adjusting the orientation of M1 and M2, the light intensity incident on PD1 and PD2 can be adjusted and balanced. The balancing of the photocurrents is monitored by observing the voltage drop across a resister <math>R_DC</math> (DC port). Here we use a multimeter to measure the voltage. The fluctuations <<math>\Delta(i_1-i_2)</math>

==='''Characterization list'''===
① Oscilloscope

② Spectrum Analyzer

== '''Process''' ==
* '''26 February 2022:'''
* Did a basic characterization of photodiode
* Inputted a sine wave signal and a laser pointer light, observed the waveform of the photodiode
<gallery widths=300px heights=200px>
File:Basic characterization of photodiode test.jpeg|'''Figure 5. Basic characterization of photodiode test'''
File:Schematic of basic characterization of photodiode test.png|'''Figure 6. Schematic of basic characterization of photodiode test'''
</gallery>
:To understand the optical response of the photodiode, we used a laser pointer to test its output waveform, because the laser is not periodic, so the waveform is not regular, but there are signals from the oscilloscope.

:Then we inputted a periodic sine signal to excite the laser diode to output laser incidents on the photodiode, and it showed a periodic sine signal with a very regular sine waveform. When the frequency increased over 1 GHz, we could not observe a regular and stable waveform.
* '''5 March 2022:'''
* Used different resistors to test the frequency response of photodiode
<gallery widths=300px heights=200px>
File:Graph of frequency response of photodiode.jpg|'''Figure 7. Graph of frequency response of photodiode'''
</gallery>
:We changed the resistors in Figure 6, from 1 kΩ to 11 kΩ and then 20 kΩ. We found that higher the resistance of the resistor higher the output voltage but less sensitive to the high frequency.
* '''12 March 2022:'''
* Build up the laser system and ensured the laser output
<gallery widths=300px heights=200px>
File:Laser diode.png|'''Figure 8. HL6501MG laser diode and schematic of internal circuit'''
File:Schematic of electronics laserconnector circuit.jpeg|'''Figure 9. Schematic of electronics laser connector circuit'''
File:Laser source setup.png|'''Figure 10. Laser source setup'''
</gallery>
:We used a HL6501MG laser diode, it is a 0.65 μm band AlGaInP laser diode (LD) with a multi-quantum well (MQW) structure. It is suitable as a light source for large-capacity optical disc memories and various other types of optical equipment. Hermetic sealing of the small package (φ=5.6 mm) assures high reliability.

:The Laser source consist of ① Laser diode; ② Thermostat; ③ Supply circuit for Laser diode and Thermostat; ④ Shell; ⑤ Focal lens; ⑥ Radiator. The Laser Diode is in the thermostat which is connected to the Radiator. We can set the temperature on the Laser power supply. The Thermostat and Radiator will keep the temperature of the laser diode as same as that set on the laser power supply. There is a focal lens in front of the laser diode. We can use it to change the focal length the enlarge the laser intensity hitting on the photo diodes. And a shell made of acrylic sheet and 4 balance posts.
* '''19 March 2022:'''
* Soldered photodiode driving circuit
* Test the feasibility
<gallery widths=300px heights=200px>
File:Photo diode outlines.png|'''Figure 11. S5972 Si PIN photodiode and schematic of internal circuit'''
File:Principle of photodiode driving circuit.png|'''Figure 12. Principle of photodiode driving circuit'''
File:Schematic photodiode driving circuit bolck.jpeg|'''Figure 13. Schematic photodiode driving circuit bolck'''
</gallery>

:We applied an S5972 high-speed Si PIN photodiode for detecting the light, it is designed for visible to near-infrared light detection. These photodiodes provide wideband characteristics at a low bias, making them suitable for optical communications and other high-speed photometry.

:We combined two photodiodes in the circuit and soldered them in the circuit chip as Figure 12 shows. After that, we tested its performance by the laser source, it was approved that the optical signal was converted into the electrical signal and was observed by oscilloscope.
* '''26 March 2022:'''
* Build up the whole system
* Tune the bias of two photodiodes
<gallery widths=300px heights=200px>
File:Whole setup.jpeg|'''Figure 14. The whole system setup'''
</gallery>
:We built up the whole setup on the optical platform. Then we tuned the bias of two photodiodes to make sure that the intensity of the laser hitting on both photodiodes is the same by adjusting the multimeter's voltage around 0.
* '''2 April 2022:'''
* Focus the laser output
* Maximize the laser power output
<gallery widths=300px heights=200px>
File:Maximize the laser power output.jpeg|'''Figure 15. Maximize the laser power output'''
</gallery>
:We found that the Laser power output in front of the RP is 20 mW. But the power detected by the photodiodes was only 0.4 mW. So, we needed to change the focal length of the focal lens to maximize the laser power output. We blocked one photodiode and the used the output voltage to calculate the output laser power.After lots of test, we get the maximum value of out put voltage, 9.17 V, which means 8.85 mW. Almost half of that detected before the RP.
* '''9 April 2022:'''
* Soldered high pass filter
* Test its feasibility
<gallery widths=300px heights=200px>
File:Highpass filter principle circuit.png|'''Figure 16. Schematic of high pass filter circuit'''
File:Graph of theoretical high pass filter frequency response.jpg.png|'''Figure 17. Graph of theoretical high pass filter frequency response'''
File:Graph of measured high pass filter frequency response.jpg|'''Figure 18. Graph of measured high pass filter frequency response'''
File:Schematic of high pass filter.jpeg|'''Figure 19. Setup of high pass filter'''
File:Setup of gain block and high pass filter.jpeg|'''Figure 20. Setup of gain block and high pass filter'''
</gallery>
:The measured total noise has a relatively flat power density in the range of 60-200 MHz. With a low pass filter of 200 MHz in the oscilloscope, we just needed a high pass filter of 60 MHz which compresses the low-frequency fluctuations. So we designed a high pass filter of 60 MHz and soldered the high pass filter.

:After that, we tested its performance. By comparing with the theoretical high pass filter graph, the measured high pass filter frequency response showed a high correspondence with it, which means it is feasible to apply it to the whole system to suppress the low-frequency fluctuations.
* '''16 April 2022:'''
* Apply the high pass filter to the circuit and test
* Record data and draw some graphs analysis
<gallery widths=300px heights=200px>
File:Autocorrelation of the total noise signal sampled at 2.5 GHz.jpeg|'''Figure 21. Autocorrelation of the total noise signal sampled at 2.5 GHz'''
File:Autocorrelation of the total noise signal sampled at 1.25 GHz 2.jpeg|'''Figure 22. Autocorrelation of the total noise signal sampled at 1.25 GHz'''
File:Autocorrelation of the total noise signal sampled at 500 MHz.jpeg|'''Figure 23. Autocorrelation of the total noise signal sampled at 500 MHz'''
File:Autocorrelation of the total noise signal sampled at 250 MHz.jpeg|'''Figure 24. Autocorrelation of the total noise signal sampled at 250 MHz'''
File:Autocorrelation of the total noise signal sampled at 100 MHz.jpeg|'''Figure 25. Autocorrelation of the total noise signal sampled at 100 MHz'''
File:Autocorrelation of the total noise signal sampled at 50 MHz.jpeg|'''Figure 26. Autocorrelation of the total noise signal sampled at 50 MHz'''
File:Autocorrelation of the total noise signal sampled at 25 MHz.jpeg|'''Figure 27. Autocorrelation of the total noise signal sampled at 25 MHz'''
File:Autocorrelation of the total noise signal sampled at 10 MHz.jpeg|'''Figure 28. Autocorrelation of the total noise signal sampled at 10 MHz'''
File:Autocorrelation of the total noise signal sampled at 5 MHz.jpeg|'''Figure 29. Autocorrelation of the total noise signal sampled at 5 MHz'''
</gallery>
'''Codes:'''(Example of autocorrelation graph at 2.5 GHz)

VarName2 = TrigTime;
[ACF,lags] = xcorr(VarName2);
plot(lags,ACF./max(ACF),'LineWidth',1);
xlim([-100,100]);
xlabel('Delay \itd','FontSize',25);
ylabel('Autocorrelation |\itA(d)|','FontSize',25);
title('Autocorrelation of the total noise signal sampled at 2.5 GHz','FontSize',25);
set(gca,'FontSize',25);
* '''23 April 2022:'''
* Processing experimental data
* Draw autocorrelation images
* Summarize and upload the experimental results

== '''Results and analysis''' ==

=== '''Results'''===

=== '''Analysis'''===

== '''References''' ==
[1] Miguel Herrero-Collantes and Juan Carlos Garcia-Escartin, Quantum random number generators, Rev. Mod. Phys, 89, 015004.

[2] Shi, Yicheng, Brenda Chng, and Christian Kurtsiefer, Random numbers from vacuum fluctuations, Applied Physics Letters, 109.4 (2016): 041101.

[3] https://www.digchip.com/datasheets/parts/datasheet/625/HL6501MG-pdf.php

[4] https://www.farnell.com/datasheets/3171163.pdf

Quantum Random Number Generator

2022-04-27T05:28:14Z

Zhang Munan: /* Setup */

== '''Team Members''' ==
Wang Yang A0228753X

Xiao Yucan A0236278W

Zhang Munan A0236273E

== '''Idea''' ==
We live in an increasingly connected world, where a superior source of entropy is the key to data security. The effectiveness of any cryptographic system is determined by the strength of the keys it used. In turn, the strength of the key is determined by the degree of randomness used in its generation. Besides, large amount of random numbers are at the core of Monte Carlo simulations, which are widely used in scientific research. Methods produce random numbers from any algorithm are called pseudo-random number generator(PRNG). And random numbers generated by PRNG are deterministic by definition and therefore unsuitable for cryptographic purposes.

In order to generate unpredictable random numbers, hardware random number generators have been widely used. These physically generated random numbers are considered "truly" random because it is either practically or fundamentally impossible to predict the outcome of such a device. Quantum Random Number Generators (QRNGs) belong to a class of hardware random number generators and leverage the random properties of quantum physics to generate a true source of entropy, improving the quality of seed content for key generation.

Early QRNGs were based on radioactive decay. And more recently, QRNGs based on Poisson statistics of photons have been developed. The core idea is shown in the figure below. Single photons generated by a laser source are incident on a semi-transparent mirror and the mutually exclusive events (reflection/transmission) are detected and associated with ‘0’ or ‘1’ bit values respectively. The unpredictability of generated numbers is ensured by the quantum nature of the process. However, such a scheme needs a reliable single photon source as well as single photon detectors and it's not possible for our project. Here, we decided to build a QRNG based on measuring vacuum fluctuations of a light field as a random source. More details will be discussed in the principle part.
[[File:Principle schematic of QRNG.png|thumb|300px|'''Figure 1. Schematic of branching path quantum random number generators''']]

=== Benefits of having a quantum random number generator: ===
* The source of randomness is unpredictable and controlled by quantum process.
* Live/real-time monitoring of entropy source is possible and highly effective as well.
* All attacks on the entropy source are detectable.

=== Application of quantum random number generator:===
* Securing data at rest in data centres
* Securing any kind of sensitive data
* Securing data in the cloud
* One-time pad for authentication in banking and other transactions
* Gaming applications and lottery
* Block-chain network
* Numerical simulations, statistical research
* IoT devices
* E-commerce and banking applications
* Cryptographic applications
* Telecom and 5G
* Monte Carlo Simulation

== '''Principles''' ==
[[File:WeChat7f083c000c217b276a91e43dbb2e62cf.png|thumb|300px|'''Figure 2. Schematic of quantum random number generator based on measuring vacuum fluctuations''']]
Figure 2 schematically shows our setup. Such a setup is known as balanced homodyne detection and can extract the information of the electrical field in the second mode entering the polarizing beam-splitter (PBS) by measuring the photocurrent difference <math>i_1-i_2</math>. A continuous wave laser (wavelength 658 nm) is incident on one input port of the PBS and used as the local oscillator (LO), while another input port is empty. So the homodyne detection is trying to measure the vacuum state of the electromagnetic field. The randomness source in our setup is the fluctuations of the vacuum field. Here we tried to balance the optical power impinging on the two photodiodes, therefore any power fluctuation coming from the laser diode will be detected simultaneously and canceled in the photocurrent difference.

Alternatively, the randomness can be seen as coming from the shot noise of the photocurrents <math>i_1</math> and <math>i_2</math> with a power proportional to the average optical power. Since the shot noise currents from the diodes are uncorrelated, the noise adds up. And the amplitude fluctuations in the laser intensity (referred to as classical noise) can be eliminated by measuring the photocurrent difference.

== '''Setup''' ==
[[File:Schematic of setup 2.png|thumb|300px|'''Figure 3. Schematic of setup''']]
The original setup was built with as few components as possible to create a baseline performance that we can compare. A schematic of setup is shown in Figure 3.

[[File:Experimental setup.png|thumb|300px|'''Figure 4. Experimental setup''']]

==='''Tool list'''===
① Laser Diode
: Laser Diode is powered by a laser driving unit. The light intensity can be changed by changing the laser current.
② Focal Lens
: By adjusting the focal length, the intensity of light that finally hits the photodiodes is adjusted.
③ RP: Rotatable Polarizer
: The polarization state of the light is adjusted by rotating the polarizer.
④ Mirror 1
: By adjusting mirror 1, the position of transmitted and reflected light spots hitting on PD1 and PD2 can be adjusted simultaneously.
⑤ PBS: Polarizing Beam Splitter
: The laser beam incident on the PBS can pass through or be reflected depending on the polarization state. If the incident beam is diagonal polarized (<math>45\degree<math>), the intensity of reflected and transmitted light is equal.
⑥ Mirror 2
: By adjusting mirror 2, the position of transmitted light spots hitting on PD2 can be tuned.
⑦&⑧: Photodiodes
: Detect the intensity of incident light.

==='''Description'''===
The total light power is changed by changing the laser current and adjusting the focal lens, while the power of the two output ports of the PBS is balanced by rotating the polarizer in front of the laser diode. Light leaving the PBS is detected by a pair of reverse biased photodiodes connected in series to perform the current subtraction. By adjusting the orientation of M1 and M2, the light intensity incident on PD1 and PD2 can be adjusted and balanced. The balancing of the photocurrents is monitored by observing the voltage drop across a resister <math>R_DC<math> (DC port). Here we use a multimeter to measure the voltage. The fluctuations <math>\Delta(i_1-i_2)<math>

==='''Characterization list'''===
① Oscilloscope

② Spectrum Analyzer

== '''Process''' ==
* '''26 February 2022:'''
* Did a basic characterization of photodiode
* Inputted a sine wave signal and a laser pointer light, observed the waveform of the photodiode
<gallery widths=300px heights=200px>
File:Basic characterization of photodiode test.jpeg|'''Figure 5. Basic characterization of photodiode test'''
File:Schematic of basic characterization of photodiode test.png|'''Figure 6. Schematic of basic characterization of photodiode test'''
</gallery>
:To understand the optical response of the photodiode, we used a laser pointer to test its output waveform, because the laser is not periodic, so the waveform is not regular, but there are signals from the oscilloscope.

:Then we inputted a periodic sine signal to excite the laser diode to output laser incidents on the photodiode, and it showed a periodic sine signal with a very regular sine waveform. When the frequency increased over 1 GHz, we could not observe a regular and stable waveform.
* '''5 March 2022:'''
* Used different resistors to test the frequency response of photodiode
<gallery widths=300px heights=200px>
File:Graph of frequency response of photodiode.jpg|'''Figure 7. Graph of frequency response of photodiode'''
</gallery>
:We changed the resistors in Figure 6, from 1 kΩ to 11 kΩ and then 20 kΩ. We found that higher the resistance of the resistor higher the output voltage but less sensitive to the high frequency.
* '''12 March 2022:'''
* Build up the laser system and ensured the laser output
<gallery widths=300px heights=200px>
File:Laser diode.png|'''Figure 8. HL6501MG laser diode and schematic of internal circuit'''
File:Schematic of electronics laserconnector circuit.jpeg|'''Figure 9. Schematic of electronics laser connector circuit'''
File:Laser source setup.png|'''Figure 10. Laser source setup'''
</gallery>
:We used a HL6501MG laser diode, it is a 0.65 μm band AlGaInP laser diode (LD) with a multi-quantum well (MQW) structure. It is suitable as a light source for large-capacity optical disc memories and various other types of optical equipment. Hermetic sealing of the small package (φ=5.6 mm) assures high reliability.

:The Laser source consist of ① Laser diode; ② Thermostat; ③ Supply circuit for Laser diode and Thermostat; ④ Shell; ⑤ Focal lens; ⑥ Radiator. The Laser Diode is in the thermostat which is connected to the Radiator. We can set the temperature on the Laser power supply. The Thermostat and Radiator will keep the temperature of the laser diode as same as that set on the laser power supply. There is a focal lens in front of the laser diode. We can use it to change the focal length the enlarge the laser intensity hitting on the photo diodes. And a shell made of acrylic sheet and 4 balance posts.
* '''19 March 2022:'''
* Soldered photodiode driving circuit
* Test the feasibility
<gallery widths=300px heights=200px>
File:Photo diode outlines.png|'''Figure 11. S5972 Si PIN photodiode and schematic of internal circuit'''
File:Principle of photodiode driving circuit.png|'''Figure 12. Principle of photodiode driving circuit'''
File:Schematic photodiode driving circuit bolck.jpeg|'''Figure 13. Schematic photodiode driving circuit bolck'''
</gallery>

:We applied an S5972 high-speed Si PIN photodiode for detecting the light, it is designed for visible to near-infrared light detection. These photodiodes provide wideband characteristics at a low bias, making them suitable for optical communications and other high-speed photometry.

:We combined two photodiodes in the circuit and soldered them in the circuit chip as Figure 12 shows. After that, we tested its performance by the laser source, it was approved that the optical signal was converted into the electrical signal and was observed by oscilloscope.
* '''26 March 2022:'''
* Build up the whole system
* Tune the bias of two photodiodes
<gallery widths=300px heights=200px>
File:Whole setup.jpeg|'''Figure 14. The whole system setup'''
</gallery>
:We built up the whole setup on the optical platform. Then we tuned the bias of two photodiodes to make sure that the intensity of the laser hitting on both photodiodes is the same by adjusting the multimeter's voltage around 0.
* '''2 April 2022:'''
* Focus the laser output
* Maximize the laser power output
<gallery widths=300px heights=200px>
File:Maximize the laser power output.jpeg|'''Figure 15. Maximize the laser power output'''
</gallery>
:We found that the Laser power output in front of the RP is 20 mW. But the power detected by the photodiodes was only 0.4 mW. So, we needed to change the focal length of the focal lens to maximize the laser power output. We blocked one photodiode and the used the output voltage to calculate the output laser power.After lots of test, we get the maximum value of out put voltage, 9.17 V, which means 8.85 mW. Almost half of that detected before the RP.
* '''9 April 2022:'''
* Soldered high pass filter
* Test its feasibility
<gallery widths=300px heights=200px>
File:Highpass filter principle circuit.png|'''Figure 16. Schematic of high pass filter circuit'''
File:Graph of theoretical high pass filter frequency response.jpg.png|'''Figure 17. Graph of theoretical high pass filter frequency response'''
File:Graph of measured high pass filter frequency response.jpg|'''Figure 18. Graph of measured high pass filter frequency response'''
File:Schematic of high pass filter.jpeg|'''Figure 19. Setup of high pass filter'''
File:Setup of gain block and high pass filter.jpeg|'''Figure 20. Setup of gain block and high pass filter'''
</gallery>
:The measured total noise has a relatively flat power density in the range of 60-200 MHz. With a low pass filter of 200 MHz in the oscilloscope, we just needed a high pass filter of 60 MHz which compresses the low-frequency fluctuations. So we designed a high pass filter of 60 MHz and soldered the high pass filter.

:After that, we tested its performance. By comparing with the theoretical high pass filter graph, the measured high pass filter frequency response showed a high correspondence with it, which means it is feasible to apply it to the whole system to suppress the low-frequency fluctuations.
* '''16 April 2022:'''
* Apply the high pass filter to the circuit and test
* Record data and draw some graphs analysis
<gallery widths=300px heights=200px>
File:Autocorrelation of the total noise signal sampled at 2.5 GHz.jpeg|'''Figure 21. Autocorrelation of the total noise signal sampled at 2.5 GHz'''
File:Autocorrelation of the total noise signal sampled at 1.25 GHz 2.jpeg|'''Figure 22. Autocorrelation of the total noise signal sampled at 1.25 GHz'''
File:Autocorrelation of the total noise signal sampled at 500 MHz.jpeg|'''Figure 23. Autocorrelation of the total noise signal sampled at 500 MHz'''
File:Autocorrelation of the total noise signal sampled at 250 MHz.jpeg|'''Figure 24. Autocorrelation of the total noise signal sampled at 250 MHz'''
File:Autocorrelation of the total noise signal sampled at 100 MHz.jpeg|'''Figure 25. Autocorrelation of the total noise signal sampled at 100 MHz'''
File:Autocorrelation of the total noise signal sampled at 50 MHz.jpeg|'''Figure 26. Autocorrelation of the total noise signal sampled at 50 MHz'''
File:Autocorrelation of the total noise signal sampled at 25 MHz.jpeg|'''Figure 27. Autocorrelation of the total noise signal sampled at 25 MHz'''
File:Autocorrelation of the total noise signal sampled at 10 MHz.jpeg|'''Figure 28. Autocorrelation of the total noise signal sampled at 10 MHz'''
File:Autocorrelation of the total noise signal sampled at 5 MHz.jpeg|'''Figure 29. Autocorrelation of the total noise signal sampled at 5 MHz'''
</gallery>
'''Codes:'''(Example of autocorrelation graph at 2.5 GHz)

VarName2 = TrigTime;
[ACF,lags] = xcorr(VarName2);
plot(lags,ACF./max(ACF),'LineWidth',1);
xlim([-100,100]);
xlabel('Delay \itd','FontSize',25);
ylabel('Autocorrelation |\itA(d)|','FontSize',25);
title('Autocorrelation of the total noise signal sampled at 2.5 GHz','FontSize',25);
set(gca,'FontSize',25);
* '''23 April 2022:'''
* Processing experimental data
* Draw autocorrelation images
* Summarize and upload the experimental results

== '''Results and analysis''' ==

=== '''Results'''===

=== '''Analysis'''===

== '''References''' ==
[1] Miguel Herrero-Collantes and Juan Carlos Garcia-Escartin, Quantum random number generators, Rev. Mod. Phys, 89, 015004.

[2] Shi, Yicheng, Brenda Chng, and Christian Kurtsiefer, Random numbers from vacuum fluctuations, Applied Physics Letters, 109.4 (2016): 041101.

[3] https://www.digchip.com/datasheets/parts/datasheet/625/HL6501MG-pdf.php

[4] https://www.farnell.com/datasheets/3171163.pdf

Quantum Random Number Generator

2022-04-27T04:30:10Z

Zhang Munan: /* Setup */

Quantum Random Number Generator

2022-04-27T04:25:34Z

Zhang Munan: /* Principles */

Quantum Random Number Generator

2022-04-23T11:39:17Z

Zhang Munan: /* Principles */

Quantum Random Number Generator

2022-04-23T11:29:27Z

Zhang Munan: /* Principles */

Quantum Random Number Generator

2022-04-23T10:51:24Z

Zhang Munan: /* Principles */

== Team Members ==
Wang Yang A0228753X

Xiao Yucan A0236278W

Zhang Munan A0236273E

== Idea ==
We live in an increasingly connected world, where a superior source of entropy is the key to data security. The effectiveness of any cryptographic system is determined by the strength of the keys it used. In turn, the strength of the key is determined by the degree of randomness used in its generation. Besides, large amount of random numbers are at the core of Monte Carlo simulations, which are widely used in scientific research. Methods produce random numbers from any algorithm are called pseudo-random number generator(PRNG). And random numbers generated by PRNG are deterministic by definition and therefore unsuitable for cryptographic purposes.

In order to generate unpredictable random numbers, hardware random number generators have been widely used. These physically generated random numbers are considered "truly" random because it is either practically or fundamentally impossible to predict the outcome of such a device. Quantum Random Number Generators (QRNGs) belong to a class of hardware random number generators and leverage the random properties of quantum physics to generate a true source of entropy, improving the quality of seed content for key generation.

Early QRNGs were based on radioactive decay. And more recently, QRNGs based on Poisson statistics of photons have been developed. The core idea is shown in the figure below. Single photons generated by a laser source are incident on a semi-transparent mirror and the mutually exclusive events (reflection/transmission) are detected and associated with ‘0’ or ‘1’ bit values respectively. The unpredictability of generated numbers is ensured by the quantum nature of the process. However, such a scheme needs a reliable single photon source as well as single photon detectors and it's not possible for our project. Here, we decided to build a QRNG based on measuring vacuum fluctuations of a light field as a random source. More details will be discussed in the principle part.
[[File:Principle schematic of QRNG.png|thumb|300px|'''Figure 1. Schematic of branching path quantum random number generators''']]

* BENEFITS OF HAVING A QUANTUM RANDOM NUMBER GENERATOR:
** The source of randomness is unpredictable and controlled by quantum process.
** Live/real-time monitoring of entropy source is possible and highly effective as well.
** All attacks on the entropy source are detectable.

* APPLICATIONS OF QUANTUM RANDOM NUMBER GENERATOR:
** Securing data at rest in data centres
** Securing any kind of sensitive data
** Securing data in the cloud
** One-time pad for authentication in banking and other transactions
** Gaming applications and lottery
** Block-chain network
** Numerical simulations, statistical research
** IoT devices
** E-commerce and banking applications
** Cryptographic applications
** Telecom and 5G
** Monte Carlo Simulation

== Principles ==
[[File:WeChat7f083c000c217b276a91e43dbb2e62cf.png|thumb|300px|'''Figure 2. Schematic of quantum random number generator based on measuring vacuum fluctuations''']]

== '''Setup''' ==
[[File:Schematic of setup.png|thumb|300px|'''Schematic of setup''']]
The original setup was created with as few components as possible to create a baseline performance that we can compare to. A schematic and a Experimental setup of the setup is shown in the image '''on the right.'''

[[File:Experimental setup.png|thumb|300px|'''Experimental setup''']]

==='''Tool list'''===
====:① Laser Diode====
: Provide a light source, by changing the laser current can change the light intensity of the light source.
:② Focal Lens: By adjusting the focal length, the intensity of light that finally hits the photodiodes is adjusted.
:③ RP: rotatable Polarizer: The proportion of light intensity passing through PBS and reflected by PBS is controlled by adjusting RP.
:④ Mirror 1: By adjusting mirror 1, the falling points of the two Laser beams after passing through PBS and reflected by PBS can be adjusted simultaneously.
:⑤ PBS: Polarizer Beam Splitter: The laser beam incident to the PBS can pass through it or be reflected by it.
:⑥ Mirror 2: By adjusting mirror 1, the falling points of the laser beam after passing through PBS can be adjusted.
:⑦&⑧: Photodiodes: Detect the intensity of incident light

==='''Description'''===
:The laser beam comes from the laser diode. After passing through the focal lens and the rotatable Polarizer the laser beam incident to the mirror 1.Then the reflected laser beam incident to the Polarizer Beam splitter. The laser beam reflected by the PBS will incident to the PD1. The laser beam passing through the PBS will incident to the PD2.

==='''Characteristic list'''===
:Oscilloscope
:Frequency spectrograph

== Process ==
* '''26 February 2022:'''
* Did a basic characterization of photodiode
* Inputted a sine wave signal and a laser pointer light, observed the waveform of the photodiode
<gallery widths=300px heights=200px>
File:Basic characterization of photodiode test.jpeg|'''Basic characterization of photodiode test'''
File:Schematic of basic characterization of photodiode test.png|'''Schematic of basic characterization of photodiode test'''
</gallery>
:To understand the optical response of the photodiode, we used a laser pointer to test its output waveform, because the laser is not periodic, so the waveform is not regular, but there are signals from the oscilloscope.

:Then we inputted a periodic sine signal to excite the laser diode to output laser incidents on the photodiode, and it showed a periodic sine signal with a very regular sine waveform. When the frequency increased over 1 GHz, we could not observe a regular and stable waveform.
* '''5 March 2022:'''
* Used different resistors to test the frequency response of photodiode
<gallery widths=300px heights=200px>
File:Graph of frequency response of photodiode.jpg|'''Graph of frequency response of photodiode'''
</gallery>
:We changed the resistors in the Schematic of basic characterization of photodiode test, from 1kΩ to 11kΩ and then 20kΩ. We found that higher the resistance of the resistor higher the output voltage but less sensitive to the high frequency.
* '''12 March 2022:'''
* Build up the laser system and ensured the laser output
<gallery widths=300px heights=200px>
File:Laser diode.png|'''HL6501MG laser diode and schematic of internal circuit'''
File:Schematic of electronics laserconnector circuit.jpeg|'''Schematic of electronics laserconnector circuit'''
File:Laser source setup.png|'''Laser source setup'''
</gallery>
:We used a HL6501MG laser diode, it is a 0.65 μm band AlGaInP laser diode (LD) with a multi-quantum well (MQW) structure. It is suitable as a light source for large-capacity optical disc memories and various other types of optical equipment. Hermetic sealing of the small package (φ=5.6 mm) assures high reliability.

:The Laser source consist of ① Laser diode; ② Thermostat; ③ Supply circuit for Laser diode and Thermostat; ④ Shell; ⑤ Focal lens; ⑥ Radiator. The Laser Diode is in the thermostat which is connected to the Radiator. We can set temperature on the Laser power supply. The Thermostat and Radiator will keep the temperature of the laser diode as same as that set on the laser power supply. There is a focal lens in front of the laser diode. We can use it to change the focal length the enlarge the laser intensity hitting on the photo diodes. And a shell made of acrylic sheet and 4 balance post.
* '''19 March 2022:'''
* Soldered photodiode driving circuit
* Test the feasibility
<gallery widths=300px heights=200px>
File:Photo diode outlines.png|The S5972 is high-speed Si PIN photodiodes designed for visible to near-infrared light detection. These photodiodes provide wideband characteristics at a low bias, making them suitable for optical communications and other high-speed photometry.
File:Principle of photodiode driving circuit.png|'''Principle of photodiode driving circuit'''
File:Schematic photodiode driving circuit bolck.jpeg|'''Schematic photodiode driving circuit bolck'''
</gallery>
* '''26 March 2022:'''
* Build up the whole system
* Tune the bias of two photodiodes
* '''2 April 2022:'''
* Focus the laser output
* Maximize the laser power output
* '''9 April 2022:'''
* Soldered high pass filter
* Test its feasibility
<gallery widths=300px heights=200px>
File:Highpass filter principle circuit.png|'''Schematic of high pass filter circuit'''
File:Graph of theoretical high pass filter frequency response.jpg.png|'''Graph of theoretical high pass filter frequency response'''
File:Graph of measured high pass filter frequency response.jpg|'''Graph of measured high pass filter frequency response'''
File:Schematic of high pass filter.jpeg|'''Setup of high pass filter'''
File:Setup of gain block and high pass filter.jpeg|'''Setup of gain block and high pass filter'''
</gallery>
:The measured total noise has a relatively flat power density in the range of 60-200 MHz. With a low pass filter of 200 MHz in the oscilloscope, we just needed a high pass filter of 60 MHz which compresses the low-frequency fluctuations. So we designed a high pass filter of 60 MHz and soldered the high pass filter.

:After that, we tested its performance. By comparing with the theoretical high pass filter graph, the measured high pass filter frequency response showed a high correspondence with it, which means it is feasible to apply it to the whole system to suppress the low-frequency fluctuations.
* '''16 April 2022:'''
* Apply the high pass filter to the circuit
* Record data and draw some graphs
* '''23 April 2022:'''
* Processing experimental data
* Draw autocorrelation images
* Summarize and upload the experimental results

== Results and analysis ==

== Background reading ==
[1]Quantum random number generators, Miguel Herrero-Collantes and Juan Carlos Garcia-Escartin, Rev. Mod. Phys. 89, 015004.

Quantum Random Number Generator

2022-04-23T10:48:34Z

Zhang Munan: /* Principles */

== Team Members ==
Wang Yang A0228753X

Xiao Yucan A0236278W

Zhang Munan A0236273E

== Idea ==
We live in an increasingly connected world, where a superior source of entropy is the key to data security. The effectiveness of any cryptographic system is determined by the strength of the keys it used. In turn, the strength of the key is determined by the degree of randomness used in its generation. Besides, large amount of random numbers are at the core of Monte Carlo simulations, which are widely used in scientific research. Methods produce random numbers from any algorithm are called pseudo-random number generator(PRNG). And random numbers generated by PRNG are deterministic by definition and therefore unsuitable for cryptographic purposes.

In order to generate unpredictable random numbers, hardware random number generators have been widely used. These physically generated random numbers are considered "truly" random because it is either practically or fundamentally impossible to predict the outcome of such a device. Quantum Random Number Generators (QRNGs) belong to a class of hardware random number generators and leverage the random properties of quantum physics to generate a true source of entropy, improving the quality of seed content for key generation.

Early QRNGs were based on radioactive decay. And more recently, QRNGs based on Poisson statistics of photons have been developed. The core idea is shown in the figure below. Single photons generated by a laser source are incident on a semi-transparent mirror and the mutually exclusive events (reflection/transmission) are detected and associated with ‘0’ or ‘1’ bit values respectively. The unpredictability of generated numbers is ensured by the quantum nature of the process. However, such a scheme needs a reliable single photon source as well as single photon detectors and it's not possible for our project. Here, we decided to build a QRNG based on measuring vacuum fluctuations of a light field as a random source. More details will be discussed in the principle part.
[[File:Principle schematic of QRNG.png|thumb|300px|'''Schematic of branching path quantum random number generators''']]

* BENEFITS OF HAVING A QUANTUM RANDOM NUMBER GENERATOR:
** The source of randomness is unpredictable and controlled by quantum process.
** Live/real-time monitoring of entropy source is possible and highly effective as well.
** All attacks on the entropy source are detectable.

* APPLICATIONS OF QUANTUM RANDOM NUMBER GENERATOR:
** Securing data at rest in data centres
** Securing any kind of sensitive data
** Securing data in the cloud
** One-time pad for authentication in banking and other transactions
** Gaming applications and lottery
** Block-chain network
** Numerical simulations, statistical research
** IoT devices
** E-commerce and banking applications
** Cryptographic applications
** Telecom and 5G
** Monte Carlo Simulation

== Principles ==
[[File:WeChat7f083c000c217b276a91e43dbb2e62cf.png|thumb|300px|'''Schematic of quantum random number generator based on measuring vacuum fluctuations''']]
In cybersecurity, a perfect random number is the root of trust. A QRNG does not rely on mathematical algorithms but on laws of quantum physics to ‘naturally’ generate random numbers. A QRNG can produce unpredictable outcomes in a robust and well-controlled way. It includes the power of complex deep-tech technologies such as semiconductors, optoelectronics, high precision electronics, and quantum physics that work together to create the highest level of randomness possible.

QRNGs use random properties of quantum physics to generate a true source of entropy. This improves the quality of seed for key generation. Since the entropy sources are derived from fundamental models, all the properties and behaviors are understandable and provably secure.

A laser-based quantum source generates the randomness in Tropos quantum random number generator. A laser produces a stream of the elementary particle, photons. The photons generated from the laser are used to generate the random numbers. These photons unlike classical objects are unpredictable under certain situations. When incidenting on a semi-transparent mirror, the photon has a 50/50 chance of being reflected or transmitted. The photon is then in a superposition of both the states (reflected and transmitted), i.e. the photon exists in both the states simultaneously. Upon measurement, it collapses to one of these states, which is intrinsically random and there is no way to predict which state the photon will collapse. This gives the inherent randomness from the photons, which cannot be influenced by any external parameters. '''This process is illustrated in the right figure.'''

== Setup ==
[[File:Schematic of setup.png|thumb|300px|'''Schematic of setup''']]
The original setup was created with as few components as possible to create a baseline performance that we can compare to. A schematic and a Experimental setup of the setup is shown in the image '''on the right.'''

[[File:Experimental setup.png|thumb|300px|'''Experimental setup''']]

==='''Tool list'''===
:① Laser Diode: Provide a light source, by changing the laser current can change the light intensity of the light source.
:② Focal Lens: By adjusting the focal length, the intensity of light that finally hits the photodiodes is adjusted.
:③ RP: rotatable Polarizer: The proportion of light intensity passing through PBS and reflected by PBS is controlled by adjusting RP.
:④ Mirror 1: By adjusting mirror 1, the falling points of the two Laser beams after passing through PBS and reflected by PBS can be adjusted simultaneously.
:⑤ PBS: Polarizer Beam Splitter: The laser beam incident to the PBS can pass through it or be reflected by it.
:⑥ Mirror 2: By adjusting mirror 1, the falling points of the laser beam after passing through PBS can be adjusted.
:⑦&⑧: Photodiodes: Detect the intensity of incident light

==='''Description'''===
:The laser beam comes from the laser diode. After passing through the focal lens and the rotatable Polarizer the laser beam incident to the mirror 1.Then the reflected laser beam incident to the Polarizer Beam splitter. The laser beam reflected by the PBS will incident to the PD1. The laser beam passing through the PBS will incident to the PD2.

==='''Characteristic list'''===
:Oscilloscope
:Frequency spectrograph

== Process ==
* '''26 February 2022:'''
* Did a basic characterization of photodiode
* Inputted a sine wave signal and a laser pointer light, observed the waveform of the photodiode
<gallery widths=300px heights=200px>
File:Basic characterization of photodiode test.jpeg|'''Basic characterization of photodiode test'''
File:Schematic of basic characterization of photodiode test.png|'''Schematic of basic characterization of photodiode test'''
</gallery>
:To understand the optical response of the photodiode, we used a laser pointer to test its output waveform, because the laser is not periodic, so the waveform is not regular, but there are signals from the oscilloscope.

:Then we inputted a periodic sine signal to excite the laser diode to output laser incidents on the photodiode, and it showed a periodic sine signal with a very regular sine waveform. When the frequency increased over 1 GHz, we could not observe a regular and stable waveform.
* '''5 March 2022:'''
* Used different resistors to test the frequency response of photodiode
<gallery widths=300px heights=200px>
File:Graph of frequency response of photodiode.jpg|'''Graph of frequency response of photodiode'''
</gallery>
:We changed the resistors in the Schematic of basic characterization of photodiode test, from 1kΩ to 11kΩ and then 20kΩ. We found that higher the resistance of the resistor higher the output voltage but less sensitive to the high frequency.
* '''12 March 2022:'''
* Build up the laser system and ensured the laser output
<gallery widths=300px heights=200px>
File:Laser diode.png|'''HL6501MG laser diode and schematic of internal circuit'''
File:Schematic of electronics laserconnector circuit.jpeg|'''Schematic of electronics laserconnector circuit'''
File:Laser source setup.png|'''Laser source setup'''
</gallery>
:We used a HL6501MG laser diode, it is a 0.65 μm band AlGaInP laser diode (LD) with a multi-quantum well (MQW) structure. It is suitable as a light source for large-capacity optical disc memories and various other types of optical equipment. Hermetic sealing of the small package (φ=5.6 mm) assures high reliability.

:The Laser source consist of ① Laser diode; ② Thermostat; ③ Supply circuit for Laser diode and Thermostat; ④ Shell; ⑤ Focal lens; ⑥ Radiator. The Laser Diode is in the thermostat which is connected to the Radiator. We can set temperature on the Laser power supply. The Thermostat and Radiator will keep the temperature of the laser diode as same as that set on the laser power supply. There is a focal lens in front of the laser diode. We can use it to change the focal length the enlarge the laser intensity hitting on the photo diodes. And a shell made of acrylic sheet and 4 balance post.
* '''19 March 2022:'''
* Soldered photodiode driving circuit
* Test the feasibility
<gallery widths=300px heights=200px>
File:Photo diode outlines.png|The S5972 is high-speed Si PIN photodiodes designed for visible to near-infrared light detection. These photodiodes provide wideband characteristics at a low bias, making them suitable for optical communications and other high-speed photometry.
File:Principle of photodiode driving circuit.png|'''Principle of photodiode driving circuit'''
File:Schematic photodiode driving circuit bolck.jpeg|'''Schematic photodiode driving circuit bolck'''
</gallery>
* '''26 March 2022:'''
* Build up the whole system
* Tune the bias of two photodiodes
* '''2 April 2022:'''
* Focus the laser output
* Maximize the laser power output
* '''9 April 2022:'''
* Soldered high pass filter
* Test its feasibility
<gallery widths=300px heights=200px>
File:Highpass filter principle circuit.png|'''Schematic of high pass filter circuit'''
File:Graph of theoretical high pass filter frequency response.jpg.png|'''Graph of theoretical high pass filter frequency response'''
File:Graph of measured high pass filter frequency response.jpg|'''Graph of measured high pass filter frequency response'''
File:Schematic of high pass filter.jpeg|'''Setup of high pass filter'''
File:Setup of gain block and high pass filter.jpeg|'''Setup of gain block and high pass filter'''
</gallery>
:The measured total noise has a relatively flat power density in the range of 60-200 MHz. With a low pass filter of 200 MHz in the oscilloscope, we just needed a high pass filter of 60 MHz which compresses the low-frequency fluctuations. So we designed a high pass filter of 60 MHz and soldered the high pass filter.

:After that, we tested its performance. By comparing with the theoretical high pass filter graph, the measured high pass filter frequency response showed a high correspondence with it, which means it is feasible to apply it to the whole system to suppress the low-frequency fluctuations.
* '''16 April 2022:'''
* Apply the high pass filter to the circuit
* Record data and draw some graphs
* '''23 April 2022:'''
* Processing experimental data
* Draw autocorrelation images
* Summarize and upload the experimental results

== Results and analysis ==

== Background reading ==
[1]Quantum random number generators, Miguel Herrero-Collantes and Juan Carlos Garcia-Escartin, Rev. Mod. Phys. 89, 015004.

Quantum Random Number Generator

2022-04-23T10:45:26Z

Zhang Munan: /* Idea */

== Team Members ==
Wang Yang A0228753X

Xiao Yucan A0236278W

Zhang Munan A0236273E

== Idea ==
We live in an increasingly connected world, where a superior source of entropy is the key to data security. The effectiveness of any cryptographic system is determined by the strength of the keys it used. In turn, the strength of the key is determined by the degree of randomness used in its generation. Besides, large amount of random numbers are at the core of Monte Carlo simulations, which are widely used in scientific research. Methods produce random numbers from any algorithm are called pseudo-random number generator(PRNG). And random numbers generated by PRNG are deterministic by definition and therefore unsuitable for cryptographic purposes.

In order to generate unpredictable random numbers, hardware random number generators have been widely used. These physically generated random numbers are considered "truly" random because it is either practically or fundamentally impossible to predict the outcome of such a device. Quantum Random Number Generators (QRNGs) belong to a class of hardware random number generators and leverage the random properties of quantum physics to generate a true source of entropy, improving the quality of seed content for key generation.

Early QRNGs were based on radioactive decay. And more recently, QRNGs based on Poisson statistics of photons have been developed. The core idea is shown in the figure below. Single photons generated by a laser source are incident on a semi-transparent mirror and the mutually exclusive events (reflection/transmission) are detected and associated with ‘0’ or ‘1’ bit values respectively. The unpredictability of generated numbers is ensured by the quantum nature of the process. However, such a scheme needs a reliable single photon source as well as single photon detectors and it's not possible for our project. Here, we decided to build a QRNG based on measuring vacuum fluctuations of a light field as a random source. More details will be discussed in the principle part.
[[File:Principle schematic of QRNG.png|thumb|300px|'''Schematic of branching path quantum random number generators''']]

* BENEFITS OF HAVING A QUANTUM RANDOM NUMBER GENERATOR:
** The source of randomness is unpredictable and controlled by quantum process.
** Live/real-time monitoring of entropy source is possible and highly effective as well.
** All attacks on the entropy source are detectable.

* APPLICATIONS OF QUANTUM RANDOM NUMBER GENERATOR:
** Securing data at rest in data centres
** Securing any kind of sensitive data
** Securing data in the cloud
** One-time pad for authentication in banking and other transactions
** Gaming applications and lottery
** Block-chain network
** Numerical simulations, statistical research
** IoT devices
** E-commerce and banking applications
** Cryptographic applications
** Telecom and 5G
** Monte Carlo Simulation

== Principles ==
[[File:WeChat7f083c000c217b276a91e43dbb2e62cf.png|thumb|300px|'''Principle of photodiode driving circuit''']]
In cybersecurity, a perfect random number is the root of trust. A QRNG does not rely on mathematical algorithms but on laws of quantum physics to ‘naturally’ generate random numbers. A QRNG can produce unpredictable outcomes in a robust and well-controlled way. It includes the power of complex deep-tech technologies such as semiconductors, optoelectronics, high precision electronics, and quantum physics that work together to create the highest level of randomness possible.

QRNGs use random properties of quantum physics to generate a true source of entropy. This improves the quality of seed for key generation. Since the entropy sources are derived from fundamental models, all the properties and behaviors are understandable and provably secure.

A laser-based quantum source generates the randomness in Tropos quantum random number generator. A laser produces a stream of the elementary particle, photons. The photons generated from the laser are used to generate the random numbers. These photons unlike classical objects are unpredictable under certain situations. When incidenting on a semi-transparent mirror, the photon has a 50/50 chance of being reflected or transmitted. The photon is then in a superposition of both the states (reflected and transmitted), i.e. the photon exists in both the states simultaneously. Upon measurement, it collapses to one of these states, which is intrinsically random and there is no way to predict which state the photon will collapse. This gives the inherent randomness from the photons, which cannot be influenced by any external parameters. '''This process is illustrated in the right figure.'''

== Setup ==
[[File:Schematic of setup.png|thumb|300px|'''Schematic of setup''']]
The original setup was created with as few components as possible to create a baseline performance that we can compare to. A schematic and a Experimental setup of the setup is shown in the image '''on the right.'''

[[File:Experimental setup.png|thumb|300px|'''Experimental setup''']]

'''Tool list'''
:① Laser Diode: Provide a light source, by changing the laser current can change the light intensity of the light source.
:② Focal Lens: By adjusting the focal length, the intensity of light that finally hits the photodiodes is adjusted.
:③ RP: rotatable Polarizer: The proportion of light intensity passing through PBS and reflected by PBS is controlled by adjusting RP.
:④ Mirror 1: By adjusting mirror 1, the falling points of the two Laser beams after passing through PBS and reflected by PBS can be adjusted simultaneously.
:⑤ PBS: Polarizer Beam Splitter: The laser beam incident to the PBS can pass through it or be reflected by it.
:⑥ Mirror 2: By adjusting mirror 1, the falling points of the laser beam after passing through PBS can be adjusted.
:⑦&⑧: Photodiodes: Detect the intensity of incident light

'''Description'''
:The laser beam comes from the laser diode. After passing through the focal lens and the rotatable Polarizer the laser beam incident to the mirror 1.Then the reflected laser beam incident to the Polarizer Beam splitter. The laser beam reflected by the PBS will incident to the PD1. The laser beam passing through the PBS will incident to the PD2.

'''Characteristic list'''
:Oscilloscope
:Frequency spectrograph

== Gallery ==
* '''26 February 2022:'''
* Did a basic characterization of photodiode
* Inputted a sine wave signal and a laser pointer light, observed the waveform of the photodiode
<gallery widths=300px heights=200px>
File:Basic characterization of photodiode test.jpeg|'''Basic characterization of photodiode test'''
File:Schematic of basic characterization of photodiode test.png|'''Schematic of basic characterization of photodiode test'''
</gallery>
:To understand the optical response of the photodiode, we used a laser pointer to test its output waveform, because the laser is not periodic, so the waveform is not regular, but there are signals from the oscilloscope.

:Then we inputted a periodic sine signal to excite the laser diode to output laser incidents on the photodiode, and it showed a periodic sine signal with a very regular sine waveform. When the frequency increased over 1 GHz, we could not observe a regular and stable waveform.
* '''5 March 2022:'''
* Used different resistors to test the frequency response of photodiode
<gallery widths=300px heights=200px>
File:Graph of frequency response of photodiode.jpg|'''Graph of frequency response of photodiode'''
</gallery>
:We changed the resistors in the Schematic of basic characterization of photodiode test, from 1kΩ to 11kΩ and then 20kΩ. We found that higher the resistance of the resistor higher the output voltage but less sensitive to the high frequency.
* '''12 March 2022:'''
* Build up the laser system and ensured the laser output
<gallery widths=300px heights=200px>
File:Laser diode.png|'''HL6501MG laser diode and schematic of internal circuit'''
File:Schematic of electronics laserconnector circuit.jpeg|'''Schematic of electronics laserconnector circuit'''
File:Laser source setup.png|'''Laser source setup'''
</gallery>
:We used a HL6501MG laser diode, it is a 0.65 μm band AlGaInP laser diode (LD) with a multi-quantum well (MQW) structure. It is suitable as a light source for large-capacity optical disc memories and various other types of optical equipment. Hermetic sealing of the small package (φ=5.6 mm) assures high reliability.

:The Laser source consist of ① Laser diode; ② Thermostat; ③ Supply circuit for Laser diode and Thermostat; ④ Shell; ⑤ Focal lens; ⑥ Radiator. The Laser Diode is in the thermostat which is connected to the Radiator. We can set temperature on the Laser power supply. The Thermostat and Radiator will keep the temperature of the laser diode as same as that set on the laser power supply. There is a focal lens in front of the laser diode. We can use it to change the focal length the enlarge the laser intensity hitting on the photo diodes. And a shell made of acrylic sheet and 4 balance post.
* '''19 March 2022:'''
* Soldered photodiode driving circuit
* Test the feasibility
<gallery widths=300px heights=200px>
File:Photo diode outlines.png|The S5972 is high-speed Si PIN photodiodes designed for visible to near-infrared light detection. These photodiodes provide wideband characteristics at a low bias, making them suitable for optical communications and other high-speed photometry.
File:Principle of photodiode driving circuit.png|'''Principle of photodiode driving circuit'''
File:Schematic photodiode driving circuit bolck.jpeg|'''Schematic photodiode driving circuit bolck'''
</gallery>
* '''26 March 2022:'''
* Build up the whole system
* Tune the bias of two photodiodes
* '''2 April 2022:'''
* Focus the laser output
* Maximize the laser power output
* '''9 April 2022:'''
* Soldered high pass filter
* Test its feasibility
<gallery widths=300px heights=200px>
File:Highpass filter principle circuit.png|'''Schematic of high pass filter circuit'''
File:Graph of theoretical high pass filter frequency response.jpg.png|'''Graph of theoretical high pass filter frequency response'''
File:Graph of measured high pass filter frequency response.jpg|'''Graph of measured high pass filter frequency response'''
File:Schematic of high pass filter.jpeg|'''Setup of high pass filter'''
File:Setup of gain block and high pass filter.jpeg|'''Setup of gain block and high pass filter'''
</gallery>
:The measured total noise has a relatively flat power density in the range of 60-200 MHz. With a low pass filter of 200 MHz in the oscilloscope, we just needed a high pass filter of 60 MHz which compresses the low-frequency fluctuations. So we designed a high pass filter of 60 MHz and soldered the high pass filter.

:After that, we tested its performance. By comparing with the theoretical high pass filter graph, the measured high pass filter frequency response showed a high correspondence with it, which means it is feasible to apply it to the whole system to suppress the low-frequency fluctuations.
* '''16 April 2022:'''
* Apply the high pass filter to the circuit
* Record data and draw some graphs
* '''23 April 2022:'''
* Processing experimental data
* Draw autocorrelation images
* Summarize and upload the experimental results

== Results and analysis ==

== Background reading ==
[1]Quantum random number generators, Miguel Herrero-Collantes and Juan Carlos Garcia-Escartin, Rev. Mod. Phys. 89, 015004.

Quantum Random Number Generator

2022-04-23T10:44:47Z

Zhang Munan: /* Idea */

== Team Members ==
Wang Yang A0228753X

Xiao Yucan A0236278W

Zhang Munan A0236273E

== Idea ==
We live in an increasingly connected world, where a superior source of entropy is the key to data security. The effectiveness of any cryptographic system is determined by the strength of the keys it used. In turn, the strength of the key is determined by the degree of randomness used in its generation. Besides, large amount of random numbers are at the core of Monte Carlo simulations, which are widely used in scientific research. Methods produce random numbers from any algorithm are called pseudo-random number generator(PRNG). And random numbers generated by PRNG are deterministic by definition and therefore unsuitable for cryptographic purposes.

In order to generate unpredictable random numbers, hardware random number generators have been widely used. These physically generated random numbers are considered "truly" random because it is either practically or fundamentally impossible to predict the outcome of such a device. Quantum Random Number Generators (QRNGs) belong to a class of hardware random number generators and leverage the random properties of quantum physics to generate a true source of entropy, improving the quality of seed content for key generation.

Early QRNGs were based on radioactive decay. And more recently, QRNGs based on Poisson statistics of photons have been developed. The core idea is shown in the figure below. Single photons generated by a laser source are incident on a semi-transparent mirror and the mutually exclusive events (reflection/transmission) are detected and associated with ‘0’ or ‘1’ bit values respectively. The unpredictability of generated numbers is ensured by the quantum nature of the process. However, such a scheme needs a reliable single photon source as well as single photon detectors and it's not possible for our project. Here, we decided to build a QRNG based on measuring vacuum fluctuations of a light field as a random source. More details will be discussed in the principle part.
[[File:Principle schematic of QRNG.png|thumb|300px|'''Schematic of branching path quantum random number generators''']]

* BENEFITS OF HAVING A QUANTUM RANDOM NUMBER GENERATOR:
** The source of randomness is unpredictable and controlled by quantum process.
** Live/real-time monitoring of entropy source is possible and highly effective as well.
** All attacks on the entropy source are detectable.
The above factors indicate that our QRNG is provably secure.

* APPLICATIONS OF QUANTUM RANDOM NUMBER GENERATOR:
** Securing data at rest in data centres
** Securing any kind of sensitive data
** Securing data in the cloud
** One-time pad for authentication in banking and other transactions
** Gaming applications and lottery
** Block-chain network
** Numerical simulations, statistical research
** IoT devices
** E-commerce and banking applications
** Cryptographic applications
** Telecom and 5G
** Monte Carlo Simulation

In today’s Y2Q world, developers have to rely on the source of entropy as quantum-enabled security keys are set to become the new normal. Organisations should, therefore, implement QRNG to protect their customers’ data.

== Principles ==
[[File:WeChat7f083c000c217b276a91e43dbb2e62cf.png|thumb|300px|'''Principle of photodiode driving circuit''']]
In cybersecurity, a perfect random number is the root of trust. A QRNG does not rely on mathematical algorithms but on laws of quantum physics to ‘naturally’ generate random numbers. A QRNG can produce unpredictable outcomes in a robust and well-controlled way. It includes the power of complex deep-tech technologies such as semiconductors, optoelectronics, high precision electronics, and quantum physics that work together to create the highest level of randomness possible.

QRNGs use random properties of quantum physics to generate a true source of entropy. This improves the quality of seed for key generation. Since the entropy sources are derived from fundamental models, all the properties and behaviors are understandable and provably secure.

A laser-based quantum source generates the randomness in Tropos quantum random number generator. A laser produces a stream of the elementary particle, photons. The photons generated from the laser are used to generate the random numbers. These photons unlike classical objects are unpredictable under certain situations. When incidenting on a semi-transparent mirror, the photon has a 50/50 chance of being reflected or transmitted. The photon is then in a superposition of both the states (reflected and transmitted), i.e. the photon exists in both the states simultaneously. Upon measurement, it collapses to one of these states, which is intrinsically random and there is no way to predict which state the photon will collapse. This gives the inherent randomness from the photons, which cannot be influenced by any external parameters. '''This process is illustrated in the right figure.'''

== Setup ==
[[File:Schematic of setup.png|thumb|300px|'''Schematic of setup''']]
The original setup was created with as few components as possible to create a baseline performance that we can compare to. A schematic and a Experimental setup of the setup is shown in the image '''on the right.'''

[[File:Experimental setup.png|thumb|300px|'''Experimental setup''']]

'''Tool list'''
:① Laser Diode: Provide a light source, by changing the laser current can change the light intensity of the light source.
:② Focal Lens: By adjusting the focal length, the intensity of light that finally hits the photodiodes is adjusted.
:③ RP: rotatable Polarizer: The proportion of light intensity passing through PBS and reflected by PBS is controlled by adjusting RP.
:④ Mirror 1: By adjusting mirror 1, the falling points of the two Laser beams after passing through PBS and reflected by PBS can be adjusted simultaneously.
:⑤ PBS: Polarizer Beam Splitter: The laser beam incident to the PBS can pass through it or be reflected by it.
:⑥ Mirror 2: By adjusting mirror 1, the falling points of the laser beam after passing through PBS can be adjusted.
:⑦&⑧: Photodiodes: Detect the intensity of incident light

'''Description'''
:The laser beam comes from the laser diode. After passing through the focal lens and the rotatable Polarizer the laser beam incident to the mirror 1.Then the reflected laser beam incident to the Polarizer Beam splitter. The laser beam reflected by the PBS will incident to the PD1. The laser beam passing through the PBS will incident to the PD2.

'''Characteristic list'''
:Oscilloscope
:Frequency spectrograph

== Gallery ==
* '''26 February 2022:'''
* Did a basic characterization of photodiode
* Inputted a sine wave signal and a laser pointer light, observed the waveform of the photodiode
<gallery widths=300px heights=200px>
File:Basic characterization of photodiode test.jpeg|'''Basic characterization of photodiode test'''
File:Schematic of basic characterization of photodiode test.png|'''Schematic of basic characterization of photodiode test'''
</gallery>
:To understand the optical response of the photodiode, we used a laser pointer to test its output waveform, because the laser is not periodic, so the waveform is not regular, but there are signals from the oscilloscope.

:Then we inputted a periodic sine signal to excite the laser diode to output laser incidents on the photodiode, and it showed a periodic sine signal with a very regular sine waveform. When the frequency increased over 1 GHz, we could not observe a regular and stable waveform.
* '''5 March 2022:'''
* Used different resistors to test the frequency response of photodiode
<gallery widths=300px heights=200px>
File:Graph of frequency response of photodiode.jpg|'''Graph of frequency response of photodiode'''
</gallery>
:We changed the resistors in the Schematic of basic characterization of photodiode test, from 1kΩ to 11kΩ and then 20kΩ. We found that higher the resistance of the resistor higher the output voltage but less sensitive to the high frequency.
* '''12 March 2022:'''
* Build up the laser system and ensured the laser output
<gallery widths=300px heights=200px>
File:Laser diode.png|'''HL6501MG laser diode and schematic of internal circuit'''
File:Schematic of electronics laserconnector circuit.jpeg|'''Schematic of electronics laserconnector circuit'''
File:Laser source setup.png|'''Laser source setup'''
</gallery>
:We used a HL6501MG laser diode, it is a 0.65 μm band AlGaInP laser diode (LD) with a multi-quantum well (MQW) structure. It is suitable as a light source for large-capacity optical disc memories and various other types of optical equipment. Hermetic sealing of the small package (φ=5.6 mm) assures high reliability.

:The Laser source consist of ① Laser diode; ② Thermostat; ③ Supply circuit for Laser diode and Thermostat; ④ Shell; ⑤ Focal lens; ⑥ Radiator. The Laser Diode is in the thermostat which is connected to the Radiator. We can set temperature on the Laser power supply. The Thermostat and Radiator will keep the temperature of the laser diode as same as that set on the laser power supply. There is a focal lens in front of the laser diode. We can use it to change the focal length the enlarge the laser intensity hitting on the photo diodes. And a shell made of acrylic sheet and 4 balance post.
* '''19 March 2022:'''
* Soldered photodiode driving circuit
* Test the feasibility
<gallery widths=300px heights=200px>
File:Photo diode outlines.png|The S5972 is high-speed Si PIN photodiodes designed for visible to near-infrared light detection. These photodiodes provide wideband characteristics at a low bias, making them suitable for optical communications and other high-speed photometry.
File:Principle of photodiode driving circuit.png|'''Principle of photodiode driving circuit'''
File:Schematic photodiode driving circuit bolck.jpeg|'''Schematic photodiode driving circuit bolck'''
</gallery>
* '''26 March 2022:'''
* Build up the whole system
* Tune the bias of two photodiodes
* '''2 April 2022:'''
* Focus the laser output
* Maximize the laser power output
* '''9 April 2022:'''
* Soldered high pass filter
* Test its feasibility
<gallery widths=300px heights=200px>
File:Highpass filter principle circuit.png|'''Schematic of high pass filter circuit'''
File:Graph of theoretical high pass filter frequency response.jpg.png|'''Graph of theoretical high pass filter frequency response'''
File:Graph of measured high pass filter frequency response.jpg|'''Graph of measured high pass filter frequency response'''
File:Schematic of high pass filter.jpeg|'''Setup of high pass filter'''
File:Setup of gain block and high pass filter.jpeg|'''Setup of gain block and high pass filter'''
</gallery>
:The measured total noise has a relatively flat power density in the range of 60-200 MHz. With a low pass filter of 200 MHz in the oscilloscope, we just needed a high pass filter of 60 MHz which compresses the low-frequency fluctuations. So we designed a high pass filter of 60 MHz and soldered the high pass filter.

:After that, we tested its performance. By comparing with the theoretical high pass filter graph, the measured high pass filter frequency response showed a high correspondence with it, which means it is feasible to apply it to the whole system to suppress the low-frequency fluctuations.
* '''16 April 2022:'''
* Apply the high pass filter to the circuit
* Record data and draw some graphs
* '''23 April 2022:'''
* Processing experimental data
* Draw autocorrelation images
* Summarize and upload the experimental results

== Results and analysis ==

== Background reading ==
[1]Quantum random number generators, Miguel Herrero-Collantes and Juan Carlos Garcia-Escartin, Rev. Mod. Phys. 89, 015004.

Quantum Random Number Generator

2022-04-23T10:44:31Z

Zhang Munan: /* Idea */

== Team Members ==
Wang Yang A0228753X

Xiao Yucan A0236278W

Zhang Munan A0236273E

== Idea ==
We live in an increasingly connected world, where a superior source of entropy is the key to data security. The effectiveness of any cryptographic system is determined by the strength of the keys it used. In turn, the strength of the key is determined by the degree of randomness used in its generation. Besides, large amount of random numbers are at the core of Monte Carlo simulations, which are widely used in scientific research. Methods produce random numbers from any algorithm are called pseudo-random number generator(PRNG). And random numbers generated by PRNG are deterministic by definition and therefore unsuitable for cryptographic purposes.

In order to generate unpredictable random numbers, hardware random number generators have been widely used. These physically generated random numbers are considered "truly" random because it is either practically or fundamentally impossible to predict the outcome of such a device. Quantum Random Number Generators (QRNGs) belong to a class of hardware random number generators and leverage the random properties of quantum physics to generate a true source of entropy, improving the quality of seed content for key generation.

Early QRNGs were based on radioactive decay. And more recently, QRNGs based on Poisson statistics of photons have been developed. The core idea is shown in the figure below. Single photons generated by a laser source are incident on a semi-transparent mirror and the mutually exclusive events (reflection/transmission) are detected and associated with ‘0’ or ‘1’ bit values respectively. The unpredictability of generated numbers is ensured by the quantum nature of the process. However, such a scheme needs a reliable single photon source as well as single photon detectors and it's not possible for our project. Here, we decided to build a QRNG based on measuring vacuum fluctuations of a light field as a random source. More details will be discussed in the principle part.
[[File:Principle schematic of QRNG.png|thumb|300px|'''Schematic of branching path quantum random number generators''']]

* BENEFITS OF HAVING A QUANTUM RANDOM NUMBER GENERATOR:
** The source of randomness is unpredictable and controlled by quantum process.
** Live/real-time monitoring of entropy source is possible and highly effective as well.
** All attacks on the entropy source are detectable.
** The above factors indicate that our QRNG is provably secure.

* APPLICATIONS OF QUANTUM RANDOM NUMBER GENERATOR:
** Securing data at rest in data centres
** Securing any kind of sensitive data
** Securing data in the cloud
** One-time pad for authentication in banking and other transactions
** Gaming applications and lottery
** Block-chain network
** Numerical simulations, statistical research
** IoT devices
** E-commerce and banking applications
** Cryptographic applications
** Telecom and 5G
** Monte Carlo Simulation

In today’s Y2Q world, developers have to rely on the source of entropy as quantum-enabled security keys are set to become the new normal. Organisations should, therefore, implement QRNG to protect their customers’ data.

== Principles ==
[[File:WeChat7f083c000c217b276a91e43dbb2e62cf.png|thumb|300px|'''Principle of photodiode driving circuit''']]
In cybersecurity, a perfect random number is the root of trust. A QRNG does not rely on mathematical algorithms but on laws of quantum physics to ‘naturally’ generate random numbers. A QRNG can produce unpredictable outcomes in a robust and well-controlled way. It includes the power of complex deep-tech technologies such as semiconductors, optoelectronics, high precision electronics, and quantum physics that work together to create the highest level of randomness possible.

QRNGs use random properties of quantum physics to generate a true source of entropy. This improves the quality of seed for key generation. Since the entropy sources are derived from fundamental models, all the properties and behaviors are understandable and provably secure.

A laser-based quantum source generates the randomness in Tropos quantum random number generator. A laser produces a stream of the elementary particle, photons. The photons generated from the laser are used to generate the random numbers. These photons unlike classical objects are unpredictable under certain situations. When incidenting on a semi-transparent mirror, the photon has a 50/50 chance of being reflected or transmitted. The photon is then in a superposition of both the states (reflected and transmitted), i.e. the photon exists in both the states simultaneously. Upon measurement, it collapses to one of these states, which is intrinsically random and there is no way to predict which state the photon will collapse. This gives the inherent randomness from the photons, which cannot be influenced by any external parameters. '''This process is illustrated in the right figure.'''

== Setup ==
[[File:Schematic of setup.png|thumb|300px|'''Schematic of setup''']]
The original setup was created with as few components as possible to create a baseline performance that we can compare to. A schematic and a Experimental setup of the setup is shown in the image '''on the right.'''

[[File:Experimental setup.png|thumb|300px|'''Experimental setup''']]

'''Tool list'''
:① Laser Diode: Provide a light source, by changing the laser current can change the light intensity of the light source.
:② Focal Lens: By adjusting the focal length, the intensity of light that finally hits the photodiodes is adjusted.
:③ RP: rotatable Polarizer: The proportion of light intensity passing through PBS and reflected by PBS is controlled by adjusting RP.
:④ Mirror 1: By adjusting mirror 1, the falling points of the two Laser beams after passing through PBS and reflected by PBS can be adjusted simultaneously.
:⑤ PBS: Polarizer Beam Splitter: The laser beam incident to the PBS can pass through it or be reflected by it.
:⑥ Mirror 2: By adjusting mirror 1, the falling points of the laser beam after passing through PBS can be adjusted.
:⑦&⑧: Photodiodes: Detect the intensity of incident light

'''Description'''
:The laser beam comes from the laser diode. After passing through the focal lens and the rotatable Polarizer the laser beam incident to the mirror 1.Then the reflected laser beam incident to the Polarizer Beam splitter. The laser beam reflected by the PBS will incident to the PD1. The laser beam passing through the PBS will incident to the PD2.

'''Characteristic list'''
:Oscilloscope
:Frequency spectrograph

== Gallery ==
* '''26 February 2022:'''
* Did a basic characterization of photodiode
* Inputted a sine wave signal and a laser pointer light, observed the waveform of the photodiode
<gallery widths=300px heights=200px>
File:Basic characterization of photodiode test.jpeg|'''Basic characterization of photodiode test'''
File:Schematic of basic characterization of photodiode test.png|'''Schematic of basic characterization of photodiode test'''
</gallery>
:To understand the optical response of the photodiode, we used a laser pointer to test its output waveform, because the laser is not periodic, so the waveform is not regular, but there are signals from the oscilloscope.

:Then we inputted a periodic sine signal to excite the laser diode to output laser incidents on the photodiode, and it showed a periodic sine signal with a very regular sine waveform. When the frequency increased over 1 GHz, we could not observe a regular and stable waveform.
* '''5 March 2022:'''
* Used different resistors to test the frequency response of photodiode
<gallery widths=300px heights=200px>
File:Graph of frequency response of photodiode.jpg|'''Graph of frequency response of photodiode'''
</gallery>
:We changed the resistors in the Schematic of basic characterization of photodiode test, from 1kΩ to 11kΩ and then 20kΩ. We found that higher the resistance of the resistor higher the output voltage but less sensitive to the high frequency.
* '''12 March 2022:'''
* Build up the laser system and ensured the laser output
<gallery widths=300px heights=200px>
File:Laser diode.png|'''HL6501MG laser diode and schematic of internal circuit'''
File:Schematic of electronics laserconnector circuit.jpeg|'''Schematic of electronics laserconnector circuit'''
File:Laser source setup.png|'''Laser source setup'''
</gallery>
:We used a HL6501MG laser diode, it is a 0.65 μm band AlGaInP laser diode (LD) with a multi-quantum well (MQW) structure. It is suitable as a light source for large-capacity optical disc memories and various other types of optical equipment. Hermetic sealing of the small package (φ=5.6 mm) assures high reliability.

:The Laser source consist of ① Laser diode; ② Thermostat; ③ Supply circuit for Laser diode and Thermostat; ④ Shell; ⑤ Focal lens; ⑥ Radiator. The Laser Diode is in the thermostat which is connected to the Radiator. We can set temperature on the Laser power supply. The Thermostat and Radiator will keep the temperature of the laser diode as same as that set on the laser power supply. There is a focal lens in front of the laser diode. We can use it to change the focal length the enlarge the laser intensity hitting on the photo diodes. And a shell made of acrylic sheet and 4 balance post.
* '''19 March 2022:'''
* Soldered photodiode driving circuit
* Test the feasibility
<gallery widths=300px heights=200px>
File:Photo diode outlines.png|The S5972 is high-speed Si PIN photodiodes designed for visible to near-infrared light detection. These photodiodes provide wideband characteristics at a low bias, making them suitable for optical communications and other high-speed photometry.
File:Principle of photodiode driving circuit.png|'''Principle of photodiode driving circuit'''
File:Schematic photodiode driving circuit bolck.jpeg|'''Schematic photodiode driving circuit bolck'''
</gallery>
* '''26 March 2022:'''
* Build up the whole system
* Tune the bias of two photodiodes
* '''2 April 2022:'''
* Focus the laser output
* Maximize the laser power output
* '''9 April 2022:'''
* Soldered high pass filter
* Test its feasibility
<gallery widths=300px heights=200px>
File:Highpass filter principle circuit.png|'''Schematic of high pass filter circuit'''
File:Graph of theoretical high pass filter frequency response.jpg.png|'''Graph of theoretical high pass filter frequency response'''
File:Graph of measured high pass filter frequency response.jpg|'''Graph of measured high pass filter frequency response'''
File:Schematic of high pass filter.jpeg|'''Setup of high pass filter'''
File:Setup of gain block and high pass filter.jpeg|'''Setup of gain block and high pass filter'''
</gallery>
:The measured total noise has a relatively flat power density in the range of 60-200 MHz. With a low pass filter of 200 MHz in the oscilloscope, we just needed a high pass filter of 60 MHz which compresses the low-frequency fluctuations. So we designed a high pass filter of 60 MHz and soldered the high pass filter.

:After that, we tested its performance. By comparing with the theoretical high pass filter graph, the measured high pass filter frequency response showed a high correspondence with it, which means it is feasible to apply it to the whole system to suppress the low-frequency fluctuations.
* '''16 April 2022:'''
* Apply the high pass filter to the circuit
* Record data and draw some graphs
* '''23 April 2022:'''
* Processing experimental data
* Draw autocorrelation images
* Summarize and upload the experimental results

== Results and analysis ==

== Background reading ==
[1]Quantum random number generators, Miguel Herrero-Collantes and Juan Carlos Garcia-Escartin, Rev. Mod. Phys. 89, 015004.

Quantum Random Number Generator

2022-04-23T10:37:33Z

Zhang Munan: /* Idea */

== Team Members ==
Wang Yang A0228753X

Xiao Yucan A0236278W

Zhang Munan A0236273E

== Idea ==
We live in an increasingly connected world, where a superior source of entropy is the key to data security. The effectiveness of any cryptographic system is determined by the strength of the keys it used. In turn, the strength of the key is determined by the degree of randomness used in its generation. Besides, large amount of random numbers are at the core of Monte Carlo simulations, which are widely used in scientific research. Methods produce random numbers from any algorithm are called pseudo-random number generator(PRNG). And random numbers generated by PRNG is deterministic by definition and therefore unsuitable for cryptographic purposes.
In order to generate unpredictable random numbers, hardware random number generators have been widely used. These physically generated random numbers are considered "truly" random because it is either practically or fundamentally impossible to predict the outcome of such a device. Quantum Random Number Generators (QRNGs) belong to a class of hardware random number generators and leverage the random properties of quantum physics to generate a true source of entropy, improving the quality of seed content for key generation.
Early QRNGs were based on radioactive decay. And more recently, QRNGs based on poisson statistics of photons have been developed. The core idea is shown in figure below. Single photon generated by a laser source are incident on a semi-transparent mirror and the mutually exclusive events (reflection/transmission) are detected and associated to ‘0’ or ‘1’ bit values respectively. The unpredictability of generated numbers is ensured by the quantum nature of the process. However, such a scheme needs reliable single photon source as well as single photon detectors and it's not possible for our project. Here, we decided to build a QRNG based on measuring vacuum fluctuations of a light field as a random source. More details will be discussed in principle part.
[[File:WeChat7f083c000c217b276a91e43dbb2e62cf.png|thumb|300px|'''Principle of photodiode driving circuit''']]

* BENEFITS OF HAVING A QUANTUM RANDOM NUMBER GENERATOR:
** The source of randomness is unpredictable and controlled by quantum process.
** The entropy source tends to produce true random output.
** Live/ real-time monitoring of entropy source is possible and highly effective as well.
** All attacks on the entropy source are detectable.
** The above factors indicate that our QRNG is provably secure.

* APPLICATIONS OF QUANTUM RANDOM NUMBER GENERATOR:
** Securing data at rest in data centres
** Securing any kind of sensitive data
** Securing data in the cloud
** One-time pad for authentication in banking and other transactions
** Gaming applications and lottery
** Block-chain network
** Numerical simulations, statistical research
** IoT devices
** E-commerce and banking applications
** Cryptographic applications
** Telecom and 5G

In today’s Y2Q world, developers have to rely on the source of entropy as quantum-enabled security keys are set to become the new normal. Organisations should, therefore, implement QRNG to protect their customers’ data.

== Principles ==
[[File:Principle schematic of QRNG.png|thumb|300px|'''Principle schematic of QRNG''']]
In cybersecurity, a perfect random number is the root of trust. A QRNG does not rely on mathematical algorithms but on laws of quantum physics to ‘naturally’ generate random numbers. A QRNG can produce unpredictable outcomes in a robust and well-controlled way. It includes the power of complex deep-tech technologies such as semiconductors, optoelectronics, high precision electronics, and quantum physics that work together to create the highest level of randomness possible.

QRNGs use random properties of quantum physics to generate a true source of entropy. This improves the quality of seed for key generation. Since the entropy sources are derived from fundamental models, all the properties and behaviors are understandable and provably secure.

A laser-based quantum source generates the randomness in Tropos quantum random number generator. A laser produces a stream of the elementary particle, photons. The photons generated from the laser are used to generate the random numbers. These photons unlike classical objects are unpredictable under certain situations. When incidenting on a semi-transparent mirror, the photon has a 50/50 chance of being reflected or transmitted. The photon is then in a superposition of both the states (reflected and transmitted), i.e. the photon exists in both the states simultaneously. Upon measurement, it collapses to one of these states, which is intrinsically random and there is no way to predict which state the photon will collapse. This gives the inherent randomness from the photons, which cannot be influenced by any external parameters. '''This process is illustrated in the right figure.'''

== Setup ==
[[File:Schematic of setup.png|thumb|300px|'''Schematic of setup''']]
The original setup was created with as few components as possible to create a baseline performance that we can compare to. A schematic and a Experimental setup of the setup is shown in the image '''on the right.'''

[[File:Experimental setup.png|thumb|300px|'''Experimental setup''']]

'''Tool list'''
:① Laser Diode: Provide a light source, by changing the laser current can change the light intensity of the light source.
:② Focal Lens: By adjusting the focal length, the intensity of light that finally hits the photodiodes is adjusted.
:③ RP: rotatable Polarizer: The proportion of light intensity passing through PBS and reflected by PBS is controlled by adjusting RP.
:④ Mirror 1: By adjusting mirror 1, the falling points of the two Laser beams after passing through PBS and reflected by PBS can be adjusted simultaneously.
:⑤ PBS: Polarizer Beam Splitter: The laser beam incident to the PBS can pass through it or be reflected by it.
:⑥ Mirror 2: By adjusting mirror 1, the falling points of the laser beam after passing through PBS can be adjusted.
:⑦&⑧: Photodiodes: Detect the intensity of incident light

'''Description'''
:The laser beam comes from the laser diode. After passing through the focal lens and the rotatable Polarizer the laser beam incident to the mirror 1.Then the reflected laser beam incident to the Polarizer Beam splitter. The laser beam reflected by the PBS will incident to the PD1. The laser beam passing through the PBS will incident to the PD2.

'''Characteristic list'''
:Oscilloscope
:Frequency spectrograph

== Gallery ==
* '''26 February 2022:'''
* Did a basic characterization of photodiode
* Inputted a sine wave signal and a laser pointer light, observed the waveform of the photodiode
<gallery widths=300px heights=200px>
File:Basic characterization of photodiode test.jpeg|'''Basic characterization of photodiode test'''
File:Schematic of basic characterization of photodiode test.png|'''Schematic of basic characterization of photodiode test'''
</gallery>
:To understand the optical response of the photodiode, we used a laser pointer to test its output waveform, because the laser is not periodic, so the waveform is not regular, but there are signals from the oscilloscope.

:Then we inputted a periodic sine signal to excite the laser diode to output laser incidents on the photodiode, and it showed a periodic sine signal with a very regular sine waveform. When the frequency increased over 1 GHz, we could not observe a regular and stable waveform.
* '''5 March 2022:'''
* Used different resistors to test the frequency response of photodiode
<gallery widths=300px heights=200px>
File:Graph of frequency response of photodiode.jpg|'''Graph of frequency response of photodiode'''
</gallery>
:We changed the resistors in the Schematic of basic characterization of photodiode test, from 1kΩ to 11kΩ and then 20kΩ. We found that higher the resistance of the resistor higher the output voltage but less sensitive to the high frequency.
* '''12 March 2022:'''
* Build up the laser system and ensured the laser output
<gallery widths=300px heights=200px>
File:Laser diode.png|'''HL6501MG laser diode and schematic of internal circuit'''
File:Schematic of electronics laserconnector circuit.jpeg|'''Schematic of electronics laserconnector circuit'''
File:Laser source setup.png|'''Laser source setup'''
</gallery>
:We used a HL6501MG laser diode, it is a 0.65 μm band AlGaInP laser diode (LD) with a multi-quantum well (MQW) structure. It is suitable as a light source for large-capacity optical disc memories and various other types of optical equipment. Hermetic sealing of the small package (φ=5.6 mm) assures high reliability.

:The Laser source consist of ① Laser diode; ② Thermostat; ③ Supply circuit for Laser diode and Thermostat; ④ Shell; ⑤ Focal lens; ⑥ Radiator. The Laser Diode is in the thermostat which is connected to the Radiator. We can set temperature on the Laser power supply. The Thermostat and Radiator will keep the temperature of the laser diode as same as that set on the laser power supply. There is a focal lens in front of the laser diode. We can use it to change the focal length the enlarge the laser intensity hitting on the photo diodes. And a shell made of acrylic sheet and 4 balance post.
* '''19 March 2022:'''
* Soldered photodiode driving circuit
* Test the feasibility
<gallery widths=300px heights=200px>
File:Photo diode outlines.png|The S5972 is high-speed Si PIN photodiodes designed for visible to near-infrared light detection. These photodiodes provide wideband characteristics at a low bias, making them suitable for optical communications and other high-speed photometry.
File:Principle of photodiode driving circuit.png|'''Principle of photodiode driving circuit'''
File:Schematic photodiode driving circuit bolck.jpeg|'''Schematic photodiode driving circuit bolck'''
</gallery>
* '''26 March 2022:'''
* Build up the whole system
* Tune the bias of two photodiodes
* '''2 April 2022:'''
* Focus the laser output
* Maximize the laser power output
* '''9 April 2022:'''
* Soldered high pass filter
* Test its feasibility
<gallery widths=300px heights=200px>
File:Highpass filter principle circuit.png|'''Schematic of high pass filter circuit'''
File:Graph of theoretical high pass filter frequency response.jpg.png|'''Graph of theoretical high pass filter frequency response'''
File:Graph of measured high pass filter frequency response.jpg|'''Graph of measured high pass filter frequency response'''
File:Schematic of high pass filter.jpeg|'''Setup of high pass filter'''
File:Setup of gain block and high pass filter.jpeg|'''Setup of gain block and high pass filter'''
</gallery>
:The measured total noise has a relatively flat power density in the range of 60-200 MHz. With a low pass filter of 200 MHz in the oscilloscope, we just needed a high pass filter of 60 MHz which compresses the low-frequency fluctuations. So we designed a high pass filter of 60 MHz and soldered the high pass filter.

:After that, we tested its performance. By comparing with the theoretical high pass filter graph, the measured high pass filter frequency response showed a high correspondence with it, which means it is feasible to apply it to the whole system to suppress the low-frequency fluctuations.
* '''16 April 2022:'''
* Apply the high pass filter to the circuit
* Record data and draw some graphs
* '''23 April 2022:'''
* Processing experimental data
* Draw autocorrelation images
* Summarize and upload the experimental results

== Results and analysis ==

== Background reading ==
[1]Quantum random number generators, Miguel Herrero-Collantes and Juan Carlos Garcia-Escartin, Rev. Mod. Phys. 89, 015004.

Main Page

2022-04-23T09:22:32Z

Zhang Munan: /* Quantum Random Number Generator */

MediaWiki has been installed.
Welcome to the main page for the PC5214 graduate module AY2122, Sem2.
Here, we leave project descriptions, literature references, and other collateral information. You will need to create an account in class to obtain write access.

Actual lecture locations will be placed here until we have reached a stable state. If you are interested and have not been able to register, please send me an email (if you have not done so already) to [mailto:phyck@nus.edu.sg phyck@nus.edu.sg].

'''Deadline for all the wiki entries will be 30 April 2022, 23:59! Please ensure that you hare happy with your entries by that time!'''

Cheers, Christian

This page is currently set up.

==Lab spaces==
* '''S11-02-04''' (next to physics dept resource room). This is where most optics-related projects should go.
* '''S12 level 4''', "year 1 teaching lab", back room, "vanderGraff lab". This is perhaps were non-optics related projects would fit.
* '''S13-01-??''' (blue door: former accoustics lab). Not sure yet who could go there, but it is a really really quiet place!
* anything else you have access to

==Projects==
Please leave a a link to your project page (or pages) here, and leave a short description what this is about. Write the '''stuff you need''' under the description too.

===[[Project 1 (example)]]===
Keep a very brief description of a project or even a suggestion here, and perhaps the names of the team members, or who to contact if there is interest to join.

===[[Confocal Microscopy]]===
Team Members: Wang Tingyu, Xue Rui, Yang Hengxing

A Confocal Microscopy or Confocal Laser Scanning Microscopy (CLSM) uses pinhole to block out all out of focus light to enhance optical resolution, very different from traditional wide-field fluorescence microscopes. To offset the block of out of focus lights, the light intensity is detected by a photomultiplier tube or avalanche photodiode, which transforms the light signal into an electrical one. We will try to build a Setup like this to enhance optical resolution and maybe get profile information about the sample.

===[[An interferometric method for measuring the resonance frequency of a vibrating system]]===

Members: [[User:Nakarin|Nakarin Jayjong]], [[User:Aucca|Joel Auccapuclla]], [[User:Xiaoyu|Xiaoyu Nie]], [[User:Haotian|Haotian Song]].

In this project, the resonance frequency of the vibrating system namely the vibration transducer is measured using a Michelson interferometer.

===[[Homodyne detection]]===
Proposed By: [[User:Johnkhootf|John Khoo]]

[https://en.wikipedia.org/wiki/Homodyne_detection ''Optical'' homodyne detection] is a method for detecting messages transmitted in optical signals, where a frequency or phase modulated signal is compared to what is misleadingly called the "local oscillator" (LO) signal, which is generated from the same source but not modulated with the message. In order to probe quantum effects, it is important to bring the noise of the detector down to the [https://en.wikipedia.org/wiki/Shot_noise ''shot-noise limit''], where the only fluctuations observed arise from the discrete nature of photons, which can be theoretically modelled as the vacuum-state fluctuations of the quantised electromagnetic field. This project's first objective is to build a homodyne detector from scratch.

'''Stuff we need''': Acousto-optical modulator, electro-optical modulator, transformer to control EOM, photodiodes, current-to-voltage converter (I'm not sure what this is - can we just use a resistor connected to the ground and measure the voltage?), Raspberry Pi (I hope the ADC is good enough for this), mirrors and beamsplitters

===[[Laser Microphone]]===
Team Members: [[User:Nicholas cjl|Nicholas Chong Jia Le]], [[User:Marcuslow|Marcus Low Zuo Wu]]

A laser spot illuminating a vibrating surface should move along with it, and tracking the motion of the spot should theoretically allow us to retrieve some of the information regarding the vibrations of the surface. If a loud enough sound causes the surface to vibrate, this should theoretically be enough for the transmission of audio information through visual means. The signal obtained will then be put through a few different digital signal processing techniques in an attempt to retrieve a (good enough) copy of the original audio.

===[[Plasma emission spectroscopy]]===
Proposed By: Park Kun Hee

Pulsed plasma in partial vacuum is characterised, by analysing [https://en.wikipedia.org/wiki/Spectral_line_ratios line intensity ratios] to determine its temperature and density.

===[[Characterization of Single Photon Counters]]===
Proposed By: Yeo Zhen Yuan

The project is to characterize an Avalanche PhotoDiode (APD) and compare its efficiency with commercial counterparts like [https://www.digikey.com/en/products/detail/excelitas-technologies/SPCM-AQRH-10-FC/6235280 this device]. It works based on the photoelectric effect to turn incident photon into photoelectron. This photoelectron is then accelerated in an electric field to produce cascading electrons and this "electron avalanche" is detected as a spike in the current. Analog signals will need to be processed via custom electronics and ultimately provide a digital readout. Current commercial detectors boast 50% Photon Detector Efficiency (PDE) at room temperature and that will be our goal. They typically cost $2000-$5000 which seems over-priced and ready for disruption. Liquid nitrogen temperatures may be needed to see how large a PDE we can get.

What is SPCM good for? Copied from the datasheet/brochure: LIDAR, Quantum Cryptography, Photon correlation spectroscopy, Astronomical observation, Optical range finding, Adaptive optics, Ultra-sensitive fluorescence, Particle sizing, Microscopy. So maybe this would become a toy/tool for next year's students.

[NEW CAPABILITY]

High throughput Oscilloscope data collection. ~700 "screenshots" per minute. Demonstration on APD, 10K screenshots of 2 Channel Digital Oscilloscope [https://github.com/zhenyuan992/OpenWave-1KB/raw/88a85a7f18741b370563b03d87a53f913b714a4c/src/results03_01_apdvoltage.png].

Semi-seamless data collection [https://www.tek.com/en/support/faqs/can-i-use-my-oscilloscope-do-data-logging].

===[[Kerr Microscope]]===
Proposed By: Sim May Inn (write up by Joel Yeo)

'''Team members: Gan Jun Herng, Joel Yeo, Sim May Inn'''

'''Project Location: S11-02-04'''

Imaging a sample can be done in many ways, depending on the light-matter interaction we are interested in observing. The magneto-optic Kerr effect describes the change in polarization and intensity of incident light when it impinges on the surface of a magnetic material. The resultant reflected light can then form an image through focusing optics which provides high contrast between areas of different magnetization.

In this project, we will be aiming to build a basic Kerr microscope using off-the-shelf polarizers, objectives, detectors and laser source. An example of a magnetic sample is the magnetic tape from an old school cassette tape. To increase the field of view, we also plan to incorporate automatic raster scanning of the sample through means of an Arduino-controlled sample stage.

'''Items needed (as of 28 Feb 2022):'''
* Light source (visibile wavelength): <s> Laser, LED </s>, laser diode
* <s> Linear polarizer (sheet) x 2Camera (CCD/CMOS) </s>
* <s> Non-polarizing beam splitter </s>
* <s> Camera (CCD/CMOS) </s>
* <s> Pinhole/aperture </s>
* <s> Magnetic samples for Kerr microscopy (eg. Magnetic film, magnets, ferromagnetic materials) </s>
* Arduino
* Microscope stage
* Piezoelectrics (?) for moving stage

===[[Electron Gun]]===
Team Members: Aliki Sofia Rotelli, Lai Tian Hao, Lim En Liang Irvin, Tan Chuan Jie

The purpose of this project is to design and build an electron gun from the initial concept in order to create a detectable electron beam through the use of a phosphor-coated screen. Additionally, the beam current will be examined in order to better define the devices' capabilities. Mass spectrometry, x-ray production for linear accelerators, and electron-beam lithography are just a few of the applications for electron gun technology.

===[[Smoke detection in air]]===
Team Members: Cheng De Hao, Huang Hai Tao, Wang Zheng Yu

Using detector to detect the scattering light and amplify the signal by using the lock-in amplifier.

===[[Anti-glare LCD]]===
Team members: Zhang Yuanyuan, Ming Xiaohan, Han Shixin

As s bad lighting phenomenon, glare phonomenon brings inconvenience to all aspects of human life, especially people's access to information on instruments. In order to suppress glare effectively, anti-glare film is put into research. The common anti-glare film in the market is an optical film using the principle of optical scattering, but it can not adapt to the change of light environment in time, which has some limitations in practical application. In this study, a two-dimensional barcode micro-region orientation structure, based on the characteristics of liquid crystal, namely a random grating structure, was designed by simulation in the lab and using MATLAB software, and its optional parameters were searched.

===[[Custom atomic beam source]]===
Team Members: Lu Tiangao, Li Putian

===[[Schlieren imaging]]===
Team members: Zhang Xingjian, Du Jinyi

===[[Contactless Conductivity Measurement]]===

Team members: Chen Guohao, Jiang Luwen

The purpose of this project is to measure the conductivity of materials without having to make electrical contact with them. Specifically, we make use of the eddy-current induced in the materials to calculate the conductivity.

===[[Quantum Random Number Generator]]===

'''Proposed by: Zhang Munan'''

'''Team members: Wang Yang, Xiao Yucan, Zhang Munan'''

'''Venue: S11-02-04'''

Random numbers are a fundamental resource in science and engineering with important applications in simulation and cryptography. The inherent randomness at the core of quantum mechanics makes quantum systems a perfect source of entropy. Quantum random number generation is one of the most mature quantum technologies with many alternative generation methods. The purpose of our project is to build a simple optics-based QRNG. We will also collect the random number generated by our device and use some methods to check the randomness.

===[[Orbits of the Galilean Moons]]===

Team Members: [[User:Matthew|Matthew Wee]]

Galileo Galilei’s discovery of celestial bodies that orbit something other than the Earth marked the beginning of the end of the geocentric model of the universe. In this project, we will perform the same observations on those moons as Galileo did 400 years ago.

===[[Capacitor array based ADC]]===

Team Members: Zhang Chengyue, Yang Ningli, Guo Diandian, Chen Jiayu

In this project, we are going to make an ADC.

==Resources==
===[[Recorded sessions]]===
Some of the sessions will be recorded and uploaded to youtube. Find a description on the [[Recorded sessions]] page.

===Devices and material===
Apart form all the stuff in the teaching lab, we have a few resources you may want to consider for your project
*...

'''Books:'''
* P.R. Bevington, D.K. Robinson: Data Reduction and Error Analysis for the Physical Sciences, 3rd edition. McGrawHill, ISBN0-07-119926-8. A very good book containing all the questions you never allowed yourself to ask about error treatment, statistics, fitting of data to models etc.
* Horrowitz/Hill: The Art of Electronics
* C.H. Moore, C.C. Davis, M.A. Coplan: Building Scientific Apparatus. 2nd or higher edition. Perseus Books, ISBN0-201-13189-7. A very comprehensive book about many dirty details in experimental physics, and ways to get simple problems solved. Appears a bit dated, but is a good start for many experimental projects up to this day!
* Christopher C. Davis: Laser and Electro-optics. Useful as a general introduction to many contemporary aspects you come across when working with lasers, with a reasonable introduction of the theory. Very practical for optics.

'''Software:'''
Some of the more common data processing tools used in experimental physics:
* [http://www.gnuplot.info/ '''Gnuplot''']: A free and very mature data display tool that works on just about any platform used that produces excellent publication-grade eps and pdf figures. Can be also used in scripts. Open source and completely free.
* Various '''Python''' extensions. [http://www.python.org/ Python] is a very powerful free programming language that runs on just about any computer platform. It is open source and completely free.
* '''Matlab''': Very common, good toolset also for formal mathematics, good graphics. Expensive. We may have a site license, but I am not sure how painful it is for us to get a license for this course. Ask me if interested.
* '''Mathematica''': More common among theroetical physicists, very good in formal maths, now with better numerics. Graphs are ok but can be a pain to make looking good. As with Matlab, we do have a campus license but an increasingly painful licensing ritual. Ask me if interested or follow the instruction to install the software in your desktop.
* '''Origin''': Very widespread data processing software with a complete graphical user interface, integrates well into a Windows environment. Most likely available in your research labs, not sure if NUS has a site license.
* '''Labview''': Many of you may have seen this in your labs, but I am not too familiar with it, and chances are it is too resource-hungry to run on the machines we have there. It keeps its promise of a fast learning curve if you want to do simple things but it can get a REAL pain if you want to do subtle things, or want to do things fast, or want to debug code. Expensive and resource-hungry, but comes with good integration of also expensive hardware. May not be worth it if you know any programming language.
* [https://www.circuitlab.com/ '''Circuit Lab''']: a convenient software to design and simulate electrical circuits directly at your browser. I think Flash is required. It works well in Chrome.

===[[Acronym database]]===
This is an attempt to clarify the countless acronyms we use in our sub-communities (follow headline link)

===[[Gnuplot tricks]]===
Follow the headline link for some of the random questions that came up with gnuplot.

== Previous PC5214 wikis ==
* [http://pc5214.org/AY1819S2 AY2018/19 Sem2]
* [http://pc5214.org/AY1415S1 AY2014/15 Sem1]
* [http://pc5214.org/AY1314S1 AY2013/14 Sem1]
* [http://pc5214.org/AY1213S1 AY2012/13 Sem1]
* [http://pc5214.org/AY1112S1 AY2011/12 Sem1]
* [http://pc5214.org/AY1011S1 AY2010/11 Sem1]

== Some wiki reference materials==
Consult the [//meta.wikimedia.org/wiki/Help:Contents User's Guide] for information on using the wiki software. Other sources:

* [//www.mediawiki.org/wiki/Manual:FAQ MediaWiki FAQ]
* [[Writing mathematical expressions]]
* [[Uploading images]]

Quantum Random Number Generator

2022-02-23T04:24:53Z

Zhang Munan: /* Background reading */

== Team Members ==
Wang Yang

Xiao Yucan

Zhang Munan A0236273E

== Idea ==

== Setup ==

== Background reading ==
[1]Quantum random number generators, Miguel Herrero-Collantes and Juan Carlos Garcia-Escartin, Rev. Mod. Phys. 89, 015004.

Quantum Random Number Generator

2022-02-23T02:28:23Z

Zhang Munan: /* Team Members */

== Team Members ==
Wang Yang

Xiao Yucan

Zhang Munan A0236273E

== Idea ==

== Setup ==

== Background reading ==

Quantum Random Number Generator

2022-02-23T02:26:27Z

Zhang Munan: /* Team Members */

== Team Members ==
Wang Yang
Xiao Yucan
Zhang Munan A0236273E

== Idea ==

== Setup ==

== Background reading ==

Quantum Random Number Generator

2022-02-23T02:25:52Z

Zhang Munan: Created page with "== Team Members == == Idea == == Setup == == Background reading =="

== Team Members ==

== Idea ==

== Setup ==

== Background reading ==

Main Page

2022-02-23T02:20:39Z

Zhang Munan: /* Projects */

MediaWiki has been installed.
Welcome to the main page for the PC5214 graduate module AY2122, Sem2.
Here, we leave project descriptions, literature references, and other collateral information. You will need to create an account in class to obtain write access.

Actual lecture locations will be placed here until we have reached a stable state. If you are interested and have not been able to register, please send me an email (if you have not done so already) to [mailto:phyck@nus.edu.sg phyck@nus.edu.sg].

'''For the session on 14 Jan and some following sessions, we were given LT29.'''

Cheers, Christian

This page is currently set up.

==Lab spaces==
* '''S11-02-04''' (next to physics dept resource room). This is where most optics-related projects should go.
* '''S12 level 4''', "year 1 teaching lab", back room, "vanderGraff lab". This is perhaps were non-optics related projects would fit.
* '''S13-01-??''' (blue door: former accoustics lab). Not sure yet who could go there, but it is a really really quiet place!
* anything else you have access to

==Projects==
Please leave a a link to your project page (or pages) here, and leave a short description what this is about. Write the '''stuff you need''' under the description too.

===[[Project 1 (example)]]===
Keep a very brief description of a project or even a suggestion here, and perhaps the names of the team members, or who to contact if there is interest to join.

===[[Confocal Microscopy]]===
Team Members: Wang Tingyu, Xue Rui, Yang Hengxing

A Confocal Microscopy or Confocal Laser Scanning Microscopy (CLSM) uses pinhole to block out all out of focus light to enhance optical resolution, very different from traditional wide-field fluorescence microscopes. To offset the block of out of focus lights, the light intensity is detected by a photomultiplier tube or avalanche photodiode, which transforms the light signal into an electrical one. We will try to build a Setup like this to enhance optical resolution and maybe get profile information about the sample.

===[[Measure index of refraction]]===

Members: Joel Auccapuclla, Xiaoyu Nie, Haotian Song, Nakarin Jayjong.
Use an interferometer to obtain the index of refraction of different materials, for instance air.

===[[Homodyne detection]]===
Proposed By: [[User:Johnkhootf|John Khoo]]

[https://en.wikipedia.org/wiki/Homodyne_detection ''Optical'' homodyne detection] is a method for detecting messages transmitted in optical signals, where a frequency or phase modulated signal is compared to what is misleadingly called the "local oscillator" (LO) signal, which is generated from the same source but not modulated with the message. In order to probe quantum effects, it is important to bring the noise of the detector down to the [https://en.wikipedia.org/wiki/Shot_noise ''shot-noise limit''], where the only fluctuations observed arise from the discrete nature of photons, which can be theoretically modelled as the vacuum-state fluctuations of the quantised electromagnetic field. This project's first objective is to build a homodyne detector from scratch.

'''Stuff we need''': Acousto-optical modulator, electro-optical modulator, transformer to control EOM, photodiodes, current-to-voltage converter (I'm not sure what this is - can we just use a resistor connected to the ground and measure the voltage?), Raspberry Pi (I hope the ADC is good enough for this), mirrors and beamsplitters

===[[Laser Microphone]]===
Team Members: Nicholas Chong Jia Le, Marcus Low Zuo Wu

A laser spot illuminating a vibrating surface should move along with it, and tracking the motion of the spot should theoretically allow us to retrieve some of the information regarding the vibrations of the surface. If a loud enough sound causes the surface to vibrate, this should theoretically be enough for the transmission of audio information through visual means. We have a few different methods through which we will attempt to realise this.

===[[Plasma emission spectroscopy]]===
Proposed By: Park Kun Hee

Pulsed plasma in partial vacuum is characterised, by analysing [https://en.wikipedia.org/wiki/Spectral_line_ratios line intensity ratios] to determine its temperature and density.

===[[Characterization of Single Photon Counters]]===
Proposed By: Yeo Zhen Yuan (Looking for Teammates!)

The project is to characterize an Avalanche PhotoDiode (APD) and compare its efficiency with commercial counterparts like [https://www.digikey.com/en/products/detail/excelitas-technologies/SPCM-AQRH-10-FC/6235280 this device]. It works based on the photoelectric effect to turn incident photon into photoelectron. This photoelectron is then accelerated in an electric field to produce cascading electrons and this "electron avalanche" is detected as a spike in the current. Analog signals will need to be processed via custom electronics and ultimately provide a digital readout. Current commercial detectors boast 50% Photon Detector Efficiency (PDE) at room temperature and that will be our goal. They typically cost $2000-$5000 which seems over-priced and ready for disruption. Liquid nitrogen temperatures may be needed to see how large a PDE we can get.

What is SPCM good for? Copied from the datasheet/brochure: LIDAR, Quantum Cryptography, Photon correlation spectroscopy, Astronomical observation, Optical range finding, Adaptive optics, Ultra-sensitive fluorescence, Particle sizing, Microscopy. So maybe this would become a toy/tool for next year's students.

===[[Kerr Microscope]]===
Proposed By: Sim May Inn (write up by Joel Yeo)

'''Team members: Gan Jun Herng, Joel Yeo'''

'''Project Location: S11-02-04'''

Imaging a sample can be done in many ways, depending on the light-matter interaction we are interested in observing. The magneto-optic Kerr effect describes the change in polarization and intensity of incident light when it impinges on the surface of a magnetic material. The resultant reflected light can then form an image through focusing optics which provides high contrast between areas of different magnetization.

In this project, we will be aiming to build a basic Kerr microscope using off-the-shelf polarizers, objectives, detectors and laser source. An example of a magnetic sample is the magnetic tape from an old school cassette tape. To increase the field of view, we also plan to incorporate automatic raster scanning of the sample through means of an Arduino-controlled sample stage.

'''Items needed (as of 08 Feb 2022):'''
* Light source: Laser, LED (visibile wavelength)
* Linear polarizer (sheet) x 2
* Non-polarizing beam splitter
* Camera (CCD/CMOS)
* Pinhole/aperture
* Magnetic samples for Kerr microscopy (eg. Magnetic film, magnets, ferromagnetic materials)
* Arduino
* Microscope stage
* Piezoelectrics (?) for moving stage

===[[Electron Gun]]===
Team Members: Aliki Sofia Rotelli, Lai Tian Hao, Lim En Liang Irvin, Tan Chuan Jie

The purpose of this project is to design and build an electron gun from the initial concept in order to create a detectable electron beam through the use of a phosphor-coated screen. Additionally, the beam current will be examined in order to better define the devices' capabilities. Mass spectrometry, x-ray production for linear accelerators, and electron-beam lithography are just a few of the applications for electron gun technology.

===[[Air biased coherent detection ]]===
Team Members: Cheng De Hao, Huang Hai Tao, Wang Zhenyu

===[[In-situ magnetic imaging and Hall detection]]===
Proposed by Sim May Inn

In computing and memory device architectures, propagation of magnetic domains play an essential role in the encoding and transport of information. Magnetic domain imaging is often employed to unveil such propagation dynamics. Additionally, other than observation and studies of their dynamics, means of detection are also of interest, and this can be achieved through the read-outs of Hall effect signals. As such, this project aims to design and modify an existing low temperature setup to be able to concurrently perform both magnetic domain imaging and Hall signal detection.

===[[Anti-glare LCD]]===
Team members: Zhang Yuanyuan, Ming Xiaohan, Han Shixin

As s bad lighting phenomenon, glare phonomenon brings inconvenience to all aspects of human life, especially people's access to information on instruments. In order to suppress glare effectively, anti-glare film is put into research. The common anti-glare film in the market is an optical film using the principle of optical scattering, but it can not adapt to the change of light environment in time, which has some limitations in practical application. In this study, a two-dimensional barcode micro-region orientation structure, based on the characteristics of liquid crystal, namely a random grating structure, was designed by simulation in the lab and using MATLAB software, and its optional parameters were searched.

===[[Custom atomic beam source]]===
Team Members: Lu Tiangao, Li Putian

===[[Schlieren imaging]]===
Team members: Zhang Xingjian, Du Jinyi

===[[Contactless Conductivity Measurement]]===

Team members: Chen Guohao, Jiang Luwen

The purpose of this project is to measure the conductivity of materials without having to make electrical contact with them. Specifically, we make use of the eddy-current induced in the materials to calculate the conductivity.

===[[Quantum Random Number Generator]]===

Team members: Wang Yang, Xiao Yucan, Zhang Munan

Random numbers are a fundamental resource in science and engineering with important applications in simulation and cryptography. The inherent randomness at the core of quantum mechanics makes quantum systems a perfect source of entropy. Quantum random number generation is one of the most mature quantum technologies with many alternative generation methods. The purpose of our project is to build a simple optics-based QRNG. We will also collect the random number generated by our device and use some methods to check the randomness.

==Resources==
===[[Recorded sessions]]===
Some of the sessions will be recorded and uploaded to youtube. Find a description on the [[Recorded sessions]] page.

===Devices and material===
Apart form all the stuff in the teaching lab, we have a few resources you may want to consider for your project
*...

'''Books:'''
* P.R. Bevington, D.K. Robinson: Data Reduction and Error Analysis for the Physical Sciences, 3rd edition. McGrawHill, ISBN0-07-119926-8. A very good book containing all the questions you never allowed yourself to ask about error treatment, statistics, fitting of data to models etc.
* Horrowitz/Hill: The Art of Electronics
* C.H. Moore, C.C. Davis, M.A. Coplan: Building Scientific Apparatus. 2nd or higher edition. Perseus Books, ISBN0-201-13189-7. A very comprehensive book about many dirty details in experimental physics, and ways to get simple problems solved. Appears a bit dated, but is a good start for many experimental projects up to this day!
* Christopher C. Davis: Laser and Electro-optics. Useful as a general introduction to many contemporary aspects you come across when working with lasers, with a reasonable introduction of the theory. Very practical for optics.

'''Software:'''
Some of the more common data processing tools used in experimental physics:
* [http://www.gnuplot.info/ '''Gnuplot''']: A free and very mature data display tool that works on just about any platform used that produces excellent publication-grade eps and pdf figures. Can be also used in scripts. Open source and completely free.
* Various '''Python''' extensions. [http://www.python.org/ Python] is a very powerful free programming language that runs on just about any computer platform. It is open source and completely free.
* '''Matlab''': Very common, good toolset also for formal mathematics, good graphics. Expensive. We may have a site license, but I am not sure how painful it is for us to get a license for this course. Ask me if interested.
* '''Mathematica''': More common among theroetical physicists, very good in formal maths, now with better numerics. Graphs are ok but can be a pain to make looking good. As with Matlab, we do have a campus license but an increasingly painful licensing ritual. Ask me if interested or follow the instruction to install the software in your desktop.
* '''Origin''': Very widespread data processing software with a complete graphical user interface, integrates well into a Windows environment. Most likely available in your research labs, not sure if NUS has a site license.
* '''Labview''': Many of you may have seen this in your labs, but I am not too familiar with it, and chances are it is too resource-hungry to run on the machines we have there. It keeps its promise of a fast learning curve if you want to do simple things but it can get a REAL pain if you want to do subtle things, or want to do things fast, or want to debug code. Expensive and resource-hungry, but comes with good integration of also expensive hardware. May not be worth it if you know any programming language.
* [https://www.circuitlab.com/ '''Circuit Lab''']: a convenient software to design and simulate electrical circuits directly at your browser. I think Flash is required. It works well in Chrome.

===[[Acronym database]]===
This is an attempt to clarify the countless acronyms we use in our sub-communities (follow headline link)

===[[Gnuplot tricks]]===
Follow the headline link for some of the random questions that came up with gnuplot.

== Previous PC5214 wikis ==
* [http://pc5214.org/AY1819S2 AY2018/19 Sem2]
* [http://pc5214.org/AY1415S1 AY2014/15 Sem1]
* [http://pc5214.org/AY1314S1 AY2013/14 Sem1]
* [http://pc5214.org/AY1213S1 AY2012/13 Sem1]
* [http://pc5214.org/AY1112S1 AY2011/12 Sem1]
* [http://pc5214.org/AY1011S1 AY2010/11 Sem1]

== Some wiki reference materials==
Consult the [//meta.wikimedia.org/wiki/Help:Contents User's Guide] for information on using the wiki software. Other sources:

* [//www.mediawiki.org/wiki/Manual:FAQ MediaWiki FAQ]
* [[Writing mathematical expressions]]
* [[Uploading images]]