Quantum Random Number Generator - Revision history

Channalyu: /* Acknowledgement */

2022-04-29T17:52:40Z

Acknowledgement

← Older revision		Revision as of 17:52, 29 April 2022
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	Then, we are also extremely grateful to Dr. Shi Yicheng, we feel very impressed and lucky for his kindness when we were doing this project with his help. Whatever we need or wherever we need to go, he always gives us very clear guidance and does us a standard demonstration to help us understand. His quick feedback and helpful guidance give us a deep impression and let us move forward. Sincerely, we want to say thank him very much again and give him best wishes for his next study period in the United States.		Then, we are also extremely grateful to Dr. Shi Yicheng, we feel very impressed and lucky for his kindness when we were doing this project with his help. Whatever we need or wherever we need to go, he always gives us very clear guidance and does us a standard demonstration to help us understand. His quick feedback and helpful guidance give us a deep impression and let us move forward. Sincerely, we want to say thank him very much again and give him best wishes for his next study period in the United States.

	At last, we would like to offer our gratitude to each other in our team. It is we that insist on and try constantly, and we can finally get ~~a relatively~~ achieved result. This camaraderie is the best thing we got than the experimental result.		At last, we would like to offer our gratitude to each other in our team. It is we that insist on and try constantly, and we can finally get an achieved result. This camaraderie is the best thing we got than the experimental result.

	== '''References''' ==		== '''References''' ==

Channalyu: /* Acknowledgement */

2022-04-29T17:52:04Z

Acknowledgement

← Older revision		Revision as of 17:52, 29 April 2022
Line 210:		Line 210:
	Then, we are also extremely grateful to Dr. Shi Yicheng, we feel very impressed and lucky for his kindness when we were doing this project with his help. Whatever we need or wherever we need to go, he always gives us very clear guidance and does us a standard demonstration to help us understand. His quick feedback and helpful guidance give us a deep impression and let us move forward. Sincerely, we want to say thank him very much again and give him best wishes for his next study period in the United States.		Then, we are also extremely grateful to Dr. Shi Yicheng, we feel very impressed and lucky for his kindness when we were doing this project with his help. Whatever we need or wherever we need to go, he always gives us very clear guidance and does us a standard demonstration to help us understand. His quick feedback and helpful guidance give us a deep impression and let us move forward. Sincerely, we want to say thank him very much again and give him best wishes for his next study period in the United States.

	At last, we would like to offer our gratitude to each other in our team. It is that we insist on and try constantly, and we can finally get a relatively achieved result. This camaraderie is the best thing we got than the experimental result.		At last, we would like to offer our gratitude to each other in our team. It is we that insist on and try constantly, and we can finally get a relatively achieved result. This camaraderie is the best thing we got than the experimental result.

	== '''References''' ==		== '''References''' ==

Channalyu: /* Autocorrelation */

2022-04-29T17:51:23Z

Autocorrelation

← Older revision		Revision as of 17:51, 29 April 2022
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	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>.		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>		:::::::::::::::::::<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.		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.

Channalyu: /* Autocorrelation */

2022-04-29T17:50:48Z

Autocorrelation

← Older revision		Revision as of 17:50, 29 April 2022
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	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>.		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>		::::::::::::::::::<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.		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.

Channalyu: /* Acknowledgement */

2022-04-29T17:48:14Z

Acknowledgement

← Older revision		Revision as of 17:48, 29 April 2022
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	First and foremost, we would like to express our deepest appreciation to Prof Christian Kurtsiefer. Thanks to his kind help to get some gadgets for this project, we have done a lot of work with his insightful ideas and suggestions.		First and foremost, we would like to express our deepest appreciation to Prof Christian Kurtsiefer. Thanks to his kind help to get some gadgets for this project, we have done a lot of work with his insightful ideas and suggestions.

	Then, we are also extremely grateful to Dr. Shi Yicheng, we feel very impressed and lucky for his kindness when we were doing this project with his help. Whatever we need or wherever we need to go, he always gives us very clear guidance and does us a standard demonstration to help us understand. His quick ~~feedbacks~~ and helpful guidance give us a deep impression and let us move forward. Sincerely, we want to say thank him very much again and give him best wishes for his next study period in the United States.		Then, we are also extremely grateful to Dr. Shi Yicheng, we feel very impressed and lucky for his kindness when we were doing this project with his help. Whatever we need or wherever we need to go, he always gives us very clear guidance and does us a standard demonstration to help us understand. His quick feedback and helpful guidance give us a deep impression and let us move forward. Sincerely, we want to say thank him very much again and give him best wishes for his next study period in the United States.

			At last, we would like to offer our gratitude to each other in our team. It is that we insist on and try constantly, and we can finally get a relatively achieved result. This camaraderie is the best thing we got than the experimental result.

	== '''References''' ==		== '''References''' ==

Channalyu: /* Acknowledgement */

2022-04-29T17:43:54Z

Acknowledgement

← Older revision		Revision as of 17:43, 29 April 2022
Line 204:		Line 204:

	== '''Acknowledgement''' ==		== '''Acknowledgement''' ==
			It is an extremely thing and a big challenge for us to conduct this experiment, during this process, we encountered a lot of problems and solved them one by one with others' help. So we want to show our appreciation to these people.

			First and foremost, we would like to express our deepest appreciation to Prof Christian Kurtsiefer. Thanks to his kind help to get some gadgets for this project, we have done a lot of work with his insightful ideas and suggestions.

			Then, we are also extremely grateful to Dr. Shi Yicheng, we feel very impressed and lucky for his kindness when we were doing this project with his help. Whatever we need or wherever we need to go, he always gives us very clear guidance and does us a standard demonstration to help us understand. His quick feedbacks and helpful guidance give us a deep impression and let us move forward. Sincerely, we want to say thank him very much again and give him best wishes for his next study period in the United States.

	== '''References''' ==		== '''References''' ==

Channalyu at 17:31, 29 April 2022

2022-04-29T17:31:03Z

← Older revision		Revision as of 17:31, 29 April 2022
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	=== '''Randomness Test'''===		=== '''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.		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.

			== '''Acknowledgement''' ==



	== '''References''' ==		== '''References''' ==

Channalyu: /* Randomness Extraction */

2022-04-29T17:30:13Z

Randomness Extraction

← Older revision		Revision as of 17:30, 29 April 2022
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	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 into a uniformly distributed binary stream. For simplicity, here we used random matrix multiplications to extract uniformly distributed random numbers.		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 into a uniformly distributed binary stream. For simplicity, here we used random matrix multiplications to extract uniformly distributed random numbers.

	[[File:WechatIMG18990.jpeg\|~~thumb~~\|350px\|center]]		[[File:WechatIMG18990.jpeg\|frameless\|350px\|center]]

	The 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.		The 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.

Channalyu: /* Randomness Extraction */

2022-04-29T17:29:00Z

Randomness Extraction

← Older revision		Revision as of 17:29, 29 April 2022
Line 192:		Line 192:
	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 into a uniformly distributed binary stream. For simplicity, here we used random matrix multiplications to extract uniformly distributed random numbers.		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 into a uniformly distributed binary stream. For simplicity, here we used random matrix multiplications to extract uniformly distributed random numbers.

	[[File:WechatIMG18990.jpeg\|thumb\|~~3500px~~\|center\|]]		[[File:WechatIMG18990.jpeg\|thumb\|350px\|center]]

	The 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.		The 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.

Channalyu: /* Randomness Extraction */

2022-04-29T17:28:22Z

Randomness Extraction

← Older revision		Revision as of 17:28, 29 April 2022
Line 192:		Line 192:
	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 into a uniformly distributed binary stream. For simplicity, here we used random matrix multiplications to extract uniformly distributed random numbers.		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 into a uniformly distributed binary stream. For simplicity, here we used random matrix multiplications to extract uniformly distributed random numbers.

	[[File:WechatIMG18990.jpeg\|~~frame~~\|3500px\|center\|]]		[[File:WechatIMG18990.jpeg\|thumb\|3500px\|center\|]]

	The 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.		The 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.