Optimization method for sampling range of analog-to-digital converter in quantum random number generator whose quantum noise satisfies Gaussian distribution

Abstract

This invention relates to the field of quantum information communication technology and discloses a method for optimizing the sampling range of an analog-to-digital converter (ADC) in a quantum random number generator whose quantum noise follows a Gaussian distribution. Specifically targeting quantum random number generators whose quantum sources follow a Gaussian distribution, the method chooses not to sample or output a digital signal for input signals that exceed the ADC's value range. Simultaneously, the optimal sampling range is determined by maximizing the product of the quantum random number generator's output minimum entropy and data utilization. By optimizing the ADC sampling range, the method maximizes the number of extractable random bits and the random number generation rate, ensuring the randomness of the output random numbers.

Description

Technical Field

[0001] The present invention relates to the field of quantum information communication technology, and in particular to a method for optimizing the sampling range of an analog-to-digital converter in a quantum random number generator whose quantum noise satisfies a Gaussian distribution. Background Art

[0002] With the development of the information age and the rapid advancement of society's informatization, random numbers play a vital role in numerous fields, such as numerical simulation, basic science, and information security. They are particularly widely used in cryptography and secure communications, which rely on the unpredictability of random numbers. With the advancement of quantum information science, quantum random number generators, designed based on the intrinsic randomness of quantum mechanics, are believed to be able to theoretically generate unpredictable true random numbers, providing important protection for information security.

[0003] Based on the type of light source, quantum random number generators can be categorized as discrete and continuous. Discrete quantum random number generators are limited by the speed of single-photon preparation and the dead time of the detector, resulting in a low random number generation rate. Continuous quantum random number generators utilize noise sources such as laser phase noise, amplified spontaneous emission noise, and vacuum state fluctuations to generate quantum random numbers, significantly increasing the random number generation rate and gradually becoming practical. Continuous quantum random number generators utilize continuous light detectors as their detection method. The output optical signal is converted into an electrical signal by the photodetector, which is typically then collected and quantized by an analog-to-digital converter (ADC), outputting a binary digital sequence to obtain the original quantum random number. Therefore, the ADC, as a physical device for signal acquisition, plays a crucial role in continuous quantum random number generators.

[0004] In a quantum random number generator, for an ADC with a given sampling accuracy, the sampling range affects the number of random bits that can be extracted and the randomness of the output. Furthermore, if the ADC sampling range is not chosen properly, it can easily lead to waste of edge sampling intervals or unnecessary saturation, ultimately affecting the randomness of the output data and making the random numbers more predictable.

[0005] The analog-to-digital converter (ADC) is an important physical device in a quantum random number generator. Its function is to discretize and sample electrical signals and quantize them into digital signals. The input signal is sampled by an n-bit ADC, and the sampling range is discretized into intervals. The input signal is quantized in quantization intervals. Haw [JYHaw, S.M.Assad, A.M.Lance, N.H.Y.Ng, V.Sharma, P.K.Lam, T.Symul.Maximization of Extractable Randomness in a Quantum Random-Number Generator [J]. Physical Review Applied, 2015, 3 (5).] et al. discussed the sampling range of the ADC and proposed an optimization method to maximize the probability of the central interval of the ADC sampling range. In this method, the input signal that exceeds the ADC sampling range is accumulated into the first and last intervals of the ADC. Although this method ensures that the edge sampling intervals of the ADC will not be saturated or wasted, the sampling range calculated by this method will also cause the probabilities of the first and last intervals to be too large, thereby affecting the randomness of the random number finally output by the quantum random number generator. Summary of the Invention

[0006] Aiming at the problem that the sampling range optimization method of the analog-to-digital converter in the existing quantum random number generator affects the randomness of the random numbers finally output by the quantum random number generator, the present invention proposes an optimization method for the sampling range of the analog-to-digital converter in a quantum random number generator whose quantum noise satisfies the Gaussian distribution. This method can maximize the number of random bits that can be extracted, improve the random number generation rate, and ensure the randomness of the output data.

[0007] In order to achieve the above object, the present invention adopts the following technical solutions:

[0008] A method for optimizing the sampling range of an analog-to-digital converter in a quantum random number generator whose quantum noise satisfies a Gaussian distribution, comprising:

[0009] When the sampling accuracy of the analog-to-digital converter ADC is n-bit and the sampling range is [-R+δ / 2, R-3δ / 2], the ADC sampling range is discretized into 2 n quantization intervals, the width of each interval is δ = R / 2 n-1 ; The center of the sampling range is 0, and the first interval i is centered on -R min =-2 n-1 , the last interval i is centered on R-δ max =2 n-1 -1; where R is the ADC sampling range parameter;

[0010] If the input signal \(v\in[-R + \delta / 2, R - 3\delta / 2]\) and \(i\delta-\delta / 2\lt v\lt i\delta+\delta / 2\), where \(i\in\{-2 n-1 ,\cdots,2 n-1 -1\}\), then the output digital signal is the binary sequence of \(i\); if the input electrical signal then discard the input electrical signal this time and do not output any digital signal;

[0011] At the same time, maximize the product value of the output minimum entropy and the signal utilization rate.

[0012] Furthermore, the electrical signal \(v\) satisfies a Gaussian distribution with a mean of 0 and a variance of and its probability distribution expression is

[0013]

[0014] Furthermore, calculate the minimum entropy in the following manner:

[0015]

[0016] \(H min =-\log_2[P max (3)

[0017] where \(P max represents the maximum probability falling into the central interval after ADC sampling and discretization; erf() is the error function; \(\sigma Q represents the standard deviation; \(H min represents the minimum entropy.

[0018] Furthermore, calculate the signal utilization rate in the following manner:

[0019]

[0020] \(r\) represents the signal utilization rate; \(\varPhi()\) represents the cumulative distribution function.

[0021] Compared with the prior art, the beneficial effects of the present invention are:

[0022] For input signals exceeding the ADC value range, the present invention chooses not to sample and output digital signals. At the same time, by maximizing the product value of the output minimum entropy and the data utilization rate of the quantum random number generator, the corresponding optimal sampling range is solved, so as to maximize the number of extractable random bits and the random number generation rate, and ensure the randomness of the output random numbers. Description of the Drawings

[0023] Figure 1Flow chart of an optimization method for the sampling range of an analog-to-digital converter in a quantum random number generator where quantum noise satisfies a Gaussian distribution according to an embodiment of the present invention;

[0024] Figure 2 Relationship diagram of ADC sampling range parameter R and parameter M according to an embodiment of the present invention. Detailed implementation manners

[0025] The present invention will be further explained and illustrated below in conjunction with the accompanying drawings and specific embodiments:

[0026] As Figure 1 shown, an optimization method for the sampling range of an analog-to-digital converter in a quantum random number generator where quantum noise satisfies a Gaussian distribution includes:

[0027] When the sampling accuracy of the analog-to-digital converter ADC is n-bit and the sampling range is [-R + δ / 2, R - 3δ / 2], discretize the ADC sampling range into 2 n quantization intervals, and the width of each interval δ = R / 2 n-1 ; the center of the sampling range is 0, and the first interval i min = -2 n-1 is centered at -R, and the last interval i max = 2 n-1 -1; where R is the ADC sampling range parameter;

[0028] If the input signal v ∈ [-R + δ / 2, R - 3δ / 2] and iδ - δ / 2 < v < iδ + δ / 2, where i ∈ {-2 n-1 ,..., 2 n-1 -1}, then the output digital signal is the binary sequence of i; if the input electrical signal then discard the input electrical signal this time and do not output any digital signal;

[0029] At the same time, maximize the product value of the output minimum entropy and the signal utilization rate.

[0030] Specifically, in a continuous quantum random number generator, the electrical signals generated by laser phase noise, amplified spontaneous emission noise, and vacuum state fluctuations all satisfy a Gaussian distribution. Without loss of generality, assume that the electrical signal v output by the detector in the quantum random number generator satisfies a Gaussian distribution with a mean of 0 and a variance of , and its probability distribution expression is

[0031]

[0032] where p Q (v) is the probability distribution of the electrical signal v.

[0033] Because the ADC will not output any digital signal when the input signal v exceeds the ADC sampling range, the input signal that satisfies the Gaussian distribution has the highest probability of falling into the center interval after being discretized by the ADC sampling, satisfying

[0034]

[0035] Among them, P max It represents the maximum probability of falling into the center interval after ADC sampling discretization; erf() is the error function; σ Q Represents standard deviation.

[0036] In the quantum random number generator scheme, due to the presence of classical information (such as electrical noise and thermal noise) in the process of quantum random number generation, the eavesdropper may use classical information to obtain part of the information in the original data. In order to accurately estimate the entropy content of the quantum noise in the entropy source, the minimum entropy is generally used to measure the quantum randomness of the entropy source, thereby determining the lower limit of the number of random bits that can be extracted from a single sampling. The worst-case minimum entropy is defined as

[0037] H min =-log2[P max ] (3)

[0038] In our method, the ADC sampling process discards signals that are not within the sampling range, which will cause a certain amount of data loss and affect the random number generation rate. Therefore, when optimizing the ADC sampling range, it is necessary to maximize the product of the minimum entropy output and the signal utilization rate to increase the number of extractable random bits and the random number generation rate. The signal utilization rate r can be measured based on the probability of falling within the ADC sampling range, and its expression is

[0039]

[0040] where Φ() represents the cumulative distribution function.

[0041] Therefore, the optimization of the ADC sampling range can be converted into a maximization problem

[0042] Max: M = r * H min (5)

[0043] Furthermore, in order to verify the effectiveness of this method, we conducted a numerical simulation and quantitative analysis. Assuming σ Q =5, n=8, according to the above formula, we can get the relationship diagram between ADC sampling range parameter R and parameter M, as shown in the figure: Figure 2 shown.

[0044] from Figure 2It can be seen that when the ADC sampling range parameter R takes a certain value, the product of the minimum entropy output of the quantum random number generator and the data utilization rate reaches a maximum value, achieving the maximum number of extractable random bits and random number generation rate.

[0045] In summary, the ADC sampling range optimization method proposed in this paper is specifically targeted at quantum random number generators whose quantum sources satisfy a Gaussian distribution. It proposes not sampling input signals outside the ADC sampling range and outputting digital signals, thereby ensuring the randomness of the output random numbers. By optimizing the ADC sampling range, the number of extractable random bits and the random number generation rate are maximized.

[0046] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A method for optimizing the sampling range of an analog-to-digital converter in a quantum random number generator whose quantum noise satisfies a Gaussian distribution, characterized in that: include: When the sampling accuracy of the analog-to-digital converter ADC is n-bit and the sampling range is [-R+δ / 2, R-3δ / 2], the ADC sampling range is discretized into 2 n quantization intervals, the width of each interval is δ = R / 2 n-1 ; The center of the sampling range is 0, and the first interval i is centered on -R min =-2 n-1 , the last interval i is centered on R-δ max =2 n-1 -1; where R is the ADC sampling range parameter; If the input signal \(v\in[-R + \delta / 2,R - 3\delta / 2]\) and \(i\delta-\delta / 2\lt v\lt i\delta+\delta / 2\), where \(i\in\{-2 n-1 ,\cdots,2 n-1 , - 1\}\), then the output digital signal is the binary sequence of \(i\); if the input electrical signal then discard the input electrical signal this time and do not output any digital signal; At the same time, the product value of output minimum entropy and signal utilization is maximized.

2. The method for optimizing the sampling range of an analog-to-digital converter in a quantum random number generator whose quantum noise satisfies a Gaussian distribution according to claim 1, characterized in that: The electrical signal v satisfies the mean of 0 and the variance of The Gaussian distribution of is expressed as 3. The method for optimizing the sampling range of an analog-to-digital converter in a quantum random number generator whose quantum noise satisfies a Gaussian distribution according to claim 1, characterized in that: The minimum entropy is calculated as follows: H min =-log2[P max ] (3) Among them, P max It represents the maximum probability of falling into the center interval after ADC sampling discretization; erf() is the error function; σ Q represents the standard deviation; H min represents minimum entropy.

4. The method for optimizing the sampling range of an analog-to-digital converter in a quantum random number generator whose quantum noise satisfies a Gaussian distribution according to claim 1, characterized in that: The signal utilization rate is calculated as follows: r represents the signal utilization rate; Φ() represents the cumulative distribution function.

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