CN115237375A - Method for optimizing sampling range of analog-to-digital converter in quantum random number generator aiming at quantum noise satisfying Gaussian distribution - Google Patents
Method for optimizing sampling range of analog-to-digital converter in quantum random number generator aiming at quantum noise satisfying Gaussian distribution Download PDFInfo
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Abstract
The invention relates to the technical field of quantum information communication, and discloses a method for optimizing the sampling range of an analog-digital converter in a quantum random number generator aiming at quantum noise satisfying Gaussian distribution. According to the invention, by optimizing the ADC sampling range, the extractable random bit number and the random number generation rate are maximized, and the randomness of the output random number is ensured.
Description
Technical Field
The invention relates to the technical field of quantum information communication, in particular to an optimization method of a sampling range of an analog-digital converter in a quantum random number generator aiming at quantum noise satisfying Gaussian distribution.
Background
With the development of the information era and the increasing degree of informatization of society, random numbers play a vital role in many fields, such as numerical simulation, basic science, information security and the like, and are widely applied in the fields of unpredictable cryptography and secret communication depending on random numbers. With the development of quantum information science, a quantum random number generator designed based on the quantum mechanical intrinsic randomness principle is considered to be capable of generating unpredictable true random numbers theoretically, and important guarantee is provided for the field of information security.
The quantum random number generator may be classified into a discrete type quantum random number generator and a continuous type quantum random number generator according to the kind of the light source. The discrete quantum random number generator is limited by the problems of single photon preparation speed, detector dead time and the like, and has the problem of low random number generation rate. The continuous quantum random number generator generates quantum random numbers by using noise sources such as laser phase noise, amplified spontaneous emission noise, vacuum fluctuation and the like, greatly improves the generation rate of the random numbers, and is gradually put into practical use. The detection means of the continuous quantum random number generator is a continuous optical detector, an output optical signal is converted into an electrical signal by the optical detector, the electrical signal is usually collected and quantized by an analog-to-digital converter (ADC), a binary digital sequence is output, and an original quantum random number is obtained. Therefore, ADCs play a crucial role as a physical device for signal acquisition in a continuous quantum random number generator.
In a quantum random number generator, for an ADC of a given sampling accuracy, the value of its sampling range affects the number of random bits that can be extracted and the output randomness. In addition, if the sampling range of the ADC is not properly selected, it is easy to cause waste of edge sampling intervals or unnecessary saturation, which finally affects the randomness of the output data, so that the random number is more easily predicted.
An analog-to-digital converter (ADC) is an important physical device in a quantum random number generator, and is used for discretizing sampling and quantizing an electrical signal into a digital signal. The input signal is sampled by an n-bit adc, the sampling range is discretized into intervals, and the input signal is quantized in quantization intervals. Haw [ J.Y.Haw, S.M.Assad, A.M.Lance, N.H.Y.Ng, V.Sharma, P.K.Lam, T.Symul.Maximilation of executable Random in a Quantum Random-NumberGenerator [ J ]. Physical Review Applied,2015,3 (5) ], et al, discuss sampling ranges of ADCs and propose an optimization method for maximizing the probability of the central interval of the ADC sampling range. In this method, input signals that exceed the sampling range of the ADC are accumulated into the first and last intervals of the ADC. Although the method ensures that no saturation or waste occurs in the edge sampling interval of the ADC, the probability of the first interval and the probability of the last interval are larger due to the sampling range calculated by the method, so that the randomness of the random number finally output by the quantum random number generator is influenced.
Disclosure of Invention
The invention provides an optimization method of the sampling range of an analog-digital converter in a quantum random number generator aiming at the problem that the sampling range optimization method of the analog-digital converter in the existing quantum random number generator influences the randomness of the random number finally output by the quantum random number generator, and the optimization method of the sampling range of the analog-digital converter in the quantum random number generator aiming at the condition that quantum noise meets Gaussian distribution can maximize the number of extractable random bits, improve the generation rate of the random number and ensure the randomness of output data.
In order to achieve the purpose, the invention adopts the following technical scheme:
a method for optimizing the sampling range of an analog-to-digital converter in a quantum random number generator in which the quantum noise satisfies a Gaussian distribution, comprising:
when the sampling precision of the ADC is n-bit, the sampling range is [ -R + delta/2,R-3 delta/2]In time, the ADC sampling range is discretized into 2 n Quantization intervals, each interval having a width δ = R/2 n-1 (ii) a The center of the sampling range is 0, and the center of-R is the first interval i min ＝-2 n-1 Centered on R-deltaIs the last interval i max ＝2 n-1 -1; wherein R is ADC sampling range parameter;
if the input signal v E [ -R + delta/2,R-3 delta/2]And i delta-delta/2<v<i delta + delta/2, wherein i ∈ { -2 n-1 ,...,2 n-1 -1}, the output digital signal is a binary sequence of i; if the input electric signal
Discarding the electrical signal input this time and not outputting any digital signal;
and simultaneously, the product value of the minimum entropy and the signal utilization rate is maximally output.
Further, the electric signal v satisfies a mean value of 0 and a variance of
Is expressed as a probability distribution of
Further, the minimum entropy is calculated as follows:
H min ＝-log 2 [P max ] (3)
wherein, P max Represents the maximum probability of falling into the central interval after the sampling discretization of the ADC; erf () is an error function; sigma Q Represents the standard deviation; h min Representing the minimum entropy.
Further, the signal utilization is calculated as follows:
r represents signal utilization; Φ () represents the cumulative distribution function.
Compared with the prior art, the invention has the following beneficial effects:
for input signals exceeding the value range of the ADC, the invention selects not to sample and output digital signals, and simultaneously solves the corresponding optimal sampling range by maximizing the product value of the output minimum entropy and the data utilization rate of the quantum random number generator, thereby realizing the maximization of the extractable random bit number and the random number generation rate and ensuring the randomness of the output random number.
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FIG. 1 is a flow chart of a method for optimizing the sampling range of an analog-to-digital converter in a quantum random number generator in which the quantum noise satisfies the Gaussian distribution according to an embodiment of the present invention;
fig. 2 is a diagram illustrating a relationship between a parameter R and a parameter M of an ADC sampling range according to an embodiment of the present invention.
Detailed Description
The invention is further illustrated by the following examples in conjunction with the accompanying drawings:
as shown in fig. 1, a method for optimizing a sampling range of an analog-to-digital converter in a quantum random number generator satisfying gaussian distribution for quantum noise includes:
when the sampling precision of the ADC is n-bit, the sampling range is [ -R + delta/2,R-3 delta/2]In time, the ADC sampling range is discretized into 2 n Quantization intervals, each interval having a width δ = R/2 n-1 (ii) a The center of the sampling range is 0, and the center of-R is the first interval i min ＝-2 n-1 With R-delta as the center as the last interval i max ＝2 n-1 -1; wherein R is ADC sampling range parameter;
if the input signal v E [ -R + delta/2,R-3 delta/2]And i delta-delta/2<v<i delta + delta/2, wherein i ∈ { -2 n-1 ,...,2 n-1 -1}, the output digital signal is a binary sequence of i; if the input electric signal
Discarding the electrical signal input this time and not outputting any digital signal;
and simultaneously, the product value of the minimum entropy and the signal utilization rate is maximally output.
Specifically, in the continuous quantum random number generator, the laser phase noise, the amplified spontaneous emission noise and the electric signals generated by the vacuum fluctuation all satisfy the gaussian distribution, and it is not assumed that the electric signals v output by the detector in the quantum random number generator satisfy the condition that the mean value is 0 and the variance is
Is expressed as a probability distribution of
Wherein p is Q (v) Is the probability distribution of the electrical signal v.
Because the ADC can not output any digital signal under the condition that the input signal v exceeds the sampling range of the ADC, the input signal meeting the Gaussian distribution has the maximum probability of falling into a central interval after the sampling discretization of the ADC, and meets the requirement of
Wherein P is max Represents the maximum probability of falling into the central interval after the sampling discretization of the ADC; erf () is an error function; sigma Q The standard deviation is indicated.
In the quantum random number generator scheme, due to the existence of classical information (such as electrical noise and thermal noise) in the quantum random number generation process, an eavesdropper may acquire partial information in original data by using the classical information, and in order to accurately estimate the entropy content of the quantum noise in an entropy source, the quantum randomness of the entropy source is generally measured by using the minimum entropy, so that the lower limit of the number of random bits extractable from a single sampling is determined. The worst-case minimum entropy is defined as
H min ＝-log 2 [P max ] (3)
In our method, the ADC sampling process discards signals that are not within the sampling range, which may cause a certain loss of data and affect the generation rate of random numbers. Therefore, when the sampling range of the ADC is optimized, it is necessary to maximize the product value of the output minimum entropy and the signal utilization rate, and increase the number of extractable random bits and the random number generation rate. The signal utilization rate r can be measured according to the probability falling into the sampling range of the ADC, and the expression is
Where Φ () represents the cumulative distribution function.
Thus, optimization of the ADC sampling range can translate into a maximization problem
Max：M＝r*H min (5)
Further, to test the effectiveness of this method, we performed numerical simulation quantitative analysis. Suppose σ Q =5,n =8, and a relationship diagram of the ADC sampling range parameter R and the parameter M can be obtained according to the above formula, as shown in fig. 2.
As can be seen from fig. 2, 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 has a maximum value, so that the extractable random bit number and the random number generation rate are maximized.
In summary, the ADC sampling range optimization method provided in the present invention is mainly directed to a quantum random number generator in which quantum sources satisfy gaussian distribution, and provides that digital signals are output without sampling input signals exceeding the ADC sampling range, so that the randomness of output random numbers can be ensured. By optimizing the ADC sampling range, maximizing the number of extractable random bits and the random number generation rate is achieved.
The above shows only the preferred embodiments of the present invention, and it should be noted that it is obvious to those skilled in the art that various modifications and improvements can be made without departing from the principle of the present invention, and these modifications and improvements should also be considered as the protection scope of the present invention.
Claims (4)
1. A method for optimizing the sampling range of an analog-to-digital converter in a quantum random number generator aiming at quantum noise satisfying Gaussian distribution is characterized by comprising the following steps:
when the sampling precision of the ADC is n-bit, the sampling range is [ -R + delta/2,R-3 delta/2]Time-discrete ADC sampling range to 2 n Quantization intervals, each interval having a width δ = R/2 n-1 (ii) a The center of the sampling range is 0, and the center of-R is the first interval i min ＝-2 n-1 With R-delta as the center as the last interval i max ＝2 n-1 -1; wherein R is ADC sampling range parameter;
if the input signal v E [ -R + delta/2,R-3 delta/2]And i delta-delta/2<v<i delta + delta/2, wherein i ∈ { -2 n-1 ,...,2 n-1 -1}, the output digital signal is a binary sequence of i; if the input electric signal
Discarding the electrical signal input this time, and not outputting any digital signal;
and simultaneously, the product value of the minimum entropy and the signal utilization rate is maximally output.
2. The method of claim 1, wherein the electrical signal v satisfies a mean of 0 and a variance of 0
Is expressed as a probability distribution of
3. The method of optimizing the sampling range of an analog-to-digital converter in a quantum random number generator in which quantum noise satisfies a gaussian distribution of claim 1, wherein the minimum entropy is calculated as follows:
H min ＝-log 2 [P max ] (3)
wherein, P max Represents the maximum probability of falling into the central interval after the sampling discretization of the ADC; erf () is an error function; sigma Q Represents the standard deviation; h min Representing the minimum entropy.
4. The method of claim 1, wherein the signal utilization is calculated as follows:
r represents signal utilization; Φ () represents a cumulative distribution function.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN117151237A (en) * | 2023-08-11 | 2023-12-01 | 正则量子(北京)技术有限公司 | Quantum random number generation method and device based on diode electron tunneling effect |
| GB2620734A (en) * | 2022-07-14 | 2024-01-24 | Cambridge Entpr Ltd | A physical random variate generator |
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| GB2620734A (en) * | 2022-07-14 | 2024-01-24 | Cambridge Entpr Ltd | A physical random variate generator |
| CN117151237A (en) * | 2023-08-11 | 2023-12-01 | 正则量子(北京)技术有限公司 | Quantum random number generation method and device based on diode electron tunneling effect |
| CN117151237B (en) * | 2023-08-11 | 2024-03-22 | 正则量子(北京)技术有限公司 | Quantum random number generation method and device based on diode electron tunneling effect |
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