CN113821943A - Randomness quantization model and method for ASE noise quantum random number generation scheme - Google Patents

Randomness quantization model and method for ASE noise quantum random number generation scheme Download PDF

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CN113821943A
CN113821943A CN202111392749.1A CN202111392749A CN113821943A CN 113821943 A CN113821943 A CN 113821943A CN 202111392749 A CN202111392749 A CN 202111392749A CN 113821943 A CN113821943 A CN 113821943A
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calculating
optical signal
noise
quantum
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吴梅
徐兵杰
杨杰
樊矾
刘金璐
李扬
黄伟
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CETC 30 Research Institute
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    • G06—COMPUTING; CALCULATING OR COUNTING
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    • G06F30/20—Design optimisation, verification or simulation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
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    • G06F7/00—Methods or arrangements for processing data by operating upon the order or content of the data handled
    • G06F7/58—Random or pseudo-random number generators
    • G06F7/588—Random number generators, i.e. based on natural stochastic processes
    • G—PHYSICS
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    • G—PHYSICS
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    • G06F—ELECTRIC DIGITAL DATA PROCESSING
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    • G06—COMPUTING; CALCULATING OR COUNTING
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    • G06F2119/10—Noise analysis or noise optimisation

Abstract

The invention discloses a randomness quantification model and a method of an ASE noise quantum random number generation scheme, wherein the method comprises the following steps: s1, calculating the number of ASE light source modesM(ii) a S2, calculating the average photon number of the ASE optical signal in each mode
Figure 676861DEST_PATH_IMAGE001
(ii) a S3, calculating the sampling voltagevAnd number of photonsnIntegrated response coefficient ofc(ii) a S4, calculating the corresponding probability distribution of the quantum signals in the sampling voltage
Figure 921898DEST_PATH_IMAGE002
And minimum entropy
Figure 232793DEST_PATH_IMAGE003
. The method can evaluate the classical electric noise ratio in the initial sequence, quantitatively evaluate the randomness generated purely by the quantum process, and thus improve the safety of the output random sequence.

Description

Randomness quantization model and method for ASE noise quantum random number generation scheme
Technical Field
The invention relates to the field of random number generation schemes, in particular to a randomness quantification model and a randomness quantification method of an ASE noise quantum random number generation scheme.
Background
Random numbers play an important role in the fields of gaming, statistical sampling, computational simulation, cryptography, information security, quantum secure communications, and the like. How to generate high-speed and high-quality true random numbers safely and reliably is the key of key security protection, and is an important research direction of cryptography and information security.
Depending on the generation approach, current generation schemes for random number generators are largely divided into two categories: pseudo-random number generators and physical random number generators. Pseudo-random number generators, which are generated using deterministic computer algorithms, are widely used in modern digital electronic information systems. However, due to the deterministic and predictable nature of the algorithm, pseudorandom numbers are not suitable for applications requiring true randomness, such as cryptographic and information security systems. Physical random number generators observe a non-deterministic physical process to obtain random sequences, and the current physical random number generators are classified into two categories: classical noise based random number generators and quantum noise based random number generators. The noise source employed by a classical noise based random number generator can be fully described in classical physics: such as thermal noise of electronic components, jitter of oscillators, clock drift and the like, it is difficult for such random number generators to establish a strict mathematical model to prove the safety of the random number generators, and the random number generation rate is low. In contrast, Quantum Random Number Generators (QRNGs) have the following advantages: 1. the QRNG generates a high-quality random sequence by observing quantum noise, has safety which can be strictly verified theoretically, and can generate a true random sequence which is infinitely long, non-periodic, independent and uniformly distributed theoretically; 2. the generation rate is high, the random number generation rate of QRNG can reach 100Gbps magnitude, and the generation rate is far beyond a random number generator based on classical noise.
Over the past decades, several QRNG schemes have been proposed and proven, including detecting photon paths, photon arrival times, photon number distribution, vacuum fluctuations, quantum phase fluctuations, and Amplified Spontaneous Emission (ASE) noise, among others. Among the constructed QRNG methods, the ASE noise scheme has been widely spotlighted and studied because of its simple structure and high rate. On one hand, spontaneous emission is a typical quantum random phenomenon, and ASE noise is an amplification result of a spontaneous emission noise signal with random intensity, can be directly measured through a Photoelectric Detector (PD), does not need a complex interference optical path and feedback control, and is good in practicability. On the other hand, ASE noise can be easily generated using a fiber amplifier or a super bright light emitting diode (SLED). In addition, ASE noise typically has a flat spectrum over a wide frequency range, and thus can be combined with high-speed detection and acquisition systems to generate high-speed random numbers.
The principle of the quantum random number generation scheme based on the ASE noise is shown in fig. 1, an amplified spontaneous emission noise optical signal is generated by an ASE light source, a random electric signal is generated by photoelectric conversion of the ASE noise optical signal by a high-speed photoelectric detector PD, a random electric signal is sampled by a high-speed analog-to-digital converter ADC to obtain an original random sequence, and a data post-processing is performed on the original random sequence by a high-speed post-processing module to obtain a final random sequence. The common data post-processing methods such as truncation exclusive or and Toeplitz are all based on the initial sequence minimum entropy calculation directly to obtain the final output random sequence length. In the actual detection process, the PD detection output result includes not only the variation caused by the noise optical signal but also the system background electrical noise. Therefore, the influence of classical electrical noise is included in the calculation of the initial sequence minimum entropy, and the final random sequence still includes classical electrical noise components. In principle, an eavesdropper can acquire the final random sequence part information by controlling the classical electric noise information of the system, and the system has potential safety hazards.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a randomness quantification model and a randomness quantification method of an ASE noise quantum random number generation scheme, which can evaluate the classical electric noise ratio in an initial sequence and quantitatively evaluate the randomness generated purely by a quantum process, thereby improving the safety of an output random sequence.
The purpose of the invention is realized by the following scheme:
a stochastic quantization model for an ASE noise quantum random number generation scheme, comprising:
ASE noise signal generator with ASE light source in each time windowiInternal, ASE light sources all emitn i Photon number is a random variable subject to independent and same distribution;
a detection device provided with a photoelectric detector for detecting photons of ASE light source and generating photocurrenti i The photocurrent of the light sourcei i And number of photonsn i Is proportional, i.e.
Figure 838702DEST_PATH_IMAGE001
Whereinc 1Is the response coefficient of the photodetector;
a sampling device, in which an analog-to-digital converter ADC is arranged for sampling the photocurrent of the photodetector and obtaining corresponding output voltagev i The voltage and the photocurrenti i Is proportional and contains classical electrical noise, i.e.
Figure 423267DEST_PATH_IMAGE002
Whereinc 2Is the response coefficient of the ADC sampling circuit.
A randomness quantification method suitable for an ASE noise quantum random number generation scheme is based on a randomness quantification model of the ASE noise quantum random number generation scheme in the scheme, and comprises the following steps:
s1, measuring the spectrum width of ASE optical signal
Figure 794206DEST_PATH_IMAGE003
Combined system electronics bandwidth
Figure 556756DEST_PATH_IMAGE004
Calculating the number of ASE light source modesM；
S2, measuring the output power of ASE optical signalPCombined with detection time windowTAnd center wavelength of optical signal
Figure 645935DEST_PATH_IMAGE005
Calculating the average photon number of the ASE optical signal in each mode
Figure 768612DEST_PATH_IMAGE006
；
S3, measuring average sampling voltage values corresponding to different optical powers
Figure 259636DEST_PATH_IMAGE007
Calculating the sampling voltagevAnd number of photonsnIntegrated response coefficient ofc；
S4, calculating the corresponding probability distribution of the quantum signals in the sampling voltage
Figure 443622DEST_PATH_IMAGE008
And minimum entropy
Figure 754518DEST_PATH_IMAGE009
。
Further, in step S1, the method includes the sub-steps of: calculating the number of ASE light source modes according to the following formulaM：
Figure 680886DEST_PATH_IMAGE010
Obeying a Gaussian shape to a spectral shapeASE optical signal of (2), number of modes thereof
Figure 308307DEST_PATH_IMAGE011
By polarization factor
Figure 458666DEST_PATH_IMAGE012
Spectral width of optical signal actually detected by photodetector
Figure 256857DEST_PATH_IMAGE013
Bandwidth of system electronics
Figure 236184DEST_PATH_IMAGE014
Directly determining; wherein, when the system is polarized light, the polarization factor
Figure 436221DEST_PATH_IMAGE015
(ii) a When the system is unpolarized, the polarization factor
Figure 960743DEST_PATH_IMAGE016
；
Figure 246231DEST_PATH_IMAGE017
Is an error function; exp refers to an exponential function with e as the base; in this embodiment, the optical signal is spectrally broad
Figure 530713DEST_PATH_IMAGE013
3dB bandwidth of an ASE light source can be measured for a spectrometer; bandwidth of system electronics
Figure 585257DEST_PATH_IMAGE014
Depending on the detector bandwidth.
Further, in step S2, the method includes the sub-steps of:
s21, calculating the average photon number of the ASE optical signal in each mode according to the following formula
Figure 280680DEST_PATH_IMAGE018
：
For containing
Figure 53464DEST_PATH_IMAGE019
The ASE optical signal of the independent mode, the statistical distribution of the photon number of which follows the glass color-Einstein distribution:
Figure 374593DEST_PATH_IMAGE020
wherein
Figure 283643DEST_PATH_IMAGE021
The average number of photons of the ASE noise light source,
Figure 415547DEST_PATH_IMAGE022
is a gamma function;
if each mode of the ASE light source has equal average photon number, the optical power before entering the photoelectric detector is measured by the optical power meterPThen calculating the average photon number of each mode
Figure 410048DEST_PATH_IMAGE023
：
Figure 36332DEST_PATH_IMAGE024
WhereinhIs the constant of the planck constant and,cis the speed of light in a vacuum,
Figure 799889DEST_PATH_IMAGE025
is the center wavelength of the optical signal,
Figure 837115DEST_PATH_IMAGE026
PD-dependent probe bandwidth;
Figure 318912DEST_PATH_IMAGE027
represents the average number of photons over the detection time,Trepresents a detection time window;
s22, mixingMAnd
Figure 247423DEST_PATH_IMAGE023
into step S21
Figure 865486DEST_PATH_IMAGE028
The calculation formula (2) calculates the theoretical distribution of photon numbers of the ASE optical signals detected in the actual detection; in this case, the theoretical photon number distribution of the ASE optical signal
Figure 604772DEST_PATH_IMAGE028
Reduced to one photon-only numbernAs a function of the argument, isn~P(n)：
Figure 308286DEST_PATH_IMAGE029
。
Further, in step S3, the method includes the sub-steps of:
s31, detecting the number of photons in each time windownWith corresponding sampled output voltagevThe relationship between is described as:
Figure 276373DEST_PATH_IMAGE030
whereineRepresenting detected electronic noise;
s32, performing experiments under different light powers by adopting a single-frequency laser with stable power; the average photon number per time window under different optical powers is calculated according to the following formula
Figure 14522DEST_PATH_IMAGE031
Figure 659130DEST_PATH_IMAGE032
Measuring corresponding average sampling voltage under different optical power
Figure 115519DEST_PATH_IMAGE033
A value; for different optical powers
Figure 126112DEST_PATH_IMAGE031
、
Figure 984347DEST_PATH_IMAGE034
Linear function fitting is carried out to obtain comprehensive response coefficientc：
Figure 534277DEST_PATH_IMAGE035
。
Further, in step S4, the method includes the sub-steps of:
s41, calculating the resolution according to the following formula:
Figure 477962DEST_PATH_IMAGE036
；
Figure 53431DEST_PATH_IMAGE037
；
Figure 500593DEST_PATH_IMAGE038
；
Figure 487003DEST_PATH_IMAGE039
which means that the rounding is made up,mthe minimum increment of the number of detection photons required for the change of the collected voltage value,
Figure 652405DEST_PATH_IMAGE040
for the expected increment due to a single photon,v max 、v min respectively the maximum and minimum values of the sampled voltage,lengththe sampling voltage is the value type.
S42, in the detection sampling output result, the measured voltage probability distribution corresponding to the quantum signal is characterized as:
Figure 264521DEST_PATH_IMAGE041
s43, calculating the minimum entropy of quantum part observation results in the sampling results
Figure 831769DEST_PATH_IMAGE042
Extracting a quantum true random sequence as a post-processing input parameter; wherein, the minimum entropy calculation formula is as follows:
Figure 254660DEST_PATH_IMAGE043
。
the beneficial effects of the invention include:
the embodiment of the invention provides a physical model capable of describing the processes of ASE noise signal generation, detection and sampling aiming at an ASE noise quantum random number generation scheme, and provides a novel randomness quantification method suitable for the ASE noise quantum random number generation scheme based on the physical model. The randomness quantization model and the method can evaluate the classical electric noise ratio in the initial sequence, quantitatively evaluate the randomness generated purely by a quantum process, and therefore the safety of the output random sequence is improved.
The physical model and the randomness quantification method provided by the invention have strong feasibility and universality and are suitable for a QRNG system for detecting the quantum state of randomly distributed photons.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to these drawings without creative efforts.
FIG. 1 is a schematic block diagram of an ASE noise quantum random number generation based scheme;
FIG. 2 is a physical model of ASE optical signal generation, detection, and sampling according to an embodiment of the present invention;
FIG. 3 shows QRNG system resolution ofmTime of flight，And sampling the probability statistical distribution of the voltage.
Detailed Description
All features disclosed in all embodiments in this specification, or all methods or process steps implicitly disclosed, may be combined and/or expanded, or substituted, in any way, except for mutually exclusive features and/or steps.
Example 1
As shown in fig. 2, a stochastic quantization model of ASE noise quantum random number generation scheme includes:
ASE noise signal generator with ASE light source in each time windowiInternal, ASE light sources all emitn i Photon number is a random variable subject to independent and same distribution;
a detection device provided with a photoelectric detector for detecting photons of ASE light source and generating photocurrenti i The photocurrent of the light sourcei i And number of photonsn i Is proportional, i.e.
Figure 641779DEST_PATH_IMAGE001
Whereinc 1Is the response coefficient of the photodetector;
a sampling device, in which an analog-to-digital converter ADC is arranged for sampling the photocurrent of the photodetector and obtaining corresponding output voltagev i The voltage and the photocurrenti i Is proportional and contains classical electrical noise, i.e.
Figure 559050DEST_PATH_IMAGE002
Whereinc 2Is the response coefficient of the ADC sampling circuit.
Example 2
It should be noted that, in this embodiment, as shown in fig. 1, a stochastic quantization method using an ASE noise quantum random number generation scheme is based on a stochastic quantization model of the ASE noise quantum random number generation scheme, and includes the following steps:
s1, measuring the spectrum width of ASE optical signal
Figure 980804DEST_PATH_IMAGE003
Combined system electronics bandwidth
Figure 574597DEST_PATH_IMAGE004
Calculating the number of ASE light source modesM；
S2, measuring the output power of ASE optical signalPCombined with detection time windowTAnd center wavelength of optical signal
Figure 714591DEST_PATH_IMAGE005
Calculating the average photon number of the ASE optical signal in each mode
Figure 402930DEST_PATH_IMAGE006
；
S3, measuring average sampling voltage values corresponding to different optical powers
Figure 944770DEST_PATH_IMAGE007
Calculating the sampling voltagevAnd number of photonsnIntegrated response coefficient ofc；
S4, calculating the corresponding probability distribution of the quantum signals in the sampling voltage
Figure 443884DEST_PATH_IMAGE008
And minimum entropy
Figure 71175DEST_PATH_IMAGE009
。
Example 3
Based on embodiment 2, it should be noted that, in this embodiment, in step S1, the sub-step is included: calculating the number of ASE light source modes according to the following formulaM：
Figure 64670DEST_PATH_IMAGE010
For ASE optical signals whose spectral shape follows Gaussian
Figure 461016DEST_PATH_IMAGE011
By polarization factor
Figure 131032DEST_PATH_IMAGE012
Spectral width of optical signal actually detected by photodetector
Figure 245618DEST_PATH_IMAGE013
Bandwidth of system electronics
Figure 541339DEST_PATH_IMAGE014
Directly determining; wherein, when the system is polarized light, the polarization factor
Figure 792192DEST_PATH_IMAGE015
(ii) a When the system is unpolarized, the polarization factor
Figure 633109DEST_PATH_IMAGE016
(ii) a erf (x) represents an error function; exp refers to an exponential function with e as the base; spectral width of optical signal
Figure 234992DEST_PATH_IMAGE013
3dB bandwidth of an ASE light source can be measured for a spectrometer; bandwidth of system electronics
Figure 570289DEST_PATH_IMAGE014
Depending on the detector bandwidth.
Example 4
Based on embodiment 2, it should be noted that, in this embodiment, in step S2, the sub-step is included:
s21, calculating the average photon number of the ASE optical signal in each mode according to the following formula
Figure 941228DEST_PATH_IMAGE018
：
For containing
Figure 953046DEST_PATH_IMAGE019
The ASE optical signal of the independent mode, the statistical distribution of the photon number of which follows the glass color-Einstein distribution:
Figure 42225DEST_PATH_IMAGE020
wherein
Figure 408310DEST_PATH_IMAGE021
The average number of photons of the ASE noise light source,
Figure 633755DEST_PATH_IMAGE022
is a gamma function;
if each mode of the ASE light source has equal average photon number, the optical power before entering the photoelectric detector is measured by the optical power meterPThen calculating the average photon number of each mode
Figure 816475DEST_PATH_IMAGE023
：
Figure 127370DEST_PATH_IMAGE024
WhereinhIs the constant of the planck constant and,cis the speed of light in a vacuum,
Figure 601208DEST_PATH_IMAGE025
is the center wavelength of the optical signal,
Figure 946739DEST_PATH_IMAGE026
depending on the photodetector bandwidth;
Figure 300360DEST_PATH_IMAGE027
represents the average number of photons over the detection time,Trepresents a detection time window;
s22, mixingMAnd
Figure 347819DEST_PATH_IMAGE023
into step S21
Figure 77878DEST_PATH_IMAGE028
The formula for the calculation of (a) is,calculating the photon number theoretical distribution of the ASE optical signal detected in the actual detection; in this case, the theoretical photon number distribution of the ASE optical signal
Figure 277915DEST_PATH_IMAGE028
Reduced to one photon-only numbernAs a function of the argument, isn~P(n)：
Figure 802437DEST_PATH_IMAGE029
。
Example 5
Based on embodiment 2, it should be noted that, in this embodiment, in step S3, the sub-step is included:
s31, detecting the number of photons in each time windownWith corresponding sampled output voltagevThe relationship between is described as:
Figure 838657DEST_PATH_IMAGE030
whereineRepresenting detected electronic noise;
s32, performing experiments under different light powers by adopting a single-frequency laser with stable power; the average photon number per time window under different optical powers is calculated according to the following formula
Figure 106827DEST_PATH_IMAGE044
Figure 364634DEST_PATH_IMAGE032
Measuring average sampling voltage values corresponding to different optical powers
Figure 122374DEST_PATH_IMAGE033
(ii) a For different optical powers
Figure 98420DEST_PATH_IMAGE031
、
Figure 950707DEST_PATH_IMAGE034
Linear function fitting is carried out to obtain comprehensive response coefficientc：
Figure 125337DEST_PATH_IMAGE035
。
Example 6
Based on embodiment 2, it should be noted that, in this embodiment, in step S4, the sub-step is included:
s41, calculating the resolution according to the following formula:
Figure 991662DEST_PATH_IMAGE036
；
Figure 455004DEST_PATH_IMAGE037
；
Figure 612447DEST_PATH_IMAGE038
；
Figure 641583DEST_PATH_IMAGE039
which means that the rounding is made up,mthe minimum increment of the number of detection photons required for the change of the collected voltage value,
Figure 944388DEST_PATH_IMAGE040
for the expected increment due to a single photon,v max 、v min respectively the maximum and minimum values of the sampled voltage,lengththe value types of the sampling voltages are obtained;
s42, in the detection sampling output result, the measured voltage probability distribution corresponding to the quantum signal is characterized as:
Figure 675453DEST_PATH_IMAGE041
s43, calculating the minimum entropy of quantum part observation results in the sampling results
Figure 292379DEST_PATH_IMAGE042
Extracting a quantum true random sequence as a post-processing input parameter; wherein, the minimum entropy calculation formula is as follows:
Figure 176021DEST_PATH_IMAGE043
。
the technical conception principle, the specific working process, the technical effect and the like of the scheme design of the invention are further explained in detail as follows: aiming at an ASE noise quantum random number generation scheme, the embodiment of the invention provides a physical model capable of describing the processes of ASE noise signal generation, detection and sampling, and simultaneously provides a randomness quantization method suitable for the ASE noise quantum random number generation scheme based on the physical model, so that the randomness purely generated by a quantum process in an initial sequence is quantized, the classic electrical noise ratio is evaluated, the data post-processing is carried out on the basis of the classic electrical noise ratio, and the safety of the output sequence of the QRNG system is improved.
The core steps of the ASE noise-based quantum random number generation scheme are as follows: the physical model of generation, detection and sampling of ASE noise signals is shown in fig. 2. From the time domain, in each detection time window of the PD (the detection time window is equal to the reciprocal of the detection bandwidth of the PD), the ASE light source generates an optical signal containing a certain number of photons, and at the same time, the PD detects the optical signal and outputs a photocurrent proportional to the number of photons, and finally, the ADC samples the photocurrent and obtains a voltage signal proportional to the magnitude of the photocurrent. The sampling voltage is in direct proportion to the number of photons in corresponding time, and the sampling voltage and the number of photons in corresponding time have consistent statistical characteristics, so that sampling voltage sequences in different time windows obey independent and same distribution and can be used for generating random numbers, and a specific model in the embodiment of the invention is constructed as follows:
(1) first, in each time windowiIn all, ASE light sources will emitn i One photon, the number of photons is a random variable subject to independent co-distribution.
(2) The PD then detects the photons and generates a photocurrenti i The photocurrent of the light sourcei i And number of photonsn i Is proportional, i.e.
Figure 649728DEST_PATH_IMAGE001
Whereinc 1Is the response coefficient of the PD.
(3) Finally, the ADC samples the photocurrent and obtains a corresponding output voltagev i The voltage and the photocurrenti i Is proportional and contains classical electrical noise, i.e.
Figure 618821DEST_PATH_IMAGE002
Whereinc 2Is the response coefficient of the ADC sampling circuit.
Based on the physical model, the embodiment of the invention provides a randomness quantification method suitable for an ASE noise quantum random number generation scheme, which comprises the following specific steps:
step 1: measuring spectral width of ASE optical signal
Figure 321329DEST_PATH_IMAGE003
Combined system electronics bandwidth
Figure 325057DEST_PATH_IMAGE004
Calculating the number of ASE light source modesM
(ii) a For ASE optical signals whose spectral shape follows GaussianMBy polarization factor
Figure 969665DEST_PATH_IMAGE012
Spectral width of optical signal actually detected by PD
Figure 426054DEST_PATH_IMAGE003
Bandwidth of system electronics
Figure 436647DEST_PATH_IMAGE004
And (4) directly determining. Wherein, when the system is polarized light, the polarization factor
Figure 29303DEST_PATH_IMAGE015
(ii) a When the system is unpolarized, the polarization factor
Figure 844812DEST_PATH_IMAGE016
(ii) a exp refers to an exponential function with e as the base; spectral width of optical signal
Figure 788497DEST_PATH_IMAGE013
Measuring the 3dB bandwidth of the ASE light source for the spectrometer; bandwidth of system electronics
Figure 98387DEST_PATH_IMAGE004
Typically depending on the detector bandwidth.
Figure 811128DEST_PATH_IMAGE010
Step 2: measuring ASE optical signal output powerPCombined with detection time windowTAnd center wavelength of optical signal
Figure 531959DEST_PATH_IMAGE005
Calculating the average photon number of the ASE optical signal in each mode
Figure 228520DEST_PATH_IMAGE018
For containingMThe ASE optical signal of the independent mode, the statistical distribution of the photon number of which follows the glass color-Einstein distribution:
Figure 309477DEST_PATH_IMAGE020
wherein
Figure 407883DEST_PATH_IMAGE021
The average number of photons of the ASE noise light source,
Figure 34037DEST_PATH_IMAGE022
is a gamma function.
Assuming that the ASE light source has an equal average number of photons per mode, the optical power before entering the PD is measured by an optical power meterPThe average photon number of each mode can be calculated
Figure 952314DEST_PATH_IMAGE023
：
Figure 604007DEST_PATH_IMAGE045
WhereinhIs the constant of the planck constant and,cis the speed of light in a vacuum,
Figure 291340DEST_PATH_IMAGE025
is the center wavelength of the optical signal,
Figure 353974DEST_PATH_IMAGE026
typically depending on the detector bandwidth.
Will be provided withMAnd
Figure 493968DEST_PATH_IMAGE023
substitution into
Figure 447886DEST_PATH_IMAGE028
Theoretically, the theoretical distribution of the number of photons of the ASE optical signal detected in the actual test can be calculated. In this case, the theoretical photon number distribution of the ASE optical signal
Figure 989726DEST_PATH_IMAGE028
Can be simplified into a number of photons onlynAs a function of the argument, can be written asn~P(n)。
Figure 488841DEST_PATH_IMAGE029
And step 3: measuring average sampling voltage values corresponding to different optical powers
Figure 381710DEST_PATH_IMAGE033
Calculating the sampling voltagevAnd number of photonsnIntegrated response coefficient ofc（
Figure 375205DEST_PATH_IMAGE046
）。
Theoretical statistical distribution of photon counts due to ASE optical signalsn~P(n) The probability that the PD detects different photon numbers is indicated, and the actual final sampling output is a series of voltage values, wherein the voltage observed values comprise system electrical noise and photon number fluctuation noise.
Consider thatvAndnthe number of photons detected in each time windownWith corresponding sampled output voltagevThe relationship between can be described as:
Figure 771552DEST_PATH_IMAGE030
whereineRepresenting detected electronic noise, for the entire QRNG system, coefficientscTheoretically remaining unchanged.
Experiments were performed with single frequency lasers of stable power at different optical powers. On the one hand, the average photon number of each time window under different optical powers is calculated
Figure 175988DEST_PATH_IMAGE031
Figure 290575DEST_PATH_IMAGE032
On the other hand, the average sampling voltage corresponding to different optical powers is measured
Figure 320716DEST_PATH_IMAGE033
The value is obtained. For different optical powers
Figure 837148DEST_PATH_IMAGE031
、
Figure 474803DEST_PATH_IMAGE034
The linear function fitting is carried out to obtain the comprehensive response coefficientc
Figure 827418DEST_PATH_IMAGE035
And 4, step 4: calculating probability distribution corresponding to quantum signal in sampling voltage
Figure 411983DEST_PATH_IMAGE047
And minimum entropy
Figure 782922DEST_PATH_IMAGE042
Since the PD cannot satisfy the requirement of analyzing each photon number in the actual detection process, the minimum increment of the detected photon number required for the change of the collected voltage value is assumed to bemWhen the number of photons is increased as shown in FIG. 3mWithin the interval, a unique voltage value is acquired.
Since the sampling voltage is proportional to the number of photons detected in each time window, and the expected increment due to a single photon is
Figure 794740DEST_PATH_IMAGE038
. Accordingly, the number of the first and second electrodes,mthe increment caused by one photon is
Figure 619606DEST_PATH_IMAGE048
In principle, the voltage to be detected should be increased by a minimum amount
Figure 273441DEST_PATH_IMAGE048
Linearly changing. The minimum increment of the sampling voltage of the actual system is
Figure 233307DEST_PATH_IMAGE049
Whereinv max 、v min Respectively the maximum and minimum values of the sampled voltage,lengththe sampling voltage is the value type. Due to the fact that
Figure 416027DEST_PATH_IMAGE050
So the system resolution can be calculated as:
Figure 539972DEST_PATH_IMAGE036
wherein the content of the first and second substances,
Figure 200760DEST_PATH_IMAGE039
meaning rounding up because the number of photons detected during the actual measurement is an integer.
Therefore, the probability distribution of the measured voltage corresponding to the quantum signal in the output result of the detection sampling can be characterized as
Figure 280712DEST_PATH_IMAGE041
And finally, calculating the minimum entropy of observation results of quantum parts in the sampling results, and taking the minimum entropy as a post-processing input parameter to extract a quantum true random sequence. Wherein, the minimum entropy calculation formula is as follows:
Figure 149179DEST_PATH_IMAGE043
the parts not involved in the present invention are the same as or can be implemented using the prior art.
The above-described embodiment is only one embodiment of the present invention, and it will be apparent to those skilled in the art that various modifications and variations can be easily made based on the application and principle of the present invention disclosed in the present application, and the present invention is not limited to the method described in the above-described embodiment of the present invention, so that the above-described embodiment is only preferred, and not restrictive.
Other embodiments than the above examples may be devised by those skilled in the art based on the foregoing disclosure, or by adapting and using knowledge or techniques of the relevant art, and features of various embodiments may be interchanged or substituted and such modifications and variations that may be made by those skilled in the art without departing from the spirit and scope of the present invention are intended to be within the scope of the following claims.

Claims (6)

1. A stochastic quantization model for an ASE noise quantum random number generation scheme, comprising:
ASE noise signal generator with ASE light source in each time windowiInternal, ASE light sources all emitn i Photon number is a random variable subject to independent and same distribution;
a detection device provided with a photoelectric detector for detecting photons of ASE light source and generating photocurrenti i The photocurrent of the light sourcei i And number of photonsn i Is proportional, i.e.
Figure 364056DEST_PATH_IMAGE001
Whereinc 1Is the response coefficient of the photodetector;
a sampling device, in which an analog-to-digital converter (ADC) is arranged for sampling the photocurrent of the photodetector and obtaining corresponding output voltagev i The voltage and the photocurrenti i Is proportional and contains classical electrical noise, i.e.
Figure 874672DEST_PATH_IMAGE002
Whereinc 2Is the response coefficient of the ADC sampling circuit.
2. A randomness quantization method applicable to ASE noise quantum random number generation scheme, based on a randomness quantization model of the ASE noise quantum random number generation scheme of claim 1, and comprising the steps of:
s1, measuring the spectrum width of ASE optical signal
Figure 841359DEST_PATH_IMAGE003
Combined system electronics bandwidth
Figure 439831DEST_PATH_IMAGE004
Calculating the number of ASE light source modesM；
S2, measuring the output power of ASE optical signalPCombined with detection time windowTAnd center wavelength of optical signal
Figure 723045DEST_PATH_IMAGE005
Calculating the average photon number of the ASE optical signal in each mode
Figure 263616DEST_PATH_IMAGE006
；
S3, measuring average sampling voltage values corresponding to different optical powers
Figure 999491DEST_PATH_IMAGE007
Calculating the sampling voltagevAnd number of photonsnIntegrated response coefficient ofc；
S4, calculating the corresponding probability distribution of the quantum signals in the sampling voltage
Figure 667233DEST_PATH_IMAGE008
And minimum entropy
Figure 804953DEST_PATH_IMAGE009
。
3. A randomness quantization method applicable to ASE noise quantum random number generation schemes according to claim 2, characterized in that in step S1, it comprises the sub-steps of: calculating the number of ASE light source modes according to the following formulaM：
Figure 510567DEST_PATH_IMAGE010
For ASE optical signals whose spectral shape follows Gaussian
Figure 733738DEST_PATH_IMAGE011
By polarization factor
Figure 939591DEST_PATH_IMAGE012
Spectral width of optical signal actually detected by photodetector
Figure 931818DEST_PATH_IMAGE013
Bandwidth of system electronics
Figure 79771DEST_PATH_IMAGE014
Directly determining; wherein, when the system is polarized light, the polarization factor
Figure 790238DEST_PATH_IMAGE015
(ii) a When the system is unpolarized, the polarization factor
Figure 268624DEST_PATH_IMAGE016
；
Figure 380937DEST_PATH_IMAGE017
Is an error function; exp refers to an exponential function with e as the base.
4. A randomness quantization method applicable to ASE noise quantum random number generation schemes according to claim 2, characterized in that in step S2, it comprises the sub-steps of:
s21, calculating the average photon number of the ASE optical signal in each mode according to the following formula
Figure 434212DEST_PATH_IMAGE018
：
For containing
Figure 631975DEST_PATH_IMAGE019
The ASE optical signal of the independent mode, the statistical distribution of the photon number of which follows the glass color-Einstein distribution:
Figure 445211DEST_PATH_IMAGE020
wherein
Figure 146450DEST_PATH_IMAGE021
The average number of photons of the ASE noise light source,
Figure 901786DEST_PATH_IMAGE022
is a gamma function;
if each mode of the ASE light source has equal average photon number, the optical power before entering the photoelectric detector is measured by the optical power meterPThen calculating the average photon number of each mode
Figure 321266DEST_PATH_IMAGE023
：
Figure 672613DEST_PATH_IMAGE025
WhereinhIs the constant of the planck constant and,cis the speed of light in a vacuum,
Figure 493938DEST_PATH_IMAGE026
is the center wavelength of the optical signal,
Figure 154595DEST_PATH_IMAGE027
depending on the photodetector bandwidth;
Figure 61372DEST_PATH_IMAGE028
represents the average number of photons over the detection time,Trepresents a detection time window;
s22, mixingMAnd
Figure 950830DEST_PATH_IMAGE023
into step S21
Figure 892241DEST_PATH_IMAGE029
The calculation formula (2) calculates the theoretical distribution of photon numbers of the ASE optical signals detected in the actual detection; in this case, the theoretical photon number distribution of the ASE optical signal
Figure 740112DEST_PATH_IMAGE029
Reduced to one photon-only numbernAs a function of the argument, isn~P(n)：
Figure 383452DEST_PATH_IMAGE030
。
5. A randomness quantization method applicable to ASE noise quantum random number generation schemes according to claim 2, characterized in that in step S3, it comprises the sub-steps of:
s31, detecting the number of photons in each time windownWith corresponding sampled output voltagevThe relationship between is described as:
Figure 76601DEST_PATH_IMAGE031
whereineRepresenting detected electronic noise;
s32, performing experiments under different light powers by adopting a single-frequency laser with stable power; the average photon number per time window under different optical powers is calculated according to the following formula
Figure 606939DEST_PATH_IMAGE032
Figure 360132DEST_PATH_IMAGE033
Measuring average sampling voltage values corresponding to different optical powers
Figure 490768DEST_PATH_IMAGE034
(ii) a For different optical powers
Figure 987608DEST_PATH_IMAGE032
、
Figure 638032DEST_PATH_IMAGE035
Linear function fitting is carried out to obtain comprehensive response coefficientc：
Figure 296547DEST_PATH_IMAGE036
。
6. A randomness quantization method applicable to ASE noise quantum random number generation schemes according to claim 2, characterized in that in step S4, it comprises the sub-steps of:
s41, calculating the resolution according to the following formula:
Figure 914479DEST_PATH_IMAGE037
；
Figure 949431DEST_PATH_IMAGE038
；
Figure 719941DEST_PATH_IMAGE039
；
Figure 814936DEST_PATH_IMAGE040
which means that the rounding is made up,mthe minimum increment of the number of detection photons required for the change of the collected voltage value,
Figure 660444DEST_PATH_IMAGE041
the expected increment for a single photon;
s42, in the detection sampling output result, the measured voltage probability distribution corresponding to the quantum signal is characterized as:
Figure 764666DEST_PATH_IMAGE042
s43, calculating the minimum entropy of quantum part observation results in the sampling results
Figure 124103DEST_PATH_IMAGE043
Extracting a quantum true random sequence as a post-processing input parameter; wherein, the minimum entropy calculation formula is as follows:
Figure 390000DEST_PATH_IMAGE044
。
CN202111392749.1A 2021-11-23 2021-11-23 Randomness quantization model and method for ASE noise quantum random number generation scheme Pending CN113821943A (en)

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