CN114416022B

CN114416022B - Practical true random number generation device and method based on marker pairing coherent state light source

Info

Publication number: CN114416022B
Application number: CN202111522506.5A
Authority: CN
Inventors: 李元昊; 费洋扬; 马智; 王卫龙; 王洪; 孟祥栋; 段乾恒; 王娜
Original assignee: Information Engineering University of PLA Strategic Support Force
Current assignee: Information Engineering University of PLA Strategic Support Force
Filing date: 2021-12-14
Publication date: 2024-06-21
Anticipated expiration: 2041-12-14

Abstract

The invention belongs to the technical field of quantum information communication, and discloses a practical true random number generation device and method based on a mark pairing coherent state light source, wherein the device comprises the following steps: the device comprises a preparation device, a measurement device and a field programmable gate array; the measuring device is connected with the field programmable gate array; the preparation device is respectively connected with the measuring device and the field programmable gate array; the preparation device and the measurement device are mutually independent and do not share randomness; the dimensions of the preparation device and the measurement device are 2; the preparation device comprises a laser, an intensity modulator, a coherent state module, a first single photon detector and a first polarizer; the coherent state module and the first single photon detector form a mark pairing coherent state light source HPCS; the measuring device comprises a second polarizer, a polarizing beam splitter, a second single photon detector and a third single photon detector. The invention considers the influence of the rear pulse probability of the single photon detector and ensures the safety of the quantum random number generator system.

Description

Practical true random number generation device and method based on marker pairing coherent state light source

Technical Field

The invention belongs to the technical field of quantum information communication, and particularly relates to a practical true random number generation device and method based on a mark pairing coherent state light source.

Background

Random numbers are widely used in many fields, such as scientific simulations and cryptography [ Knuth D e.the Art of Computer programming, china MACHINE PRESS,1976 ]. The pseudo-random number generator uses a computer algorithm to generate a random sequence starting from an initial seed string, the security of which depends on the computational complexity of its sequence expansion algorithm, which may be threatened by quantum computation in the future. Therefore, in the field where the randomness requirement for random numbers is relatively high, the security of pseudo random numbers is not satisfactory for these applications.

True random number generators based on unpredictable physical processes have attracted extensive attention over the last decades, particularly Quantum Random Number Generators (QRNGs). Quantum random number generators based on quantum theory inherent randomness are considered to be the most efficient method of generating unpredictable random numbers [ Born M.quantimechnik derZ Phys 37:863.1926 ]. Over the past decades, various quantum random number generation protocols based on different sources have been proposed, such as detection of photon paths, photon arrival times, vacuum state fluctuations, laser phase noise, amplified spontaneous emission noise and other quantum phenomena. However, these protocols are truly random only if the device is trusted and the theoretical model conditions are met. In practice, real-world devices are often not trusted or perfect, and deviate from the theoretical model, which results in an inability to guarantee that the random numbers generated are truly random.

To solve this problem, researchers have proposed device independent quantum random number generators and semi-device independent quantum random number generators. The device-independent quantum random number generator is very impractical in both prior art and practical applications due to the detection vulnerability problem and extremely low random number generation rate limitations in Bell inequality experimental implementations. The half-device independent quantum random number generator uses the general assumption that the realization is easier, so that the compromise between the trusted requirement and the random number generation rate is realized, and the real requirement is met. Among them, in recent years, half device independent quantum random number generation protocols based on dimension witness have been attracting attention.

Although there have been many studies on quantum random number generation protocols based on dimension witnessing, in such studies, the implementation of the protocol must satisfy a precondition assumption that a single photon source is used as the quantum random source. Unfortunately, in the current art, there is no ideal single photon source. In experiments, researchers generally use Weak Coherent (WCS) light sources to replace ideal single photon sources to generate random numbers, and then a decoy state method is utilized, so that the influence of non-ideal single photon sources on random number generation can be solved to a certain extent. However, if the probability of vacuum component and multiphoton component in the coherent light source is large, the generation rate of random number is seriously affected.

Disclosure of Invention

Aiming at the problem that when a Weak Coherent (WCS) light source is used for replacing an ideal single photon source to generate random numbers, if the probability of a vacuum component and a multiphoton component in the coherent light source is high, the generation rate of the random numbers can be seriously influenced, the invention provides a practical true random number generation device and method based on a mark pairing coherent state light source, the HPCS is used as a quantum random source, higher minimum entropy can be obtained, more random bits are provided from original data, and the generation rate of the random numbers is improved.

In order to achieve the above purpose, the present invention adopts the following technical scheme:

In one aspect, the present invention provides a practical true random number generating device based on a marker pairing coherent state light source, including: the device comprises a preparation device, a measurement device and a field programmable gate array; the measuring device is connected with the field programmable gate array; the preparation device is respectively connected with the measuring device and the field programmable gate array; the preparation device and the measurement device are mutually independent and do not share randomness; the dimensions of the preparation device and the measurement device are 2;

The preparation device comprises a laser, an intensity modulator, a coherent state module, a first single photon detector and a first polarizer; the coherent state module is used for generating a pairing coherent state light source; the coherent state module and the first single photon detector form a mark pairing coherent state light source HPCS;

the measuring device comprises a second polarizer, a polarizing beam splitter, a second single photon detector and a third single photon detector.

Further, the laser, the intensity modulator, the coherent state module and the first polarizer are connected in sequence; the coherent state module is sequentially connected with the first single photon detector and the field programmable gate array; the first polarizer is connected to the field programmable gate array.

Further, the second polarizer, the polarizing beam splitter, the second single photon detector and the field programmable gate array are connected in sequence; the second polarizer, the polarization beam splitter, the third single photon detector and the field programmable gate array are connected in sequence; the second polarizer is connected to the field programmable gate array.

The invention also provides a practical true random number generation method based on the mark pairing coherent state light source, which comprises the following steps:

In the state preparation process, the preparation device attenuates pulses generated by the laser to different intensities by using an intensity modulator to generate a signal state, a decoy state and a vacuum state, and the signal state, the decoy state and the vacuum state are used as pump light for matching a coherent state; the pulse intensity lambda epsilon { mu, v, o }, mu, v, o represent the pulse intensities of the signal state, the decoy state and the vacuum state respectively, and satisfy mu > v > o; only when the first single photon detector responds will the pulse be encoded and sent to the measuring device;

According to the random number generated by the field programmable gate array, the preparation device uses a first polarizer to prepare the light pulse into a quantum state rho _x according to the random input bits x epsilon {0,1,2,3 }; then, the preparation device sends the prepared state rho _x to the measurement device through a quantum channel;

After receiving an input state, the measuring device randomly selects a y base according to a random number generated by the field programmable gate array to carry out projection measurement on the received state, and records all measurement results b, wherein y is {0,1}, and b is {0,1}; maintaining the polarization state of the light pulse unchanged or rotated by 45 degrees by using a second polarizer; the measuring device performs measurement of different bases according to the mode; the polarization beam splitter is utilized to split the light pulse, the measuring device obtains a measuring result according to the response of the second single photon detector and the third single photon detector, and the measuring result forms the original data R _raw;

After obtaining enough original data R _raw, the field programmable gate array obtains projection probability Pr (b|x, y) of a single photon state according to a measurement result, wherein Pr (b|x, y) represents the projection probability of the single photon state that the preparation device inputs x, the measurement device inputs y and the measurement result is b;

Estimating a single photon pulse conditional probability q ₁(b|x,y);q₁ (b|x, y) representing the contribution of the single photon pulse based on Pr (b|x, y) by using a decoy state method, wherein the single photon pulse conditional probability represents the single photon pulse with the preparation device input of x, the measurement device input of y and the measurement result of b; the dimension witness value W is obtained through q ₁ (b|x, y), then the upper bound of the average maximum guess probability p _guess is calculated according to W, the lower bound of the minimum entropy H _min, namely the random bit number which can be extracted by each running experiment, is determined, and finally the random bit number R _end＝H_min×R_raw which is extracted from the original data R _raw is obtained by a post-processing method.

Further, the dimension witness value W is derived according to the following formula:

further, under the condition that both x and y satisfy the uniform distribution, an average maximum guess probability p _guess is calculated according to the following formula:

further, the minimum entropy H _min is calculated according to the following formula:

H_min＝-log₂p_guess。

compared with the prior art, the invention has the beneficial effects that:

The invention can well estimate the contribution of the single photon pulse in the light pulse under the condition of no ideal single photon source, thereby accurately estimating the minimum entropy of the system. By using HPCS as a quantum random source, higher minimum entropy can be obtained, more random bits are proposed from the original data, and the generation rate of random numbers is improved. The invention considers the influence of the rear pulse probability of the single photon detector and ensures the safety of the quantum random number generator system.

Drawings

FIG. 1 is a schematic diagram of a practical true random number generating device based on a marker-pairing coherent light source according to an embodiment of the present invention;

FIG. 2 is a diagram illustrating the lower and upper bounds of the ideal q ₁ (b|x, y) and q ₁ (b|x, y) under practical test conditions;

FIG. 3 is a graph of HPCS and WCS light source minimum entropy as a function of overall detection efficiency η;

FIG. 4 is a graph of minimum entropy with overall first order post pulse rate Is a variation graph of (a).

Detailed Description

The invention is further illustrated by the following description of specific embodiments in conjunction with the accompanying drawings:

As shown in fig. 1, a practical true random number generating device based on a marker pairing coherent state light source includes: a preparation device (Alice), a measurement device (Bob) and a Field Programmable Gate Array (FPGA); the measuring device is connected with the field programmable gate array; the preparation device is respectively connected with the measurement device and the field programmable gate array in sequence; the preparation device and the measurement device are mutually independent and do not share randomness; the dimensions of the preparation device and the measurement device are 2;

The preparation device comprises a Laser (Laser), an Intensity Modulator (IM), a coherent state module (PCS), a first single photon detector (D) and a first Polarizer (POL); the coherent state module is used for generating a pairing coherent state light source; the coherent state module and the first single photon detector form a mark pairing coherent state light source HPCS;

The measuring device comprises a second polarizer, a Polarizing Beam Splitter (PBS), a second single photon detector (D0) and a third single photon detector (D1).

Based on the above embodiment, the present invention further provides a practical true random number generating method based on the marker pairing coherent state light source, including:

During state preparation Alice attenuates the laser generated pulses to different intensities using an Intensity Modulator (IM) to generate signal states, a decoy state and a vacuum state, which are used as pump light for the paired coherent states. The intensities λ ε { μ, v, o }, μ, v, o of the pulses represent the pulse intensities of the signal, spoof, and vacuum states, respectively, and satisfy μ > v > o. Only when single photon detector D responds will the pulse be encoded and transmitted to Bob.

From Random Numbers (RNs) generated by Field Programmable Gate Arrays (FPGAs), alice prepares light pulses into quantum states ρ _x (i.e., signal, spoof, or vacuum states) from random input bits xe {0,1,2,3} using Polarizers (POL). Alice then sends the prepared state ρ _x to Bob via a quantum channel.

After receiving the input state, bob randomly selects a y base according to the random number generated by the FPGA to perform projection measurement on the received state, and records all measurement results b, wherein y epsilon {0,1}, and b epsilon {0,1}. With POL the polarization state of the light pulse kept unchanged or rotated 45 °, bob can achieve measurements on different bases. The light pulses are split using a Polarizing Beam Splitter (PBS) and Bob knows from the response of detectors D ₀ and D ₁ whether the measurement results are 1 or 0, which constitute the raw data.

After obtaining enough original data R _raw, the projection probability Pr (b|x, y) of the single photon state can be obtained according to the measurement result, pr (b|x, y) represents the projection probability of the single photon state with the preparation device input of x, the measurement device input of y and the measurement result of b, and the projection probability is satisfiedTr () represents a tracing function,/>Representing the measurement operator.

Estimating a single photon pulse conditional probability q ₁(b|x,y);q₁ (b|x, y) representing the contribution of the single photon pulse based on Pr (b|x, y) by using a decoy state method, wherein the single photon pulse conditional probability represents the single photon pulse with the preparation device input of x, the measurement device input of y and the measurement result of b; after the conditional probability q ₁ (b|x, y) of the single photon pulse is obtained, the dimension witness value W can be further estimated. Then, according to the calculated dimension witness value, the upper bound of the average maximum guess probability p _guess can be calculated, and the lower bound of the minimum entropy H _min, that is, the number of random bits which can be extracted in each running experiment, can be further determined. Thus, the random number of bits that can be finally extracted from the original data using post-processing methods is R _end＝H_min×R_raw. The average maximum guess probability p _guess can be expressed by the equation under the assumption that both x and y satisfy the uniform distributionCalculating; minimum entropy H _min satisfies H _min＝-log₂p_guess.

Specifically, the properties of the coherent state light source HPCS are as follows:

The PCS is first proposed [Agarwal G S.Generation of Pair Coherent States and Squeezing via the Competition of Four-Wave Mixing and Amplified Spontaneous Emission[J].Physical Review Letters,1986,57(7):827.], by Agwal, which is essentially an optical number-dependent state. By applying photon prediction techniques on the PCS, a so-called HPCS can be generated, in which the probability of a vacuum state can be reduced to a negligible level. PCS is a coherent state of two-mode association, which can be written as:

Where μ is the average intensity of the pulse and I ₀ (x) is a modified Bessel function of the first type. By using photonic prophetic techniques, one mode of the HPCS may be triggered and the other mode used to encode information.

Considering that the detection efficiency of the detector at Alice end is η _A and the dark count rate is d _A, the probability that Alice end emits n photons can be written as:

Wherein P _post (μ) is the post-selection probability, satisfying

For WCS light sources, the probability of including n photons in the emitted pulse is such that the poisson distribution is satisfied:

The composition of the HPCS and WCS light sources was compared by selecting different light intensities, as shown in table 1, in which the detection efficiency η _A =0.75 and the dark count rate of Alice-side detector is d _A＝10^-6.

Table 1 probabilities of inclusion of vacuum, single photon and multiphoton in HPCS and WCS at different light intensities.

Further, the safety analysis of the method of the invention is as follows:

First, we need to build a quantum channel model and a detection model. The transmission loss in the quantum channel is denoted as t _AB, the detection efficiency at Bob end is denoted as η _Bob, and the overall transmission and detection efficiency between Alice and Bob can be expressed as η=t _ABη_Bob. The threshold Single Photon Detector (SPD) used by the Bob end has the advantages that due to the imperfect SPD device, the dark count and the back pulse of the SPD device can influence the safety of the QRNG system, the dark count is d, the back pulse probability is P _ap, and the effective event of single click of the SPD in the k-photon state is that:

The post-pulse of the SPD has a considerable effect on the high-speed QRNG system, increasing the response probability of the detector. For a decoy qng scheme, the post-pulse may affect the estimation of the single photon state contribution, potentially resulting in an overestimation of the minimum entropy. The post-pulse of the SPD is non-markov in nature, and its probability can be expressed as:

Wherein the method comprises the steps of The first order post pulse rate representing the whole is an intrinsic feature of the SPD,/>Is the previous response ratio of the ignored post pulse. Considering the condition that the contribution of the rear pulse to the two SPDs is completely unbalanced, i.e. one SPD always responds earlier than the other, the rear pulse probability of the SPD can be rewritten as/>

The overall observation probability Q _λ for a light intensity λ can be expressed as:

Wherein λ ε { μ, v, o } represents the intensity of light; q _i (b|x, y) represents the conditional probability that when i photons are transmitted, alice inputs x, bob inputs y, the measurement is b, and can be written as:

Wherein the method comprises the steps of Representing the two coefficients. By taking the equation (4) and the equation (7) into the equation (6), it is possible to obtain:

To estimate the randomness of the protocol, q ₁ (b|x, y) representing the single photon state contribution should be derived, but not directly from the measurement results. Using the decoy-state approach, the upper and lower bounds of q ₁ (b|x, y) can be estimated. When v < μ, q ₁ (b|x, y) lower bound can be estimated by:

The first inequality applies the relationship a ⁱ-bⁱ≤a²-b² when a.gtoreq.b.gtoreq.0 and i.gtoreq.2. Therefore, the lower bound of q ₁ (b|x, y) is:

Wherein Q ₀＝1+(d-1)(1-P_ap).

Likewise, the upper bound of q ₁ (b|x, y) can be estimated from the following inequality:

Wherein the method comprises the steps of To prove the inequality in the equation. Thus, the upper bound of q ₁ (b|x, y) is:

further considering the existence of vacuum state, the upper bound of the correction is:

Strictly speaking, equations (10) and (13) cannot be used for parameter estimation in practical experiments, which are affected by the limited total number of pulses, and thus statistical fluctuation effects should be taken into account in our analysis. Assuming that the total number of pulses transmitted by Alice consists of three cases, n=n _μ+N_v+N_o,N_μ is the number of signal state pulses, N _v is the number of decoy state pulses, and N _o is the number of vacuum states. From the statistical fluctuation analysis, it can be derived that the following equation corrects the estimation of q ₁ (b|x, y):

where σ is the standard deviation one chooses for statistical fluctuation analysis. Thus (2) And/>Can be written as:

Considering actual light sources, physical devices, and statistical fluctuations, the dimension witness value W can be calculated by:

Based on the equation (16) and the equation (17), the lower bound of W can be estimated. Then, according to definition of average maximum guess probability p _guess Its upper bound can be estimated. Further, the minimum entropy H _min＝-log₂p_guess of the QRNG system can be calculated, and the number of random bits that can be extracted per run experiment can be determined. And finally, extracting the random bit number R _end＝H_min×R_raw from the original data R _raw by a post-processing method.

To verify the effect of the invention, the following experiments were performed:

Numerical simulation is performed on the method provided by the invention, the projection probability is Pr (0|0, 0) =Pr (0|2, 1) =0, pr (0|1, 0) =Pr (0|3, 1) =1, pr (0|2, 0) =Pr (0|3, 0) =Pr (0|0, 1) =Pr (0|1, 1) =0.5, the dark count rate of the bob end is d=10 ^-6, the detection efficiency of the Alice end is η _A =0.75, the dark count rate is d _A＝10^-6, the standard difference sigma is equal to 6.3, the corresponding failure probability is 10 ^-7, the signal state light intensity mu is 0.5, and the decoy light intensity v is 0.1.

The expression q ₁ (b|x, y), q ₁(b|x,y)＝(1-η)[1-(1-d_A)(1-η_A) ]+ηpr (b|x, y) under progressive conditions can be known from equation (7). In a limited case, the lower and upper bounds of q ₁ (b|x, y) can be estimated from equation (16) and equation (17). The value of q ₁ (b|x, y) is divided into three cases according to Pr (b|x, y) = 0,1,0.5, and the overall first-order post pulse rate of the detector is assumedThe total pulse number n=10 ^-9, 0.05, shows the variation of q ₁ (b|x, y) with the overall detection efficiency η, and the results are shown in fig. 2. We can find that the lower and upper bounds of q ₁ (b|x, y) overlap almost with the ideal case of using an infinite number of decoy states. Based on the estimated result, the minimum entropy H _min is further calculated. Fig. 3 shows the variation of the minimum entropy H _min with the overall detection efficiency η under asymptotic conditions and under practical experimental conditions, where n=10 ^-5,10^-7,10^-9. With the increase of the value of N, the minimum entropy calculated by using the three-intensity decoy method proposed by us is closer to the asymptotic case of using infinite decoy states. In fig. 3, we also compare the minimum entropy of QRNGs using HPCS light sources and WCS light sources. It can be seen that a higher minimum entropy can be obtained using the HPCS light source with a total number of light pulses of n=10 ^-9.

The impact of post-pulse probability on the QRNG system is further investigated below. In this numerical simulation, we assume that the overall detection efficiency η=0.75, the total number of light pulses is n=10 ^-5, the minimum entropy H _min and the overall first order post pulse rateThe relationship of (2) is shown in FIG. 4. We can find that the post-pulse probability has a significant effect on the minimum entropy, when/>Increasing from 0 to 0.1, the minimum entropy is reduced by approximately 4.3%. Therefore, in practical experiments, if the influence of the post pulse is not considered, information leakage of the QRNG system may be caused, and the safety of the QRNG system is threatened.

To sum up, since in practice there is no ideal single photon source, one generally uses WCS light sources instead of ideal single photon sources. However, the probability of single photons contained in the single photon source is low, and a large amount of vacuum components exist, which is unfavorable for the generation of random numbers. The invention creatively proposes to use HPCS as a random source to replace the conventional WCS light source. The HPCS light source contains a higher probability of single photon component, and the vacuum and multiphoton components are smaller than those in the WCS light source, so that the HPCS light source is more suitable for a quantum random number generator of a decoy state scheme. In order to accurately estimate the contribution of single photon pulses, we propose to use a three-intensity decoy-state scheme in the quantum random number generation protocol, which can better estimate the minimum entropy of the system. Compared to WCS-based quantum random number generators, quantum random number generators designed with HPCS can generate higher minimum entropy.

The invention creatively considers the imperfection of an actual device, and in a high-speed quantum random number generator, the rear pulse probability of a single photon detector at the Bob end has larger influence on the randomness of the generated random number. In the method, the actual post-pulse influence is considered, the minimum entropy of the quantum random number generator under the condition can be accurately estimated under the condition that the post-pulse probability of the detector is known, and the system is ensured not to be influenced by the post-pulse probability.

The foregoing is merely illustrative of the preferred embodiments of this invention, and it will be appreciated by those skilled in the art that changes and modifications may be made without departing from the principles of this invention, and it is intended to cover such modifications and changes as fall within the true scope of the invention.

Claims

1. A practical true random number generating device based on a marker pairing coherent state light source, which is characterized by comprising: the device comprises a preparation device, a measurement device and a field programmable gate array; the measuring device is connected with the field programmable gate array; the preparation device is respectively connected with the measuring device and the field programmable gate array; the preparation device and the measurement device are mutually independent and do not share randomness; the dimensions of the preparation device and the measurement device are 2;

The measuring device comprises a second polarizer, a polarizing beam splitter, a second single photon detector and a third single photon detector;

a practical true random number generation method based on a marker pairing coherent state light source based on the true random number generation device comprises the following steps:

2. The practical true random number generating device based on a marker-pairing coherent state light source according to claim 1, wherein the laser, the intensity modulator, the coherent state module and the first polarizer are connected in sequence; the coherent state module is sequentially connected with the first single photon detector and the field programmable gate array; the first polarizer is connected to the field programmable gate array.

3. The practical true random number generating device based on the mark pairing coherent state light source according to claim 1, wherein the second polarizer, the polarizing beam splitter, the second single photon detector and the field programmable gate array are connected in sequence; the second polarizer, the polarization beam splitter, the third single photon detector and the field programmable gate array are connected in sequence; the second polarizer is connected to the field programmable gate array.

4. The practical true random number generating device based on the mark pairing coherent state light source according to claim 1, wherein the dimension witness value W is obtained according to the following formula:

5. the practical true random number generating device based on the marker-pairing coherent light source according to claim 1, wherein the average maximum guess probability p _guess is calculated according to the following formula under the condition that x and y satisfy uniform distribution:

6. The practical true random number generating device based on the mark pairing coherent state light source according to claim 1, wherein the minimum entropy H _min is calculated according to the following formula:

H_min＝-log₂p_guess。