A measurement device-independent quantum random number generation method

Abstract

The present invention proposes a method for generating quantum random numbers independently of measurement devices in four-intensity entrapped states, which can be applied to quantum information processing systems that have higher requirements for security and loss resistance. In the present invention, the transmitting end randomly prepares light pulses of four different intensities, one of which is used as a signal state and the other three as entrapped states; the measuring end can compactly and effectively estimate the channel parameters through the data in the three entrapped states with different intensities, optimize the randomness of the system, and thus improve the final quantum random number generation rate and transmission distance. The present invention proposes for the first time a method for generating quantum random numbers independently of measurement devices in four-intensity entrapped states, which greatly improves the loss resistance of channel transmission and the efficiency of quantum random number generation compared with previous similar methods.

Description

Technical Field

[0001] The present invention relates to the transmission security (ability to resist channel loss) of four-intensity decoy states of a weak coherent source (WCS) light source and a random coding rate extraction system, and in particular to a measurement device-independent quantum random number generation method suitable for a WCS light source. Background Art

[0002] Random numbers have a wide range of applications in cryptography, secure communications, and quantitative finance. How to quickly generate a large number of random numbers is a core technical challenge. Although some computer-generated random numbers (called pseudo-random numbers) can be authenticated by various programs, they depend on given algorithms and random number seeds, which can be predicted in theory and may introduce security vulnerabilities into applications. In recent years, with the development of quantum information technology, people have discovered that the inherent randomness of quantum mechanics can be used to generate true random numbers, called quantum random number generators (QRNGs), which have extremely high uncertainty and can be used in uncertain physical processes, such as measuring collapse and vacuum fluctuations.

[0003] Based on whether the device is trustworthy, quantum random number generators are divided into three categories: device-trusted quantum random number generators, device-independent quantum random number generators (Device Independent-QRNG, DI-QRNG), and semi-device-independent quantum random number generators (Semi Device Independent-QRNG, SDI-QRNG). Device-trusted quantum random number generators assume that the device is completely trustworthy and can generate random numbers at high speed under ideal conditions. This type of quantum random number generator technology is relatively mature and has gradually been commercialized. However, the perfect assumption of the device may not meet the actual application, leading to corresponding security issues. The device-independent quantum random number generator assumes that the device is completely untrustworthy, mainly based on the violation of Bell inequality. From the perspective of security, the device-independent quantum random number generator has the highest security, but due to the limitations of existing experimental technology, its random number generation rate is very low. Therefore, a compromise method is proposed, namely the semi-device-independent random number generator, which only makes partial assumptions about the device, but can greatly increase the random number generation rate and has higher security than the device-trusted quantum random number generator.

[0004] The semi-device-independent quantum random number generator protocol includes a source end for preparing quantum states and a measurement end for measuring the prepared states, and generates a series of random bit strings through the measurement results. The semi-device-independent quantum random number generator is further divided into a source device-independent quantum random number generator (Source Independent-QRNG, SI-QRNG) and a measurement device-independent quantum random number generator (Measurement Device Independent QRNG, MDI-QRNG). Among them, the measurement device-independent quantum random number generator assumes that the measurement device is unreliable, and can continue to generate random numbers even if the detector is inefficient.

[0005] Although the measurement device-independent quantum random number generator can continuously generate random bit strings under low efficiency, the random bit rate generated by previous methods is often low and has poor resistance to channel loss. In this case, the security of the system is bound to be affected, so it is necessary to improve the random key generation rate and resistance to channel loss of the quantum random number generator. Summary of the invention

[0006] The purpose of the present invention is to address the insufficiency of the MDI-QRNG based on the three-intensity decoy state of the weak coherent state light source in the ability to resist channel loss, and propose a measurement device-independent quantum random number generator protocol based on the four-intensity decoy state of the WCS light source. The method is used in the random bit rate extraction system. In the state preparation stage of random bit generation, the optical pulse is divided into a signal state s, a decoy state v, a decoy state w and a decoy state φ. The signal state prepares a quantum state +, and the decoy state randomly prepares one of the four states 0, 1, +, +i for testing. The user sends the quantum state to a special measurement party for measurement, and there is no need to require the credibility of the measurement party. The present invention has the security of being independent of the measurement device, and can resist the side channel attack on the measurement device. Compared with the MDI-QRNG protocol based on the three-intensity decoy state of the weak coherent state light source, the present invention greatly improves the channel transmission loss resistance and random coding rate.

[0007] The technical solution adopted by the present invention to solve its technical problems is: a measurement device-independent quantum random number generator protocol based on a WCS light source, which mainly includes a state preparation phase and a measurement phase. In the state preparation phase, Alice prepares a + state and a decoy state through the signal state of the light source to randomly prepare one of the four states 0, 1, +, +i, and then sends the quantum state to the measuring party Bob, who measures the received quantum state. In the measurement phase, the measurement end is subjected to a quantum tomography process through different decoy states, and the POVM parameters are calculated. Finally, the signal state s is measured by the Z basis vector to extract the final randomness size R.

[0008] Invention content: To achieve the above technical effects, the present invention proposes a method for generating quantum random numbers based on a WCS light source and a measurement device-independent four-intensity entrapped state, which uses a measurement device-independent protocol to extract random bits and is applied to a random number generation system that enhances the channel's anti-loss capability. The method includes a quantum state preparation phase and a quantum state measurement phase, involving the sender Alice and the measurer Bob.

[0009] A measurement device-independent quantum random number generation method of the present invention comprises the following steps:

[0010] Step 1: Alice randomly modulates N light source pulses into four different intensities using a seed random number, represented as intensities φ, v, w, and s, and then divides all light pulses into four subsets: S φ ,S v ,S w and S s ,The four subsets are the vacuum state φ, the decoy state v, the decoy state w, and the signal state s set, which encode the four light source intensities and send them to Bob's end;

[0011] Step 2: Bob performs POVM measurement on all transmitted light pulses, estimates the results after POVM measurement to obtain the contribution of single photons, and finally performs Z basis vector measurement on the signal state s to extract the randomness size R.

[0012] Furthermore, in step 2, Bob performs POVM measurement on all transmitted optical pulses, estimates the results after POVM measurement to obtain the contribution of single photons, and finally performs Z basis vector measurement on the signal state s to extract the randomness size R, which specifically includes the following steps:

[0013] Step 2.1, Bob performs POVM measurement on all transmitted optical pulses;

[0014] The POVM measurement of the source intensity γ is expressed as:

[0015]

[0016] In the formula, p k|γ represents the probability of k photons under the light source intensity γ, F b|k represents a POVM measurement with output b at k photons.

[0017] The trapped state of the light pulse is randomly projected to (I+σ z ) / 2、(I-σ z ) / 2、(I+σ x ) / 2、(I+σ y) / 2, the probability of the output result being b when the light source intensity is γ(γ∈{s,v,w}) and the preparation state is m(m∈{0,1,+,+i}) is expressed as:

[0018]

[0019] Among them, a b|k represents the probability of getting output b when sending k photons, b∈{0,1}, σ=(σ x ,σ y ,σ z ) represents the Pauli operator, represents a three-dimensional real vector on the Bloch sphere with output b under k photons,

[0020] If the pulse sent comes from the vacuum state, then no matter what the encoded information and the measurement operator are, the probability of the output being b is always a. b|0 , that is, Q b|φ =a b∣0 .

[0021] Step 2.2, estimate the contribution of single photons based on the results after POVM measurement, specifically:

[0022] Define the estimated probability p k|γ The upper and lower bounds of and

[0023]

[0024] Where N γ is the number of γ pulses sent, ξ(m',q) is the error function;

[0025] For a 0|1 The upper and lower bounds of the joint estimation are calculated to calculate the parameter a 0|1 The lower bound for:

[0026]

[0027] in, It represents the estimated lower bound of the probability that the output result of sending a single photon is 0 under statistical fluctuations. represents the estimated upper bound of the probability of getting an output of 0 when sending zero photons, taking into account statistical fluctuations.

[0028]

[0029] In the above formula, c1≥0 should be satisfied, which is equivalent to requiring the inequality For the convenience of calculation, let uw =2u v , and set Then the above inequality can be established. Similarly, for a 0|1 The upper bound of Do a similar tight estimate:

[0030]

[0031] in, It represents an estimated lower bound on the probability of getting a zero output result from sending zero photons, taking into account statistical fluctuations.

[0032] Furthermore, according to the calculation Parameters and The lower bounds are calculated separately:

[0033]

[0034]

[0035] in, They represent the three-dimensional vector when the output result is 0 under single photon The second and third elements of

[0036] Step 2.3, perform Z basis vector measurement on the signal state s and extract the randomness size R;

[0037] Under the following constraints:

[0038] 0≤a 0|k ≤1,b=0,1,k=0,1,2…,

[0039]

[0040] Finally, the random key extraction rate is obtained:

[0041]

[0042] in, represents the lower bound estimate of the probability of a single photon in signal state s under statistical fluctuations, N s represents the number of pulse photons in the signal state, N represents the total number of pulse photons sent by the light source, and H ∞ (x) = -log2max(x, 1-x) represents the binary minimum entropy function.

[0043] Furthermore, in step 2.1, F b|k It represents a POVM measurement with an output of b under the condition of k photons. The POVM measurement process of the quantum state sent by the detector is related to the measurement basis, output and pulse photon number, which is expressed as follows:

[0044]

[0045] Among them, a b|k , Satisfy the constraints:

[0046] a b|k ≥0,a 0|k +a 1|k =1,

[0047]

[0048] Furthermore, in step 2.1, Bob performs POVM measurement on all transmitted optical pulses. When the detector at the receiving end is triggered, all output results b∈{0,1} will be output as a random bit sequence. The value of b depends on which of the two detectors is responded. If the two detectors do not respond or both respond at the same time, then the user can randomly take the value 0 or 1.

[0049] Furthermore, in step 1, the intensities of the four light sources are encoded respectively, specifically:

[0050] The decoy states v and w are randomly encoded into one of the four states 0, 1, +, +i, where The signal state s is encoded as |+a state.

[0051] The beneficial effects are: compared with the previous quantum random number generation method based on three-intensity entrapped states of weak coherent state light source, the method of the present invention adopts a measurement device-independent quantum random number generator protocol based on four-intensity entrapped states. Compared with the quantum random number generation method based on three-intensity entrapped states of weak coherent state light source, its random number generation rate and ability to resist channel loss are greatly improved under given conditions, ensuring the security of transmission. Simulation results show that it has good performance in all aspects. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 It is a schematic diagram of the method of the present invention.

[0053] Figure 2 It is a specific flow chart of the method of the present invention.

[0054] Figure 3 When the number of light source pulses is N = 10 12 Below is a comparison chart of the random number generation rates of the method of the present invention and the three-intensity decoy state MDI-QRNG.

[0055] Figure 4 It is a comparison chart of the random number generation rate and channel loss resistance capability of the method of the present invention under different pulse numbers.

[0056] Figure 5 It is a comparison diagram of the randomness generation rate of the method of the present invention and the three-intensity decoy state based on the weak coherent state light source at 10dB loss being affected by different light source pulse numbers. DETAILED DESCRIPTION

[0057] In order to deepen the understanding of the present invention, the present invention will be further described in detail below in conjunction with examples. The examples are only used to explain the present invention and do not constitute a limitation on the protection scope of the present invention.

[0058] The present invention proposes a method for generating quantum random numbers based on a weak coherent state light source and a four-intensity entrapped state measurement device-independent method. The method uses a measurement device-independent protocol to extract random bit rates and is applied to a random number generation system that improves random coding rate and channel loss resistance. The method includes a quantum state preparation phase and a quantum state measurement phase, involving the user Alice and the measurement party Bob.

[0059] The specific steps include:

[0060] Step 1, preparing quantum state;

[0061] Alice is the quantum state preparer and sender. Alice randomly modulates N light source pulses into four different intensities (φ, v, w, s) using a seed random number, and then divides all light pulses into four subsets: S φ ,S v ,S w ,S s , with S φ +S v +S w +S s ={1,2,…,N}, the four subsets represent the vacuum state φ, the decoy state v, the decoy state w, and the signal state s respectively.

[0062] The decoy states v and w are randomly encoded into one of the four states 0, 1, +, +i, where And all signal states s are encoded as |+a state;

[0063] Step 2, measuring the quantum state;

[0064] Bob is the receiver and the measuring party. Bob performs generalized measurement POVM on the state sent by Alice.

[0065] In step 2.1, Bob performs POVM measurement on all transmitted optical pulses. When the detector at the receiving end is triggered, all output results b∈{0,1} will be output as a random bit sequence. The value of b depends on which of the two detectors is responded. If the two detectors do not respond or both respond at the same time, then the user can randomly take the value 0 or 1.

[0066] Step 2.2, estimate the result after POVM measurement to obtain the contribution of single photons, and finally perform Z basis vector measurement on the signal state s to extract the final randomness size R.

[0067] Any two-dimensional POVM measurement can be expressed as follows:

[0068]

[0069] Corresponding to output 0, 1 respectively, are all three-dimensional real vectors, is a vector composed of three Pauli matrices, and the parameters in F0 and F1 satisfy:

[0070] a0,a1≥0,a0+a1=1,

[0071]

[0072] The probability of measuring a quantum state ρ and outputting the result 0 or 1 is:

[0073] Pr(0|ρ)=Tr(ρF0),

[0074] Pr(1|ρ)=Tr(ρF1).

[0075] Extended to multi-photon states, the POVM measurement operator acting on a k-photon pulse with a measurement result of b is expressed as F b|k , then:

[0076]

[0077] In the above formula, a b|k represents the probability of getting output b when sending k photons, σ=(σ x ,σ y ,σ z ) represents the Pauli operator, represents a three-dimensional real vector on the Bloch sphere with output b for k photons. If a pulse is in the vacuum state, the actual POVM measurement is assumed to be F b∣0 =a b∣0 I, all parameters satisfy:

[0078] a b|k≥0,a 0|k +a 1|k =1,k≥0,

[0079]

[0080] Furthermore, the POVM measurement of the light source intensity γ is expressed as:

[0081]

[0082] In the formula, p k|γ represents the probability of k photons under the light source intensity γ.

[0083] The trapped state of the light pulse is randomly projected to (I+σ z ) / 2、(I-σ z ) / 2、(I+σ x ) / 2、(I+σ y ) / 2, the probability of the output result being b when the light source intensity is γ(γ∈{s,v,w}) and the preparation state is m(m∈{0,1,+,+i}) is expressed as:

[0084]

[0085] If the pulse sent comes from the vacuum state, then no matter what the encoded information and the measurement operator are, the probability of the output being b is always a. b|0 , i.e. Q b|φ =a b∣0 .

[0086] For all Q b∣(γ,m) To expand further:

[0087] Q 0|φ =a b∣0 ,b∈{0,1},

[0088]

[0089] In the above formula, Q 0∣(s,+) Take Q as an example for analysis. 0∣(s,+) Expand into the following three parts:

[0090] Q 0∣(s,+) =Prob(0) = Prob(0|vacuum)e -u +Prob(0|singlephoton)ue -u

[0091] +Prob(0|multiphoton)(1-e -u -ue -u )

[0092] In the above formula, Prob(0) represents the probability value Q that the output result is 0 when the light source intensity is s and the preparation state is |+ 0∣(s,+) , Prob(0|vacuum), Prob(0|singlephoton), Prob(0|multiphoton) represent Q 0∣(s,+) The corresponding probability values ​​of zero photon, single photon and multi-photon pulses measured by POVM and outputting the result as 0 are further expressed as follows:

[0093] Tue -u / 2≤Q 0∣(s,+) ≤tue -u / 2+(e u -1-u)e -u .

[0094] In the above formula, the overall system efficiency t is expressed as: t = 0.145 × 10 -0.1d . Among them, 0.145 represents the detection efficiency of the detector at the measuring end, 10 -0.1d It represents the channel transmission efficiency, and d represents the channel attenuation (unit: dB).

[0095] In actual implementation, the number of pulses is often limited, expressed as N, and N is defined as φ , N v , N w , N s is the subset of light pulses S φ ,S v ,S w ,S s The number of vacuum state, decoy state and signal state pulses is N = N φ +N v +N w +N s In the present application method, for the convenience of calculation, the number of signal state light pulses N s Half is used for parameter estimation and the other half is used for random number coding. bφ and Q b(γ,m) can be recorded directly in the experiment, however, p k|γ It cannot be directly measured in experiments, so its value needs to be estimated taking into account statistical fluctuations.

[0096] The estimated probability p is defined respectively. k|γ The upper and lower bounds of and

[0097]

[0098] Where N γis the number of γ pulses sent, ξ(m',q) is the error function, and its specific meaning is as shown in the following expression of △(m',q). If the statistical data λ m ' is measured by POVM for m' observation samples If we make a measurement and output q measurement results, then for any ε>0, it can be represented by the following set:

[0099]

[0100] In the above formula, For m' samples, the observable After POVM measurement, we get the observable probability value of q output events, and introduce △(m',q) to estimate the frequency λ m 'With probability λ ∞ The fluctuations between m 'Contained in the interval [λ ∞ -△(m',q),λ ∞ +△(m',q)] with a probability of at least 1-ε.

[0101] Further, according to the above statistical fluctuation analysis, the contribution to single photons, that is, several POVM related parameters: Perform calculation and solution operations.

[0102] Get parameter a 0|1 The lower bound for:

[0103]

[0104] In the above formula, It represents the estimated lower bound of the probability that the output result of sending a single photon is 0 under statistical fluctuations. It represents an estimated upper bound on the probability of getting a zero output result when sending zero photons, taking into account statistical fluctuations.

[0105] in:

[0106]

[0107] In the above formula, c1≥0 should be satisfied, which is equivalent to requiring the inequality For the convenience of calculation, let u w =2u v , and set Then the above inequality can be established. Similarly, for a 0|1 The upper bound of Do a similar tight estimate:

[0108]

[0109] in, It represents an estimated lower bound on the probability of getting a zero output result from sending zero photons, taking into account statistical fluctuations.

[0110] Furthermore, according to the results derived above, the parameters and The lower bound values ​​are calculated separately, and finally we get:

[0111]

[0112] Furthermore, under the constraints:

[0113] 0≤a 0|k ≤1,b=0,1,k=0,1,2…,

[0114]

[0115] Finally, the random key extraction rate is obtained:

[0116]

[0117] in, represents the lower bound estimate of the probability of a single photon in signal state s under statistical fluctuations, N s represents the number of pulse photons in the signal state, N represents the total number of pulse photons sent by the light source, and H ∞ (x) = -log2max(x, 1-x) represents the binary minimum entropy function.

[0118] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in combination with specific simulation results and with reference to the accompanying drawings.

[0119] Figure 1 The schematic diagram of the principle of the method of the present invention is based on the measurement device-independent quantum random number generation method of the weak coherent state light source four-intensity decoy state. The present invention is based on the MDI-QRNG protocol, the sending end is Alice, the receiving end is Bob, Alice sends N light source pulses, and the light pulses are randomly divided into four subsets by random number seeds: S φ ,S v ,S w ,S s , there is S φ +S v +S w +S s={1,2,…,N}, the four subsets represent the vacuum state φ, the decoy state v, the decoy state w and the signal state s respectively. The decoy state v and the decoy state w are randomly encoded into one of the four states 0, 1, +, +i, while all signal states s are encoded into +a state. All pulses are sent to the measurement end, and the contribution of single photons is obtained by performing POVM measurement on different decoy states. Finally, the final randomness size R is extracted by performing Z basis vector measurement on the signal state s.

[0120] Figure 2 The specific process steps of a proposed method for generating quantum random numbers independently of a device using four-intensity trapped-state measurements based on a WCS light source are demonstrated.

[0121] Figure 3 It shows that when the number of pulses is N = 10 12 When the random number generation rate and channel loss resistance of the three-intensity and four-intensity entrapped state measurement device-independent quantum random number generation methods are compared, here, the weak coherent state light source (WCS), the photon distribution obeys the Poisson distribution:

[0122]

[0123] Among them, u γ represents the photon intensity at the light pulse intensity γ.

[0124] from Figure 3 It can be obtained that when the number of optical pulses is N = 10 12 When the random number generation rate of three-intensity decreases faster and faster than that of four-intensity, it can no longer be coded when it reaches 11dB loss, while the channel loss resistance of four-intensity can reach 13dB. Therefore, both in terms of random key extraction rate and channel loss resistance, four-intensity has significant advantages over three-intensity. The reason why the four-intensity decoy state protocol is higher than the three-intensity decoy state protocol in terms of random key extraction rate and channel loss resistance is that for the linear programming optimal solution problem, as the number of constraints increases, it will be closer to the theoretical limit value, and the curve will be tighter. In the four-intensity decoy state scheme, collective constraints and joint estimation are used to further reduce the impact of statistical fluctuations and improve the random key generation rate. Therefore, compared with the three-intensity decoy state MDI-QRNG scheme, this method brings a higher random key coding rate.

[0125] Attached Figure 4 The comparison chart of the random number generation rate and channel loss resistance of the four-intensity decoy state MDI-QRNG based on the weak coherent state light source under different pulse numbers of the present invention is shown. Figure 4 From left to right, the number of pulses is N = 10 12 , N = 10 13 , N = 1014 , N = 10 15 It can be clearly seen from the figure that as the number of pulses increases, the ability of the quantum random number generator to resist channel loss increases significantly. As the number of pulses increases from N = 10 15 Decrease to N = 10 12 , the channel tolerance is attenuated from 24dB to 13dB.

[0126] Figure 5 A comparison chart of the influence of the number of photon pulses on the random number generation rate of the three-intensity and four-intensity lured-state MDI-QRNG based on weak coherent state light source at a loss of 10dB is shown. From the figure, it can be seen that at a loss of 10dB, the random number generation rate will increase with the increase of the number of light pulses, and the difference in the random key extraction rate between the four-intensity and three-intensity will gradually decrease with the increase of the number of pulses.

Claims

1. A measurement device-independent quantum random number generation method, characterized in that: The steps include: Step 1: Alice randomly modulates N light source pulses into four different intensities using a seed random number, represented as intensities φ, v, w, and s, and then divides all light pulses into four subsets: S φ ,S v ,S w and S s ,The four subsets are the vacuum state φ, the decoy state v, the decoy state w, and the signal state s set, which encode the four light source intensities and send them to Bob's end; Step 2: Bob performs POVM measurement on all transmitted optical pulses, estimates the results after POVM measurement to obtain the contribution of single photons, and finally performs Z basis vector measurement on the signal state s to extract the randomness size R. The specific steps include: Step 2.1, Bob performs POVM measurement on all transmitted optical pulses; The POVM measurement of the source intensity γ is expressed as: In the formula, p k|γ represents the probability of k photons under the light source intensity γ, F b|k represents a POVM measurement with output b at k photon number; The trapped state of the light pulse is randomly projected to (I+σ z ) / 2、(I-σ z ) / 2、(I+σ x ) / 2、(I+σ y ) / 2 On one of the density matrices, the probability of the output result being b when the light source intensity is γ(γ∈{s,v,w}) and the preparation state is m is expressed as: Among them, m∈{0,1,+,+i}, a b|k represents the probability of getting output b when sending k photons, b∈{0,1}, σ=(σ x ,σ y ,σ z ) represents the Pauli operator, represents a three-dimensional real vector on the Bloch sphere with output b under k photons, If the pulse sent comes from the vacuum state, then no matter what the encoded information and the measurement operator are, the probability of the output being b is always a. b|0 , i.e. Q b|φ =a b∣0 ; Step 2.2, estimate the contribution of single photons based on the results after POVM measurement, specifically: Define the estimated probability p k|γ The upper and lower bounds of and Where N γ is the number of γ pulses sent, ξ(m',q) is the error function, m' represents the number of observation samples, and q represents the number of measurement result outputs; Calculation parameter a 0|1 The lower bound for: in, It represents the estimated lower bound of the probability that the output result of sending a single photon is 0 under statistical fluctuations; represents the estimated upper bound of the probability of getting an output of 0 when sending zero photons, taking into account statistical fluctuations; in: In the above formula, c1≥0 should be satisfied, which is equivalent to requiring the inequality For the convenience of calculation, let u w =2u v , and set Then the above inequality holds. Similarly, for a 0|1 The upper bound of Do a tight estimate: in, represents an estimated lower bound on the probability of getting a zero output when sending zero photons, taking into account statistical fluctuations; Furthermore, for the parameters and The lower bounds are calculated separately: in, They represent the three-dimensional vector when the output result is 0 under single photon The second and third elements of Step 2.3, perform Z basis vector measurement on the signal state s to extract the randomness size R; Under the constraints: 0≤a 0|k ≤1,b=0,1,k=0,1,2…, Finally, the random key extraction rate is obtained: in, represents the lower bound estimate of the probability of a single photon in signal state s under statistical fluctuations, N s represents the number of pulse photons in the signal state, N represents the total number of pulse photons sent by the light source, and H ∞ (x) = -log2 max(x, 1-x) represents the binary minimum entropy function.

2. A measurement device-independent quantum random number generation method according to claim 1, characterized in that: Step 2.1 F b|k The POVM measurement with output b under k photon number is expressed as follows: Among them, a b|k , Satisfy the constraints:

3. The method for generating quantum random numbers independent of measurement equipment according to claim 1, characterized in that: In step 2.1, Bob performs POVM measurement on all transmitted optical pulses. When the detector at the receiving end is triggered, all output results b∈{0,1} will be output as a random bit sequence. The value of b depends on which of the two detectors is responded. If the two detectors do not respond or both respond at the same time, then the user randomly takes the value 0 or 1.

4. The method for generating quantum random numbers independent of measurement equipment according to claim 1, characterized in that: In step 1, the intensities of the four light sources are encoded separately, specifically: The decoy states v and w are randomly encoded into one of the four states |0>, |1>, |+>, |+i>, where The signal state s is encoded as a state |+>.

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