Light field orbital angular momentum coding quantum key distribution performance improvement method based on neural network

Abstract

The invention discloses a light field orbital angular momentum coding quantum key distribution performance improvement method based on a neural network. The method comprises the following steps: when a plurality of photons are subjected to communication transmission in atmospheric turbulence, the transmission efficiency of the plurality of photons is obtained, and the plurality of photons are coded through orbital angular momentum in the transmission process; determining an initial security key rate of the plurality of photons under high-dimensional quantum key distribution based on the transmission efficiency of the plurality of photons; and based on the initial security key rate of the plurality of photons under the high-dimensional quantum key distribution, obtaining the security key length of the high-dimensional quantum key distribution under the finite length effect. According to the method, the technical problems of wide calculation range, low speed and long calculation time when quantum communication is transmitted in a free space and a security key is calculated by a polarization coding technology are solved.

Description

Technical Field

[0001] The present invention relates to the technical field of quantum cryptography, and in particular to a method for improving the performance of light field orbital angular momentum encoding quantum key distribution based on a neural network. Background Art

[0002] Driven by the grand vision of the global quantum Internet, achieving long-distance, high-code-rate, all-weather quantum communication has become a research hotspot in the field of quantum information, leading and promoting the rapid development of quantum information technology. Quantum Key Distribution (QKD) relies on the quantum properties of single photons to encode, decode, transmit, receive and post-process information, and can generate theoretically untapped and tamper-proof security keys between the two communicating parties. At present, most research on quantum communication is based on two-dimensional quantum systems implemented by polarization states or phase encoding of photons. Although these systems have significant advantages in quantum bit manipulation, due to the boundedness of Hilbert space, the information capacity is always limited to 1 bit / photon. In order to break the information entropy threshold of the system, high-dimensional quantum key distribution (HD-QKD) provides a feasible idea and has developed rapidly in theory and experiment. Among them, the use of the transverse degree of freedom of photons - orbital angular momentum (OAM) for high-dimensional quantum state encoding provides advantages for improving the transmission performance of free-space quantum communication systems:

[0003] 1) Utilize the coding advantages of infinite-dimensional Hilbert space in a single quantum system to improve the transmission efficiency and fidelity of coded photon states, thereby enhancing the anti-noise capability and communication bandwidth per unit time of the quantum communication system;

[0004] 2) Combining the rotational invariance characteristics of the vortex light field, the problem of aligning the reference frame of the ground-to-air scene is effectively avoided, providing a new coding scheme for building a high-speed and stable mobile quantum communication network based on a high-speed mobile aerial platform.

[0005] However, atmospheric turbulence destroys the OAM spiral phase structure, resulting in received wavefront distortion. The transmission efficiency of OAM in turbulent channels also fluctuates, causing random fading of the signal. Currently available statistical distribution models mainly focus on describing light field intensity fluctuations, and it is difficult to characterize the complexity of OAM transmittance coefficient fluctuations in turbulent channels. Therefore, characterizing the fluctuations of OAM transmission coefficients in turbulent channels is crucial for analyzing the security of OAM-coded QKD systems.

[0006] At present, there is still a lack of complete theoretical analysis on the combination of OAM transmittance statistical distribution in atmospheric turbulence and QKD. The transmittance fluctuations caused by atmospheric turbulence lead to time-varying quantum bit errors (QBER). In order to solve this problem, the signal-to-noise ratio is improved by post-selecting high transmittance. This post-selection method relies on optimizing the transmittance threshold after receiving all signals. However, this operation method causes a huge computational burden. Optimizing QKD system parameters through machine learning methods has a significant effect on improving the operating speed and realizing parameter prediction. This method is of great significance for airborne free-space QKD missions. Based on the above analysis, a study on OAM-coded QKD key estimation method under turbulent conditions is carried out, and a threshold selection QKD performance improvement method based on neural network is proposed. Summary of the invention

[0007] The embodiment of the present invention provides a method for improving the performance of quantum key distribution using orbital angular momentum encoding of a light field based on a neural network, so as to at least solve the technical problems of wide range, slow speed and long time in calculating security keys using polarization coding technology during quantum communication transmission in free space.

[0008] According to one aspect of an embodiment of the present invention, a method for improving the performance of light field orbital angular momentum encoding quantum key distribution based on a neural network is provided. The method may include: when a plurality of photons are used for communication transmission in atmospheric turbulence, obtaining the transmission efficiency of the plurality of photons, wherein the plurality of photons encode the photons by orbital angular momentum during transmission; determining the initial security key rate of the plurality of photons under high-dimensional quantum key distribution based on the transmission efficiency of the plurality of photons; obtaining the security key length of the high-dimensional quantum key distribution under finite length effect based on the initial security key rate of the plurality of photons under high-dimensional quantum key distribution; determining the security key rate of the high-dimensional quantum key distribution under finite length effect based on the security key length of the high-dimensional quantum key distribution under finite length effect and the number of the plurality of photons; comparing the security key rate of the high-dimensional quantum key distribution under finite length effect with the initial security key rate of the plurality of photons under high-dimensional quantum key distribution, and determining the optimal threshold of the security key rate of the high-dimensional quantum key distribution under finite length effect; determining the target security key rate of the photons when encoding by orbital angular momentum under finite length effect based on the optimal threshold of the security key rate of the high-dimensional quantum key distribution under finite length effect and the transmission efficiency of the photons under finite length effect.

[0009] Optionally, the expression for the transmission efficiency of a number of photons is:

[0010]

[0011] Among them, η(t) is the transmission efficiency of a number of photons, is the weighting factor related to the distortion caused by atmospheric turbulence, is the intensity distribution of the orbital angular momentum mode.

[0012] Optionally, based on the transmission efficiency of a number of photons, an expression for determining the initial security key rate of a number of photons under high-dimensional quantum key distribution is:

[0013]

[0014] Among them, R Ratewise is the initial security key rate of several photons in high-dimensional quantum key distribution, P(η) is the probability corresponding to the transmission efficiency of several photons, and R(η) is the security key rate corresponding to the transmission efficiency of several photons in high-dimensional quantum key distribution.

[0015] Optionally, based on the security key rate of several photons in high-dimensional quantum key distribution, the expression of the security key length of high-dimensional quantum key distribution under the finite length effect is obtained as follows:

[0016]

[0017] Among them, K OAM,L is the security key length of orbital angular momentum basis for high-dimensional quantum key distribution under finite length effect, is the lower limit of the number of single-photon pulses in the key after OAM sieving, is the total amount of OAM-based key after screening, is the upper limit of the phase error rate of the key after the single-photon signal state SUP basis sieve, is the upper limit of the quantum bit error rate of the key after the signal state OAM basis sieving, H d (x)=-(1-x)log2(1-x)-xlog2[x / (d-1)] represents the Shannon entropy in d dimension.

[0018] Optionally, based on the security key length of high-dimensional quantum key distribution under finite length effect and the number of photons, an expression for determining the security key rate of high-dimensional quantum key distribution under finite length effect is:

[0019]

[0020] Among them, R L is the secure key rate of high-dimensional quantum key distribution under finite length effect, and N is the number of photons.

[0021] After comparing the security key rate of high-dimensional quantum key distribution under finite length effect with the initial security key rate of several photons under high-dimensional quantum key distribution, and determining the optimal threshold of the security key rate of high-dimensional quantum key distribution under finite length effect, the method also includes: inputting three parameters used in determining the security key rate of high-dimensional quantum key distribution under finite length effect into a successfully trained BP neural network, and determining the optimal threshold of the security key rate of high-dimensional quantum key distribution under finite length effect; wherein the three parameters are respectively the dimensionless ratio of the root mean square value of the orbital angular momentum beam radius to the Fried atmospheric coherence length, the orbital angular momentum angular index, and the Fried atmospheric coherence length.

[0022] Beneficial effects of the present invention:

[0023] The present invention proposes a method for improving the performance of light field orbital angular momentum encoded quantum key distribution based on a neural network, combines the transmittance probability density function (PDF) of OAM in turbulence with the HD-QKD security key rate formula, and realizes the comprehensive theoretical modeling of OAM encoded QKD statistical distribution; adopts a neural network method to simplify the process of the traditional threshold selection method, realizes accurate and efficient parameter prediction and performance optimization, solves the technical problems of wide range, slow speed and long time when polarization coding technology calculates security keys during quantum communication transmission in free space, and achieves the technical effect of reducing the calculation range of security keys, increasing speed and shortening time by adopting the idea of ​​combining orbital angular momentum coding with finite length effect and neural network during quantum communication transmission in free space. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] The drawings described herein are used to provide a further understanding of the present invention and constitute a part of this application. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings:

[0025] Figure 1 is a flow chart of a method for improving the performance of light field orbital angular momentum encoding quantum key distribution based on a neural network according to an embodiment of the present invention;

[0026] Figure 2 is a schematic diagram of a comparison of security key rates between a full code rate integration method and a threshold selection optimization method according to an embodiment of the present invention;

[0027] Figure 3 is the optimal threshold η under different Ω and l conditions according to the embodiment of the present invention T Schematic diagram of

[0028] Figure 4 is a schematic diagram of the probability density distribution of the transmission coefficient η under different Ω and r0 conditions according to an embodiment of the present invention;

[0029] Figure 5 is a schematic diagram of the probability density distribution of the transmission coefficient η under different Ω and l conditions according to an embodiment of the present invention;

[0030] Figure 6 is a schematic diagram of the relationship between the security key rate R and Ω under different conditions according to an embodiment of the present invention;

[0031] Figure 7 is a schematic diagram of the relationship between the security key rate R and Ω under different dimensional conditions according to an embodiment of the present invention;

[0032] Figure 8 is a schematic diagram of the relationship between the security key rate R and Ω under different finite length effects according to an embodiment of the present invention;

[0033] Fig. 9 is a schematic diagram comparing a traditional process and an intelligent process according to an embodiment of the present invention;

[0034] Fig.10 is a schematic diagram of the structure of a BP neural network according to an embodiment of the present invention;

[0035] Fig.11 It is a schematic diagram of the optimal threshold prediction effect obtained by using the BP neural network according to an embodiment of the present invention. DETAILED DESCRIPTION

[0036] In order to enable those skilled in the art to better understand the scheme of the present invention, the technical scheme in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only embodiments of a part of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.

[0037] It should be noted that the terms "first", "second", etc. in the specification and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence. It should be understood that the terms used in this way can be interchangeable where appropriate, so that the embodiments of the present invention described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions, for example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units that are clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0038] Example 1

[0039] According to an embodiment of the present invention, a method for improving the performance of light field orbital angular momentum encoded quantum key distribution based on a neural network is provided. It should be noted that the steps shown in the flowchart of the accompanying drawings can be executed in a computer system comprising at least one set of computer executable instructions, and, although a logical order is shown in the flowchart, in some cases, the steps shown or described may be executed in an order different from that shown here.

[0040] Figure 1 is a flow chart of a method for improving the performance of light field orbital angular momentum encoding quantum key distribution based on a neural network according to an embodiment of the present invention. Figure 1 As shown, the method may include the following steps:

[0041] Step S101, when a plurality of photons are transmitted for communication in atmospheric turbulence, the transmission efficiency of the plurality of photons is obtained, wherein the plurality of photons are encoded by orbital angular momentum during the transmission process.

[0042] In the technical solution provided in the above step S101 of the present invention, under the premise of normalization of the initial light intensity, the OAM transmission coefficient is equal to the received power. Since the mathematical model of the detection power of the OAM optical channel is fundamentally different from that of the traditional free-space optical channel, the currently widely accepted probability distribution function of the optical radiation intensity fluctuation caused by atmospheric turbulence may not be applicable to the transmission coefficient fluctuation of the turbulent OAM optical channel. The transmission of OAM in turbulence does not obey the log-normal and Gamma-Gamma distribution models commonly used in classical Gaussian light. In general, it is difficult to directly establish a statistical distribution model suitable for the transmission coefficient of the turbulent optical OAM channel fluctuation through analytical mathematical derivation. Therefore, a Monte Carlo simulation is used to generate random samples of the transmission coefficient, thereby proposing a suitable transmission coefficient fluctuation distribution model. First, according to the analysis of the literature [Chen C, Yang H. Characterizing the statistical distribution for transmission coefficient of turbulent optical orbital-angular-momentum channels [J]. Optics Express, 2019, 27 (20): 28968-28982.], the instantaneous transmission coefficient under turbulent optical OAM is theoretically derived.

[0043] Step S102, based on the transmission efficiency of the plurality of photons, determining the initial security key rate of the plurality of photons under high-dimensional quantum key distribution.

[0044] In the technical solution provided in the above step S102 of the present invention, the probability corresponding to the transmission efficiency of a number of photons and the security key rate corresponding to the probability corresponding to the transmission efficiency of a number of photons are used to determine the initial security key rate of a number of photons under high-dimensional quantum key distribution.

[0045] Step S103, based on the initial security key rate of a number of photons under high-dimensional quantum key distribution, obtain the security key length of high-dimensional quantum key distribution under finite length effect.

[0046] In the technical solution provided in the above step S103 of the present invention, a derivation formula in the calculation process of the initial security key rate of several photons under high-dimensional quantum key distribution is obtained, and the security key length of high-dimensional quantum key distribution under the finite length effect is obtained.

[0047] Step S104, determining a security key rate of high-dimensional quantum key distribution under finite length effect based on the security key length of high-dimensional quantum key distribution under finite length effect and the number of photons.

[0048] In the technical solution provided in the above step S104 of the present invention, the security key length of high-dimensional quantum key distribution under the finite length effect and the number of photons are calculated to obtain the security key rate of high-dimensional quantum key distribution under the finite length effect.

[0049] Step S105, comparing the security key rate of high-dimensional quantum key distribution under finite length effect with the initial security key rate of several photons under high-dimensional quantum key distribution, and determining the optimal threshold of the security key rate of high-dimensional quantum key distribution under finite length effect.

[0050] In the technical solution provided in the above step S105 of the present invention, the security key rate of high-dimensional quantum key distribution under the finite length effect and the initial security key rate of several photons under the high-dimensional quantum key distribution are compared under different thresholds to obtain the optimal threshold of the security key rate of high-dimensional quantum key distribution under the finite length effect. In the process of integrating the security key rate according to the code rate, due to the statistical distribution characteristics of the transmission coefficient of OAM light in free space, almost no key is generated under certain transmission efficiency conditions. However, in actual situations, this part of the data needs to be post-processed, resulting in a waste of computing resources. Combined with the time-varying transmission characteristics caused by atmospheric turbulence in free space, using threshold selection to filter information, realize post-selection, reduce the amount of data calculation, and increase the rate of security key generation per unit time is the main means to improve system performance. This simplified security key rate of threshold selection can be expressed as follows:

[0051]

[0052] According to the above formula, change the threshold ηT , observe the changes in the security key generation rate. Figure 2 is a schematic diagram of a comparison of security key rates between a full code rate integration method and a threshold selection optimization method according to an embodiment of the present invention, wherein Figure 2 It can be seen that when the OAM index l = 1, the set threshold value is almost the same as the fixed value obtained by integrating the bit rate in the initial range, and then it will drop significantly. An ideal threshold value can be found according to the actual scenario to simplify the calculation. For example, in the low Ω scenario (Ω = 10 -1 ), a higher threshold value (η T =0.65), which can improve the efficiency of data processing. Among them, the full code rate integration method is the initial security key rate method of several photons under high-dimensional quantum key distribution, and the security key rate of the threshold selection optimization method is the initial security key rate of several photons under high-dimensional quantum key distribution. In order to further describe the choice of threshold more vividly, a three-dimensional image of Ω, l and η is established. Figure 3 is the optimal threshold η under different Ω and l conditions according to the embodiment of the present invention T Schematic diagram, such as Figure 3 As shown, we can intuitively observe the influence of different variables on η. Figure 3 (a) It can be seen that the influence of Ω on η is much greater than the influence of l on η. As Ω increases, the optimal threshold is gradually reduced. This conclusion is consistent with Figure 2 However, when Ω>1, further observation of the relationship between the three, such as Figure 3 As shown in (b), the relationship between the three has changed. Both l and Ω have a dramatic impact on the setting of η. As l increases, the choice of the optimal threshold also decreases. Therefore, when Ω<1, the impact of l on the selection of the optimal threshold can be ignored. When Ω>1, the impact of l needs to be taken into account.

[0053] Step S106, based on the optimal threshold of the security key rate of high-dimensional quantum key distribution under the finite length effect and the transmission efficiency of photons under the finite length effect, determine the target security key rate of photons in orbital angular momentum encoding under the finite length effect.

[0054] In the technical solution provided in the above step S106 of the present invention, the minimum threshold 0 in determining the security key rate of high-dimensional quantum key distribution under the finite length effect is replaced with the optimal threshold, thereby obtaining the target security key rate of photons when encoding orbital angular momentum under the finite length effect.

[0055] The above method of this embodiment is further introduced below.

[0056] As an optional embodiment, in step S101, the expression of the transmission efficiency of a plurality of photons is:

[0057]

[0058] Among them, η(t) is the transmission efficiency of a number of photons, is the weighting factor related to the distortion caused by atmospheric turbulence, is the intensity distribution of the orbital angular momentum mode.

[0059] In this embodiment, 1. The instantaneous transmission coefficient η(t) under turbulent optical OAM:

[0060]

[0061] in represents the ratio of the Laguerre-Gaussian beam width r to the Friedel atmospheric coherence length r0, It represents the dimensionless ratio of the root mean square value of the OAM beam radius to r0, l represents the OAM angular index, and the radial index of the OAM currently considered is 0. w0 is the beam waist radius, represents the Rayleigh distance, k = 2π / λ represents the wave number, λ is the wavelength, and i is the imaginary unit. represents the random phase screen. Wz represents the beam waist radius after beam transmission and is an important parameter in Ω.

[0062] 2. Generation of random phase screen

[0063] In the above formula In fact, it can be described as a random phase screen to represent the phase disturbance, which in turn causes the transmittance η(t) to fluctuate in real time. The key to achieving random samples of transmittance is to obtain a random phase screen. Due to the advantage of integration over θ, a sparse spectrum based method is chosen to generate the phase screen.

[0064]

[0065] where a n represents a random complex amplitude, represents the position vector of the random phase screen in the two-dimensional plane, Re(z) represents the real part of z, Represents a random position vector, the probability density function of the vector size is:

[0066]

[0067] Where K n-1 ≤K≤K n , K n =κ0exp[(n / N)ln(κ m / κ0)], 1≤n≤N, κ0=2π / L0, κ m=2π / l0, l0 and L0 represent the inner and outer scales of turbulence respectively (1mm and 100m). The azimuth angles follow a uniform distribution between -π and π. In addition, a n is a random complex amplitude, normally distributed and follows:

[0068] n >=0, n a m >=0,

[0069] The angle brackets <> represent the statistical mean. If m = n, δ mn =1, if m≠n, δ mn = 0. By using N to generate a n and The random realization of, based on formula (4), can be at any position Direct calculation of phase screen In the Monte Carlo simulation, in order to make the spectral interval consistent with the standard pure Kolmogorov spectrum, the inner and outer scales of the turbulence were set to 1 mm and 100 m, respectively.

[0070] 3. Model of transmittance coefficient probability distribution based on double Johnson SB distribution

[0071] In order to mathematically characterize the statistical distribution of the transmission coefficient, a linearly scaled double-Johnson SB distribution with four independent control parameters is fitted to the random fluctuations of the measured signal of the turbulent optical OAM channel. The PDF probability density distribution of this distribution is expressed as

[0072]

[0073] in,

[0074]

[0075] Among them, P J (η|γ,δ) represents the probability density function of Johnson SB distribution. The four independent control parameters γ1,γ2,δ1,δ2>0 represent the statistical characteristics of the simulation samples. In order to conveniently use the double Johnson SB distribution in practical applications, the four control parameters are directly linked to the channel conditions and OAM mode parameters. The relationship between (Ω,l,r0) and (γ1,δ1,γ2,δ2) can be regarded as a mapping from three-dimensional space to four-dimensional space. Although it is difficult to establish a mathematical expression to describe this mapping, the Monte Carlo simulation and probability distribution fitting based on maximum likelihood estimation can reflect this mapping relationship.

[0076] ​​In order to further explore the influence mechanism of Ω and r0 on the statistical distribution of the transmission coefficient, the probability density distribution of the transmission coefficient η under different Ω and r0 conditions is characterized. Figure 4 Schematic diagram of the probability density distribution of the transmission coefficient η under different Ω and r0 conditions according to an embodiment of the present invention, and the PDF of the transmission coefficient under different Ω and r0 conditions. Figure 4 It can be seen that under the same Ω and different r0 conditions, although there are slight differences, the PDF curves of the transmission coefficient show similar trends. However, under the same r0 and different Ω conditions, the PDF curves show large differences. This shows that the influence of Ω on the PDF of the transmission coefficient is stronger than the influence of r0. At the same time, as Ω increases, the "peak" of the PDF gradually moves to the left, indicating that the probability of η achieving high transmittance is gradually decreasing, further indicating that the channel transmittance attenuation caused by turbulence is enhanced. When Ω is near 1 (such as Figure 4 (b)), the PDF curve will have serious tailing phenomenon and is not easy to be described by the existing PDF model.

[0077] Next, we further study how the change of l affects the statistical distribution of transmittance under the given r0. Considering the transmission characteristics of OAM and the experimental settings, the atmospheric coherence length r0 = 10 cm.

[0078] Figure 5 is a schematic diagram of the probability density distribution of the transmission coefficient η under different Ω and l conditions according to an embodiment of the present invention, Figure 5 (a) It can be seen that the PDF curves of different OAM indices are basically merged together, indicating that when Ω is small, l has little effect on PDF. Figure 5 (b) and Figure 5 (c) When Ω≥1, there is a difference between the curves, proving that the statistical distribution of the OAM optical transmission coefficient has an obvious mode-dependent effect. This mode-dependent turbulence effect is due to the superposition of two reasons: (1) higher-order OAM has a larger beam cross-section, resulting in a worse turbulent environment; (2) higher-order OAM has a multi-layer phase structure that is more sensitive to phase perturbations from turbulence.

[0079] As an optional embodiment, in step S102, based on the transmission efficiency of the plurality of photons, an expression for the initial security key rate of the plurality of photons under high-dimensional quantum key distribution is determined as follows:

[0080]

[0081] Among them, R Ratewise is the initial security key rate of several photons in high-dimensional quantum key distribution, P(η) is the probability corresponding to the transmission efficiency of several photons, and R(η) is the security key rate corresponding to the transmission efficiency of several photons in high-dimensional quantum key distribution.

[0082] In this embodiment, the HD-QKD security key analysis based on the spoofed BB84 protocol is based on the fact that, in the turbulent OAM channel, there is currently a lack of theoretical support for the dependence of the security key generation rate R on the transmittance coefficient η. On the basis of the statistical distribution analysis of the transmittance of the OAM turbulent channel, combined with the GLLP formula, the QKD system parameters of the transmitter and receiver are fixed, and the key rate under the spoofed BB84 protocol is expressed as a single function of R(η). Therefore, estimating the system security code rate in the turbulent channel comes down to the problem of finding the integral of R(η) over the probability distribution of η. Integration based on code rate is the most common way to obtain the system security key rate, that is, using all the information of the channel transmittance probability distribution to integrate R(η) over all value ranges of the PDF. First, consider the asymptotic case of sending an infinite number of pulses, given by Figure 4 Figure 5 It can be seen that the channel transmittance η corresponding to each signal transmission period has been measured and all transmittance information has been mastered. The security key rate according to the code rate integration method can be expressed as: OAM, as the spatial degree of freedom of the light field, can be mapped into an infinite-dimensional Hilbert space. In the high-dimensional quantum state space, the SUP basis and the OAM basis form two mutually unbiased bases (MUBs) to ensure the security of QKD. The OAM basis is composed of different OAM states, and the Fourier conjugated SUP basis is composed of the superposition of OAM states with a fixed relative phase between adjacent OAM components. The expressions of the OAM basis and the SUP basis are:

[0083]

[0084] Where d represents the dimension of the Hilbert space, L represents the maximum OAM quantum number used, and the two satisfy 2L+1=d. The key receiver Bob uses the results of the OAM basis to calculate the key and uses the results of the SUP basis to verify the security of the key distribution. After error correction and privacy methods, a secure key is extracted. For weak coherent light sources, the secure key rate of the decoyed state HD-QKD can be estimated as:

[0085]

[0086] Among them, q m Represents the basis selection probability, which depends on the QKD protocol. represents the error correction efficiency of the signal state, and represent the gain and QBER of the signal state respectively. and denote the gain and bit error of the single photon state, respectively, which can be estimated by the decoy state method. d(x)=-(1-x)log2(1-x)-xlog2[x / (d-1)] represents the Shannon entropy in d dimension.

[0087] For the decoy state OAM coded HD-QKD system, the single-photon signal transmission efficiency η sys Including transmission efficiency η and detection efficiency η D ,therefore, The expression is:

[0088]

[0089] Where Y0 = 2p d represents the yield when the transmitter does not emit photons, p d represents the dark count of the detector, and μ represents the average number of photons in the signal state. At the same time, considering that the received bit error is affected by the pointing error and mode crosstalk, The expression is:

[0090]

[0091] Unlike the usual two-dimensional QKD system, the dark count error rate of HD-QKD is e0 = (d-1) / d. By adopting the "weak + vacuum decoy state" method, Y1 OAM and The expression is:

[0092]

[0093] The parameter settings of the QKD system are shown in Table 1.

[0094] Table 1. Parameters of OAM-QKD numerical simulation

[0095]

[0096]

[0097] Firstly, the influence of OAM index on the security key rate is simulated. Figure 6 is a schematic diagram of the relationship between the security key rate R and Ω under different conditions according to an embodiment of the present invention, Figure 6 The relationship between Ω and the security key rate is shown. As Ω increases, the security key rate gradually decreases, indicating that Ω reflects the disturbance and attenuation characteristics of the atmospheric turbulence channel to a certain extent. However, the change of the OAM index l has little effect on the key rate curve. Therefore, we can further consider the application of high-dimensional quantum systems to improve the information transmission rate when changing Ω.

[0098] Figure 7 is a schematic diagram of the relationship between the security key rate R and Ω under different dimensional conditions according to an embodiment of the present invention, Figure 7 The relationship between the security key rate and Ω in the high-dimensional QKD system is shown. The figure shows the changing trend of the high-dimensional QKD key rate surface when Ω is a variable. It can be seen from the figure that the higher the dimension of the QKD system, the higher the transmission security key rate and the longer the transmission distance, which shows that when the QKD system uses Ω as a variable, it can give full play to the advantages of high-dimensional coding. Since the high-dimensional QKD system will have effects such as mode-dependent diffraction (SDD) when transmitted in the atmosphere, it will cause mismatch in receiving efficiency, resulting in security vulnerabilities and reduced security key rate. According to Figure 3 and Figure 4 As a result, high-dimensional quantum systems can be used more in low-Ω scenarios, because the OAM index l has little effect on key generation at this time.

[0099] 2. Decoy-state OAM-coded HD-QKD finite-length secure key estimation method

[0100] Due to the differences between HD-QKD and 2D-QKD in key analysis, the security of the HD-QKD system is analyzed under asymptotic conditions, especially in the limit of infinite key effects. The yield and bit error rate of single-photon states required by the formula for the secure key rate of the decoyed state HD-QKD can be accurately estimated by the OAM-encoded QKD measurement values ​​and converge to the approximate true value. Then the final key length of the OAM-encoded QKD can be safely obtained. However, in actual HD-QKD systems, the number of quantum signal pulses emitted is limited, so there are statistical fluctuations between the observed values ​​and the true values ​​of the system parameters. When analyzing the security of the HD-QKD system, it is necessary to consider the impact of statistical fluctuations on the final secure key rate in response to the finite key effect. For the observed value ζ>0, using the Chernoff inequality, the expression for the confidence interval of the expected value E[ζ] of the observed parameter can be obtained as:

[0101]

[0102] Among them, E U [ζ] and E L [ζ] represents the upper and lower limits of the confidence interval, δ L and δ U It can be obtained by the following formula:

[0103]

[0104] Among them, ε represents the failure probability used to estimate the expected value of the confidence interval.

[0105] As an optional embodiment, in step S103, based on the security key rate of a number of photons under high-dimensional quantum key distribution, the expression of the security key length of high-dimensional quantum key distribution under the finite length effect is obtained as follows:

[0106]

[0107] Among them, K OAM,L is the orbital angular momentum-based security key length of high-dimensional quantum key distribution under finite length effect, is the lower limit of the number of single-photon pulses in the key after OAM sieving, is the total amount of OAM-based key after screening, is the upper limit of the phase error rate of the key after the single-photon signal state SUP basis sieve, is the upper limit of the quantum bit error rate of the key after the signal state OAM basis sieving, H d (x)=-(1-x)log2(1-x)-xlog2[x / (d-1)] represents the Shannon entropy in d dimension.

[0108] According to the above formula for the confidence interval of the expected value of the observation parameter E[ζ], the upper and lower bounds of the global gain and bit error rate in the signal state and the decoy state under statistical fluctuations can be obtained. Combined, we get Y1 OAM and The formula can be used to obtain the upper and lower limits of the total gain and bit error rate of single-photon pulses. On this basis, the expression of the security key length of the OAM basis of the HD-QKD system under the finite length effect is obtained as follows:

[0109]

[0110] in, is the lower limit of the number of single-photon pulses in the key after OAM sieving, is the total amount of OAM-based key after screening, is the upper limit of the phase error rate of the key after the single-photon signal state SUP basis sieve, It is the upper limit of the quantum bit error rate of the key after the signal state OAM basis sieving.

[0111] As an optional embodiment, in step S104, based on the security key length of high-dimensional quantum key distribution under finite length effect and the number of photons, the expression of the security key rate of high-dimensional quantum key distribution under finite length effect is determined as:

[0112]

[0113] Among them, R L is the secure key rate of high-dimensional quantum key distribution under finite length effect, and N is the number of photons.

[0114] In this embodiment, after obtaining the security key length of the OAM basis of the HD-QKD system under the finite length effect, let the number of quantum signal pulses transmitted by Alice (transmitter) be N, then the expression of the finite length security key rate of the HD-QKD system is:

[0115]

[0116] Therefore, the system security key rate formula under the finite length effect can be recalculated:

[0117]

[0118] Figure 8 is a schematic diagram of the relationship between the security key rate R and Ω under different finite length effects according to an embodiment of the present invention; Figure 8 The key rate curves for different data sizes and asymptotic conditions are compared in . Figure 8 It can be seen that as the data size gradually increases, the security key rate also increases accordingly. When the number of quantum pulses N sent is greater than or equal to 1012, it almost coincides with the key rate curve in the asymptotic case. Considering the practical scenarios and costs, in order to save the resources for sending signals, in actual situations, N = 1012 can be selected as the scheme for sending pulses in the HD-QKD system.

[0119] As an optional implementation manner, in step S105, after comparing the security key rate of high-dimensional quantum key distribution under finite length effect with the initial security key rate of several photons under high-dimensional quantum key distribution to determine the optimal threshold of the security key rate of high-dimensional quantum key distribution under finite length effect, the method further includes: inputting three parameters used in determining the security key rate of high-dimensional quantum key distribution under finite length effect into a successfully trained BP neural network to determine the optimal threshold of the security key rate of high-dimensional quantum key distribution under finite length effect; wherein the three parameters are respectively the dimensionless ratio of the root mean square value of the orbital angular momentum beam radius to the Fried atmospheric coherence length, the orbital angular momentum angular index and the Fried atmospheric coherence length.

[0120] In this embodiment, since the statistical distribution of the transmission coefficient of OAM in turbulence is obtained through Monte Carlo simulation, the data is discrete and has certain volatility. In order to further optimize the threshold value, a method for adaptive threshold selection using an artificial neural network is proposed, and the most widely used error back propagation (BP) neural network is selected as the prediction model. Fig. 9 is a schematic diagram comparing the traditional process and the intelligent process of an embodiment of the present invention, Fig. 9 It shows that the optimal threshold η is obtained by the initial parameters (Ω, l, r0) T The whole process is clear, but it requires high computing resources. By using machine learning intelligence to train the initial parameters, we can not only obtain the optimal threshold η T , and can also realize data prediction, showing its practical advantages, Fig.10Schematic diagram of the structure of the BP neural network of the embodiment of the present invention. The input layer output value of the model is 3, the number of hidden layers is 3, and the number of neurons is 15, 10 and 1 respectively. The output value of the output layer is 1. The transfer function of the hidden layer is the tansig transfer function, the output layer adopts the linear transfer function, the learning function is the Levenberg-Marquardt (LM) variable gradient algorithm, and the performance function adopts the MSE mean square error function. The number of training times is 2000, and the learning rate is 0.01. When Ω is 10- 2 to 10 1.4 , the OAM index l is in the range of 0 to 16, and the optimal threshold η of 18*17 samples is established T The data set is used to train the neural network and predict the optimal choice of threshold under different conditions. The prediction results of the BP neural network for the optimal threshold are as follows: Fig.10 shown. Fig.11 is a schematic diagram of the optimal threshold prediction effect obtained by using the BP neural network in an embodiment of the present invention, Fig.11 (a) is the fitting effect curve. The horizontal axis represents the number of samples selected by the neural network. The vertical axis represents the sample value selected by the optimal threshold. The blue dots represent the original data. The red triangles represent the predicted data. Fig.11 (b) is the training error curve, where the ordinate represents the error between the model prediction value and the original data value in the training set. Fig.11 As can be seen in (a), the original data curve and the predicted data points show a similar periodic change pattern. This is because in the process of selecting the original data, the optimal threshold is selected in the order of increasing the same OAM index l, that is, every time 18 Ω of the same OAM index are selected, the Ω under the next OAM index is selected again until 17 OAM index points are selected. The fitting curve of the predicted data generated by the BP neural network is basically consistent with the original data curve. Fig.11 (b) shows the training error of the sample set 10 -3 This indicates that the neural network has high prediction accuracy and can be used as an effective model for adaptive optimal threshold selection in OAM-QKD systems, which improves the speed of data processing and has strong guiding significance for system parameter prediction and optimization.

[0121] In an embodiment of the present invention, when a plurality of photons are used for communication transmission in atmospheric turbulence, the transmission efficiency of the plurality of photons is obtained, wherein the plurality of photons are encoded by orbital angular momentum during the transmission process; based on the transmission efficiency of the plurality of photons, the initial security key rate of the plurality of photons under high-dimensional quantum key distribution is determined; based on the initial security key rate of the plurality of photons under high-dimensional quantum key distribution, the security key length of the high-dimensional quantum key distribution under finite length effect is obtained; based on the security key length of the high-dimensional quantum key distribution under finite length effect and the number of photons, the security key rate of the high-dimensional quantum key distribution under finite length effect is determined; the security key rate of the high-dimensional quantum key distribution under finite length effect and the number of photons are added together; The initial security key rates of photons under high-dimensional quantum key distribution are compared to determine the optimal threshold of the security key rate of high-dimensional quantum key distribution under the finite length effect; based on the optimal threshold of the security key rate of high-dimensional quantum key distribution under the finite length effect and the transmission efficiency of photons under the finite length effect, the target security key rate of photons in orbital angular momentum encoding under the finite length effect is determined, which solves the technical problems of wide range, slow speed and long time in calculating the security key by polarization coding technology during quantum communication in free space transmission. This achieves the technical effect of reducing the calculation range of the security key, increasing the speed and shortening the time by combining orbital angular momentum coding with finite length effect and neural network during quantum communication in free space transmission.

[0122] The serial numbers of the above embodiments of the present invention are only for description and do not represent the advantages or disadvantages of the embodiments.

[0123] In the above embodiments of the present invention, the description of each embodiment has its own emphasis. For parts that are not described in detail in a certain embodiment, reference can be made to the relevant descriptions of other embodiments.

[0124] In the several embodiments provided in this application, it should be understood that the disclosed technical content can be implemented in other ways. Among them, the device embodiments described above are only schematic. For example, the division of units can be a logical function division. There may be other division methods in actual implementation. For example, multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be through some interfaces, indirect coupling or communication connection of units or modules, which can be electrical or other forms.

[0125] The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed over multiple units. Some or all of the units may be selected according to actual needs to achieve the purpose of the present embodiment.

[0126] In addition, each functional unit in each embodiment of the present invention may be integrated into a first processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit. The above-mentioned integrated unit may be implemented in the form of hardware or in the form of software functional units.

[0127] If the integrated unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution can be embodied in the form of a software product, and the computer software product is stored in a storage medium, including a number of instructions for a computer device (which can be a personal computer, a server or a network device, etc.) to perform all or part of the steps of the methods of each embodiment of the present invention. The aforementioned storage medium includes: U disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), mobile hard disk, magnetic disk or optical disk and other media that can store program codes.

[0128] The above are only preferred embodiments of the present invention. It should be pointed out that, for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A method for improving the performance of light field orbital angular momentum encoding quantum key distribution based on neural network, characterized in that: include: When a plurality of photons are transmitted for communication in atmospheric turbulence, the transmission efficiency of the plurality of photons is obtained, wherein the plurality of photons are encoded by orbital angular momentum during the transmission process; Based on the transmission efficiency of several photons, determine the initial security key rate of several photons under high-dimensional quantum key distribution; Based on the initial security key rate of several photons in high-dimensional quantum key distribution, the security key length of high-dimensional quantum key distribution under finite length effect is obtained; Based on the secure key length of high-dimensional quantum key distribution under finite length effect and the number of several photons, the secure key rate of high-dimensional quantum key distribution under finite length effect is determined; The security key rate of high-dimensional quantum key distribution under the finite length effect is compared with the initial security key rate of several photons under the high-dimensional quantum key distribution, and the optimal threshold of the security key rate of high-dimensional quantum key distribution under the finite length effect is determined; Based on the optimal threshold of the security key rate of high-dimensional quantum key distribution under the finite length effect and the transmission efficiency of photons under the finite length effect, the target security key rate of photons in orbital angular momentum encoding under the finite length effect is determined.

2. The method according to claim 1, characterized in that The expression of the transmission efficiency of several photons is: Among them, η(t) is the transmission efficiency of a number of photons, is the weighting factor related to the distortion caused by atmospheric turbulence, is the intensity distribution of the orbital angular momentum mode.

3. The method according to claim 1, characterized in that Based on the transmission efficiency of several photons, the expression for determining the initial security key rate of several photons in high-dimensional quantum key distribution is: Among them, R Ratewise is the initial security key rate of several photons in high-dimensional quantum key distribution, P(η) is the probability corresponding to the transmission efficiency of several photons, and R(η) is the security key rate corresponding to the transmission efficiency of several photons in high-dimensional quantum key distribution.

4. The method according to claim 1, characterized in that: Based on the security key rate of several photons in high-dimensional quantum key distribution, the expression of the security key length of high-dimensional quantum key distribution under the finite length effect is obtained as follows: Among them, K OAM,L is the security key length of orbital angular momentum basis for high-dimensional quantum key distribution under finite length effect, is the lower limit of the number of single-photon pulses in the key after OAM sieving, is the total amount of OAM-based key after screening, is the upper limit of the phase error rate of the key after the single-photon signal state SUP basis sieve, is the upper limit of the quantum bit error rate of the key after the signal state OAM basis sieving, H d (x)=-(1-x)log2(1-x)-xlog2[x / (d-1)] represents the Shannon entropy in d dimension.

5. The method according to claim 1, characterized in that Based on the secure key length of high-dimensional quantum key distribution under finite length effect and the number of photons, the expression for the secure key rate of high-dimensional quantum key distribution under finite length effect is determined as follows: Among them, R L is the secure key rate of high-dimensional quantum key distribution under finite length effect, and N is the number of photons.

6. The method according to claim 1, characterized in that After comparing the security key rate of high-dimensional quantum key distribution under finite length effect with the initial security key rate of a plurality of photons under high-dimensional quantum key distribution and determining the optimal threshold of the security key rate of high-dimensional quantum key distribution under finite length effect, the method further comprises: The three parameters that determine the security key rate of high-dimensional quantum key distribution under the finite length effect are input into the successfully trained BP neural network to determine the optimal threshold of the security key rate of high-dimensional quantum key distribution under the finite length effect; among them, the three parameters are the dimensionless ratio of the root mean square value of the orbital angular momentum beam radius to the Friedel atmospheric coherence length, the orbital angular momentum angular index and the Friedel atmospheric coherence length.

7. A processor, characterized in that: The processor is used to run a program, wherein the program executes the method according to any one of claims 1 to 6 when running.

8. A computer-readable storage medium, characterized in that: The computer-readable storage medium includes a stored program, wherein when the program is executed, the device where the computer-readable storage medium is located is controlled to execute the method according to any one of claims 1 to 6.

Images