A method for improving the performance of light field orbital angular momentum encoded quantum key distribution based on neural networks

Abstract

This invention discloses a method for improving the performance of optical field orbital angular momentum encoding quantum key distribution based on neural networks. The method includes: obtaining the transmission efficiency of several photons during communication transmission in atmospheric turbulence, wherein the photons are encoded using orbital angular momentum during transmission; determining the initial secure key rate of the photons in high-dimensional quantum key distribution based on the transmission efficiency; and obtaining the secure key length of high-dimensional quantum key distribution under finite-length effects based on the initial secure key rate of the photons in high-dimensional quantum key distribution. This invention solves the technical problems of wide computation range, slow speed, and long computation time when calculating secure keys using polarization encoding technology in free-space quantum communication.

Description

Technical Field

[0001] This invention relates to the field of quantum cryptography technology, and more specifically, to a method for improving the performance of light field orbital angular momentum encoded quantum key distribution based on neural networks. Background Technology

[0002] Driven by the grand vision of a global quantum internet, achieving long-distance, high-rate, and 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 for information encoding, decoding, transmission, reception, and post-processing, generating theoretically secure keys that are impossible to eavesdrop on or tamper with between communicating parties. Currently, most research on quantum communication is based on two-dimensional quantum systems implemented using photon polarization states or phase encoding. Although these systems have significant advantages in qubit manipulation, the information capacity is always limited to 1 bit / photon due to the boundedness of Hilbert space. To break the information entropy threshold of the system, high-dimensional quantum key distribution (HD-QKD) provides a feasible approach and is developing rapidly in both theory and experiment. Among these approaches, using the photon's transverse degree of freedom—orbital angular momentum (OAM)—for high-dimensional quantum state encoding offers advantages for improving the transmission performance of free-space quantum communication systems.

[0003] 1) Utilizing the coding advantage of the infinite-dimensional Hilbert space in a single quantum system improves the transmission efficiency and fidelity of the encoded photon state, thereby enhancing the noise resistance and communication bandwidth per unit time of the quantum communication system;

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

[0005] However, atmospheric turbulence disrupts the helical phase structure of OAM, leading to received wavefront distortion. The transmission efficiency of OAM in turbulent channels also fluctuates, causing random signal fading. Current statistical distribution models primarily focus on describing optical field intensity fluctuations, making it difficult to characterize the complexity of OAM transmittance coefficient fluctuations in turbulent channels. Therefore, characterizing the fluctuations in OAM transmission coefficients in turbulent channels is crucial for analyzing the security of OAM-coded QKD systems.

[0006] Currently, a complete theoretical analysis is lacking regarding the combination of the statistical distribution of OAM transmittance in atmospheric turbulence and QKD. Transmittance fluctuations caused by atmospheric turbulence lead to time-varying qubit errors (QBER). To address this issue, a post-selection method for high transmittance is used to improve the signal-to-noise ratio. This post-selection method relies on optimizing the transmittance threshold after receiving all signals. However, this computational approach incurs a significant burden. Optimizing QKD system parameters using machine learning methods has a significant effect on improving operating speed and achieving parameter prediction, and this method is of great importance for airborne free-space QKD missions. Based on the above analysis, this paper studies OAM-encoded QKD key estimation methods under turbulent conditions and proposes a neural network-based threshold selection QKD performance improvement method. Summary of the Invention

[0007] This invention provides a method for improving the performance of optical field orbital angular momentum coding quantum key distribution based on neural networks, in order to at least solve the technical problems of wide computation range, slow speed and long time when polarization coding technology calculates security keys during quantum communication in free space transmission.

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

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

[0010]

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

[0012] Optionally, based on the transmission efficiency of several photons, the expression for the initial secure key rate of several photons in high-dimensional quantum key distribution is as follows:

[0013]

[0014] Among them, R Ratewise Let P(η) be the initial secure key rate for a number of photons in high-dimensional quantum key distribution, P(η) be the probability corresponding to the transmission efficiency of the number of photons, and R(η) be the secure key rate corresponding to the transmission efficiency of the number of photons in high-dimensional quantum key distribution.

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

[0016]

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

[0018] Optionally, based on the secure key length and the number of photons in high-dimensional quantum key distribution under the finite-length effect, the expression for the secure key rate in high-dimensional quantum key distribution under the finite-length effect is determined as follows:

[0019]

[0020] Among them, R L Let N be the secure key rate for high-dimensional quantum key distribution under finite-length effects, where N is the number of photons.

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

[0022] The beneficial effects of this invention are:

[0023] This invention proposes a method for improving the performance of optical field orbital angular momentum encoded quantum key distribution based on neural networks. It combines the transmittance probability density function (PDF) of OAM in turbulent flow with the HD-QKD security key rate formula, achieving a comprehensive theoretical modeling of the statistical distribution of OAM-encoded QKD. The neural network method simplifies the process of traditional threshold selection methods, enabling accurate and efficient parameter prediction and performance optimization. This solves the technical problems of wide computation range, slow speed, and long time required for polarization encoding technology to calculate security keys in free-space quantum communication. By combining orbital angular momentum encoding, finite-length effects, and neural networks, this invention achieves the technical effect of reducing the computation range, speed, and time of security keys in free-space quantum communication. Attached Figure Description

[0024] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this application, illustrate exemplary embodiments of the invention and, together with their description, serve to explain the invention and do not constitute an undue limitation thereof. In the drawings:

[0025] Figure 1 This is a flowchart of a method for improving the performance of optical field orbital angular momentum encoded quantum key distribution based on neural networks, according to an embodiment of the present invention;

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

[0027] Figure 3 The optimal threshold η is under different Ω and l conditions according to embodiments of the present invention. T A schematic diagram;

[0028] Figure 4 This 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 This 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 This is a schematic diagram illustrating the relationship between the security key rate R and Ω under different l conditions according to embodiments of the present invention;

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

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

[0033] Figure 9 This is a schematic diagram comparing the traditional process and the intelligent process in an embodiment of the present invention;

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

[0035] Figure 11 This is a schematic diagram illustrating the optimal threshold prediction effect obtained using a BP neural network in an embodiment of the present invention. Detailed Implementation

[0036] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort 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, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such terms can be used interchangeably where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0038] Example 1

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

[0040] Figure 1 This is a flowchart illustrating a method for improving the performance of optical field orbital angular momentum encoded 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 several photons are transmitting communication in atmospheric turbulence, the transmission efficiency of several photons is obtained, wherein the photons are encoded by orbital angular momentum during transmission.

[0042] In the technical solution provided in step S101 of this invention, under the premise of initial light intensity normalization, 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 widely accepted probability distribution function of light radiation intensity fluctuations caused by atmospheric turbulence may not be applicable to the transmission coefficient fluctuations of the turbulent OAM optical channel. The transmission of OAM in turbulence does not conform to the log-normal and Gamma-Gamma distribution models commonly used in classical Gaussian light. Generally, it is difficult to directly establish a statistical distribution model suitable for the fluctuating transmission coefficient of the turbulent optical OAM channel through analytical mathematical derivation. Therefore, Monte Carlo simulation is used to generate random samples of the transmission coefficient, thereby proposing a suitable transmission coefficient fluctuation distribution model. First, based on the analysis in 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 several photons, determine the initial secure key rate of several photons under high-dimensional quantum key distribution.

[0044] In the technical solution provided by step S102 of the present invention, the initial security key rate of several photons under high-dimensional quantum key distribution is determined by the probability corresponding to the transmission efficiency of several photons and the security key rate corresponding to the probability corresponding to the transmission efficiency of several photons.

[0045] Step S103: Based on the initial secure key rate of several photons in high-dimensional quantum key distribution, obtain the secure key length of high-dimensional quantum key distribution under the finite length effect.

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

[0047] Step S104: Determine the secure key rate of high-dimensional quantum key distribution under the finite-length effect based on the secure key length and the number of photons in the high-dimensional quantum key distribution under the finite-length effect.

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

[0049] Step S105 compares the secure key rate of high-dimensional quantum key distribution under the finite-length effect with the initial secure key rate of several photons under high-dimensional quantum key distribution to determine the optimal threshold for the secure key rate of high-dimensional quantum key distribution under the finite-length effect.

[0050] In the technical solution provided in step S105 of the present invention, the secure key rate of high-dimensional quantum key distribution under the finite-length effect and the initial secure key rate of several photons under high-dimensional quantum key distribution are compared at different thresholds to obtain the optimal threshold for the secure key rate of high-dimensional quantum key distribution under the finite-length effect. During the integration of the secure key rate according to the code rate, due to the statistical distribution characteristics of the transmission coefficients of OAM light in free space, almost no key is generated under certain transmission efficiency conditions. However, in practice, this data still needs to be post-processed, resulting in a waste of computational resources. Combining the time-varying transmission characteristics caused by free-space atmospheric turbulence, using threshold selection to filter information and achieve post-selection reduces the amount of data computation and increases the secure key generation rate per unit time, which is the main means to improve system performance. This simplified secure key rate with threshold selection can be expressed as follows:

[0051]

[0052] Based on the above formula, change the threshold ηT Observe the changes in the security key generation rate. Figure 2 This is a schematic diagram comparing the secure key rate of the full code rate integration method and the threshold selection optimization method according to embodiments of the present invention. Figure 2 It can be seen that when the OAM exponent l=1, the set threshold value is almost equal to the fixed value obtained by integrating according to the bit rate in the initial range, and only then will it show a significant decrease. An ideal threshold value can be found based on the actual scenario to simplify the calculation; for example, in a low Ω scenario (Ω=10...). -1 Under this condition, a higher threshold value (η) can be selected. T =0.65), which can improve the efficiency of data processing. Among them, the full code rate integration method is the initial secure key rate method for several photons in high-dimensional quantum key distribution, and the secure key rate of the threshold selection optimization method is also the initial secure key rate for several photons in high-dimensional quantum key distribution. In order to further characterize the selection of the threshold more vividly, a three-dimensional image of Ω, l, and η is established. Figure 3 The optimal threshold η is under different Ω and l conditions according to embodiments of the present invention. T A schematic diagram, such as Figure 3 As shown, the influence of different variables on η can be observed intuitively. 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 gradually decreases. This conclusion is consistent with... Figure 2 This aligns with the conclusion. However, when Ω > 1, further observation of the relationship among the three factors reveals... Figure 3 As shown in (b), the relationship between the three has changed. Both l and Ω have a significant impact on the setting of η. As l increases, the selection of the optimal threshold decreases. Therefore, when Ω < 1, the influence of l on the selection of the optimal threshold can be ignored. When Ω > 1, the influence of l needs to be taken into account.

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

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

[0055] The method described in this embodiment will be further described below.

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

[0057]

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

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

[0060]

[0061] in This represents the ratio of the Laguerre-Gaussian beam width r to the Fried atmospheric coherence length r0. The root mean square value of the OAM beam radius is represented by the dimensionless ratio of r0, and l represents the angular exponent of OAM. Currently, the radial exponent of OAM is considered to be 0. w0 is the waist radius. Let k = 2π / λ represent the Rayleigh distance, k = 2π / λ represent the wave number, λ be the wavelength, and i be the imaginary unit. This represents the random phase screen. Wz represents the beam waist radius after beam propagation, which is an important parameter in Ω.

[0062] 2. Generation of random phase screens

[0063] In the above formula In practice, this can be described as a random phase screen representing the phase perturbation, which in turn causes the transmittance η(t) to fluctuate in real time. The key to achieving random transmittance sampling is obtaining the random phase screen. Due to the integration advantage over θ, a sparse spectrum-based method is chosen to generate the phase screen.

[0064]

[0065] Where a n This represents a random complex amplitude. Let z represent the position vector of the random phase screen in the two-dimensional plane, and Re(z) represent the real part of z. Let represent a random position vector, and the probability density function of the vector magnitude be:

[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, where l0 and L0 represent the internal and external scales of the turbulence (1 mm and 100 m, respectively). Vector The azimuth angle follows a uniform distribution between -π and π. Furthermore, a n It is a random complex amplitude that follows a normal distribution and obeys the following rules:

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

[0069] Where angle brackets <> denote the statistical average, and if m = n, δ mn =1, if m≠n, δ mn =0. A is generated by using N. n and The random implementation, based on formula (4), can be achieved at any position. Direct calculation of phase screen In the Monte Carlo simulation, in order to make the spectral spacing 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. A model for the probability distribution of transmittance coefficients based on the double Johnson SB distribution.

[0071] To mathematically characterize the statistical distribution of the transmission coefficient, a bi-Johnson SB distribution with a linear scaling transformation and four independent control parameters is fitted to the random fluctuations of the measurement signal in the turbulent optics OAM channel. The expression for the PDF probability density distribution of this distribution is:

[0072]

[0073] in,

[0074]

[0075] Among them, P J (η|γ,δ) represents the probability density function of the Johnson SB distribution. Four independent control parameters γ1, γ2, δ1, δ2 > 0 represent the statistical characteristics of the simulated samples. To facilitate the use of the dual 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 viewed as a mapping from three-dimensional space to four-dimensional space. Although it is difficult to establish a mathematical expression describing this mapping, Monte Carlo simulation and probability distribution fitting based on maximum likelihood estimation can reflect this mapping relationship.

[0076] ​​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 was characterized. Figure 4 This 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, and a PDF of the transmission coefficient under different Ω and r0 conditions. From Figure 4 As can be seen, under the same Ω but different r0 conditions, the PDF curves of the transmission coefficient show a similar trend despite subtle differences. However, under the same r0 but different Ω conditions, the PDF curves show a significant difference. This indicates that Ω has a stronger influence on the PDF of the transmission coefficient than r0. Simultaneously, as Ω increases, the "peak" of the PDF gradually shifts to the left, indicating that the probability of η achieving high transmittance gradually decreases, further demonstrating the enhanced channel transmittance attenuation caused by turbulence. When Ω is near 1 (e.g....), Figure 4 (b) As shown, the PDF curve exhibits severe tailing and is not easily described by existing PDF models.

[0077] The next step is to investigate how variations in l affect the statistical distribution of transmittance given r0. Considering the transmission characteristics of OAM and the experimental setup, the atmospheric coherence length r0 = 10 cm is set.

[0078] Figure 5 This 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 for different OAM indices are basically merged together, indicating that when Ω is small, l has little effect on PDF. However, for Figure 5 (b) and Figure 5 (c) At this point, Ω≥1, and differences appear between the curves, proving that there is a significant mode-dependent effect in the statistical distribution of the OAM optical transmission coefficient. This mode-dependent turbulence effect is due to the superposition of two reasons: (1) higher-order OAMs have larger beam cross-sections, resulting in a worse turbulent environment; (2) higher-order OAMs have multi-layer phase structures, making them more sensitive to phase disturbances from turbulence.

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

[0080]

[0081] Among them, R Ratewise Let P(η) be the initial secure key rate for a number of photons in high-dimensional quantum key distribution, P(η) be the probability corresponding to the transmission efficiency of the number of photons, and R(η) be the secure key rate corresponding to the transmission efficiency of the number of photons in high-dimensional quantum key distribution.

[0082] In this embodiment, HD-QKD secure key analysis based on the decoy BB84 protocol addresses the current lack of theoretical support for the dependence of the secure key generation rate R on the transmittance coefficient η in turbulent OAM channels. Based on the statistical distribution analysis of transmittance in OAM turbulent channels, and combined with the GLLP formula, by fixing the QKD system parameters at the transmitter and receiver, the key rate under the decoy BB84 protocol is expressed as a single function of R(η). Therefore, estimating the system secure key rate in a turbulent channel boils down to finding the integral of R(η) over the probability distribution η. Integrating the key rate is the most common method for obtaining the system secure key rate; that is, using all the information from the channel transmittance probability distribution, R(η) is integrated over all values ​​of the PDF. First, the asymptotic case of transmitting an infinite number of pulses is considered. Figure 4 Figure 5 It is known that the channel transmittance η for each signal transmission period has been measured and all transmittance information has been obtained. The secure key rate based on the code rate integral method can be expressed as: OAM, as the spatial degree of freedom of the optical field, can be mapped to an infinite-dimensional Hilbert space. In this 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 conjugate SUP basis is composed of the superposition of OAM states with a fixed relative phase between adjacent OAM components. The expressions for the OAM basis and the SUP basis are:

[0083]

[0084] Where d represents the dimension of the Hilbert space, and L represents the maximum OAM quantum number used, both satisfying 2L+1=d. Key receiver Bob calculates the key using the result of the OAM basis and verifies the security of the key distribution using the result of the SUP basis. After error correction and privacy methods, a secure key is extracted. For weakly coherent light sources, the secure key rate of decoy-state HD-QKD can be estimated using the following expression:

[0085]

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

[0087] For a 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 p represents the yield when the transmitter does not emit photons. d This represents the dark count of the detector, and μ represents the average number of photons in the signal state. Meanwhile, considering that the receiving bit error is affected by pointing error and mode crosstalk, The expression is:

[0090]

[0091] Unlike typical two-dimensional QKD systems, HD-QKD has a dark counting bit error rate e0 = (d-1) / d. By employing a "weak + vacuum decoy state" method, Y1 OAM and The expression is:

[0092]

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

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

[0095]

[0096]

[0097] First, the impact of the OAM index on the security key rate was simulated. Figure 6 This is a schematic diagram illustrating the relationship between the security key rate R and Ω under different l conditions according to embodiments of the present invention. Figure 6 The relationship between Ω and the secure key rate is shown. As Ω increases, the secure key rate gradually decreases, indicating that Ω reflects, to some extent, the disturbance and attenuation characteristics of the signal caused by atmospheric turbulence. However, changes in the OAM exponent l have little impact on the key rate curve. Therefore, it is possible to further consider applying high-dimensional quantum systems to improve the information transmission rate by changing Ω.

[0098] Figure 7 This is a schematic diagram illustrating the relationship between the security key rate R and Ω under different dimensional conditions according to embodiments of the present invention. Figure 7 This paper illustrates the relationship between the security key rate and Ω in a high-dimensional QKD system. The figure shows the trend of the high-dimensional QKD key rate surface when Ω is a variable. As can be seen from the figure, the higher the dimension of the QKD system, the higher the transmission security key rate and the longer the transmission distance, indicating that the QKD system can fully utilize the advantages of high-dimensional coding when Ω is the variable. However, due to effects such as mode-dependent diffraction (SDD) during atmospheric transmission of high-dimensional QKD systems, receiving efficiency mismatch can lead to security vulnerabilities and a decrease in the 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 exponent l has a very weak effect on key generation at this time.

[0099] 2. Deceptive OAM-encoded HD-QKD Finite-Length Security Key Estimation Method

[0100] Due to the differences in key analysis between HD-QKD and 2D-QKD, the security of HD-QKD systems is analyzed under asymptotic conditions, especially in the infinite key effect limit. The yield and bit error rate of the single-photon state required by the formula for the secure key rate of decoy-state HD-QKD can be accurately estimated from the OAM-encoded QKD measurements and converge to approximate true values. Therefore, the final key length of the OAM-encoded QKD can be securely obtained. However, in practical HD-QKD systems, the number of emitted quantum signal pulses is finite, resulting in statistical fluctuations between the observed and true values ​​of system parameters. When analyzing the security of HD-QKD systems, the impact of statistical fluctuations on the final secure key rate of the finite key effect response needs to be considered. For the observed value ζ>0, using the Chernov inequality, the expression for the confidence interval of the expected value E[ζ] of the observed parameter can be obtained as follows:

[0101]

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

[0103]

[0104] Where 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 secure key rate of several photons in high-dimensional quantum key distribution, the expression for the secure key length of high-dimensional quantum key distribution under the finite length effect is obtained as follows:

[0106]

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

[0108] Based on the formula for the confidence interval of the expected value E[ζ] of the observed parameters, the upper and lower bounds of the global gain and bit error rate of the signal state and decoy state under statistical fluctuations can be obtained. Combined with this, Y1 is obtained. OAM and The formula provides the upper and lower limits of the total gain and bit error rate of a single-photon pulse. Based on this, the expression for the secure key length of the OAM basis of the HD-QKD system under the finite-length effect is obtained as follows:

[0109]

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

[0111] As an optional embodiment, step S104, based on the secure key length of high-dimensional quantum key distribution under the finite-length effect and the number of photons, determines the expression for the secure key rate of high-dimensional quantum key distribution under the finite-length effect as follows:

[0112]

[0113] Among them, R L Let N be the secure key rate for high-dimensional quantum key distribution under finite-length effects, where N is the number of photons.

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

[0115]

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

[0117]

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

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

[0120] In this embodiment, since the statistical distribution of the OAM transport coefficient in turbulent flow is obtained from Monte Carlo simulations, and the data is discrete and exhibits some volatility, an adaptive threshold selection method using an artificial neural network is proposed to further optimize the threshold. The most widely used backpropagation (BP) neural network is chosen as the prediction model. Figure 9 This is a schematic diagram comparing the traditional process and the intelligent process in an embodiment of the present invention. Figure 9 This demonstrates how to obtain the optimal threshold η using the initial parameters (Ω, l, r0). T The process is clear in its steps, but it demands significant computing resources. By utilizing machine learning to train the initial parameters, it is possible to obtain the optimal threshold η. T It can also perform data prediction, demonstrating its practical advantages. Figure 10This is a schematic diagram of the BP neural network structure according to an embodiment of the present invention. The input layer output value is 3, the number of hidden layers is 3, and the number of neurons is 15, 10, and 1 respectively. The output layer output value is 1. The transfer function of the hidden layers is the tansig transfer function, the output layer uses a linear transfer function, the learning function is the Levenberg-Marquardt (LM) variable gradient algorithm, and the performance function is the mean squared error function (MSE). The training iterations are 2000, and the learning rate is 0.01. When Ω is 10⁻⁶... 2 Up to 10 1.4 The OAM index l is in the range of 0 to 16, and the optimal threshold η is established for 18*17 samples. T The dataset is used to train a neural network to predict the optimal threshold selection under different conditions. The prediction results of the BP neural network for the optimal threshold are as follows: Figure 10 As shown. Figure 11 This is a schematic diagram illustrating the optimal threshold prediction performance obtained using a BP neural network according to an embodiment of the present invention. Figure 11 (a) shows the fitting effect curve, where the horizontal axis represents the number of samples selected by the neural network, and the vertical axis represents the sample values ​​selected by the optimal threshold. Blue dots represent the original data, and red triangles represent the predicted data. Figure 11 (b) is the training error curve, where the vertical axis represents the error between the model's predicted values ​​and the original data values ​​in the training set. Figure 11 As shown in (a), the original data curve and the predicted data points exhibit a similar periodic variation pattern. This is because, during the selection of the original data, the optimal threshold is selected in ascending order of the same OAM index l. That is, after selecting 18 Ω values ​​for the same OAM index, the selection of Ω values ​​for the next OAM index is performed, 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. Figure 11 (b) Showing the training error of the sample set 10 -3 The magnitude 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, improving data processing speed and providing strong guidance for system parameter prediction and optimization.

[0121] In this embodiment of the invention, the transmission efficiency of several photons is obtained when they communicate and transmit in atmospheric turbulence, wherein the photons are encoded by their orbital angular momentum during transmission. Based on the transmission efficiency of the photons, the initial secure key rate of the photons under high-dimensional quantum key distribution is determined. Based on the initial secure key rate of the photons under high-dimensional quantum key distribution, the secure key length of high-dimensional quantum key distribution under the finite-length effect is obtained. Based on the secure key length of high-dimensional quantum key distribution under the finite-length effect and the number of photons, the secure key rate of high-dimensional quantum key distribution under the finite-length effect is determined. The secure key rate of high-dimensional quantum key distribution under the finite-length effect and the number of photons are then used to determine the secure key rate of high-dimensional quantum key distribution under the finite-length effect. By comparing the initial secure key rates of photons in high-dimensional quantum key distribution, the optimal threshold for the secure key rate of high-dimensional quantum key distribution under the finite-length effect is determined. Based on the optimal threshold for the secure 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 secure key rate of photons in orbital angular momentum encoding under the finite-length effect is determined. This solves the technical problems of wide computation range, slow speed, and long time when calculating secure keys using polarization encoding technology in free space transmission of quantum communication. It achieves the technical effect of reducing the computation range, speed, and time of secure keys in free space transmission of quantum communication by combining orbital angular momentum encoding, the finite-length effect, and neural networks.

[0122] The sequence numbers of the above embodiments of the present invention are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.

[0123] In the above embodiments of the present invention, the descriptions of each embodiment have different focuses. For parts not described in detail in a certain embodiment, please refer 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. The device embodiments described above are merely illustrative; for example, the division of units can be a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the displayed or discussed mutual couplings, direct couplings, or communication connections may be through some interfaces; indirect couplings or communication connections between units or modules may be electrical or other forms.

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

[0126] Furthermore, the functional units in the various embodiments of the present invention can be integrated into a first processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0127] If the integrated unit is implemented as 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. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, read-only memory (ROM), random access memory (RAM), portable hard drives, magnetic disks, or optical disks.

[0128] The above are merely preferred embodiments of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A neural network-based performance improvement method for light field orbital angular momentum encoding quantum key distribution, characterized in that, The method comprises the following steps: When a plurality of photons are transmitted 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 transmission; 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 high-dimensional quantum key distribution under finite length effect is obtained; Based on the security key length of high-dimensional quantum key distribution under finite length effect and the number of the plurality of photons, the security key rate of high-dimensional quantum key distribution under finite length effect is determined; The optimal threshold of the security key rate of high-dimensional quantum key distribution under finite length effect is determined by comparing the security key rate of 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; Based on the optimal threshold of the security key rate of high-dimensional quantum key distribution under finite length effect and the transmission efficiency of the plurality of photons under finite length effect, the target security key rate of the plurality of photons under orbital angular momentum encoding under finite length effect is determined.

2. The method of claim 1, wherein, The expression of the transmission efficiency of the plurality of photons is: wherein is the transmission efficiency for a number of photons, is a weighting factor related to the distortion caused by atmospheric turbulence, is the intensity distribution of the orbital angular momentum mode.

3. The method of claim 1, wherein, Based on the transmission efficiency of the plurality of photons, the expression of the initial security key rate of the plurality of photons under high-dimensional quantum key distribution is determined; wherein, is the initial security key rate of several photons in high-dimensional quantum key distribution, is the probability corresponding to the transmission efficiency of several photons, is the security key rate corresponding to the transmission efficiency of several photons in high-dimensional quantum key distribution.

4. The method of claim 1, wherein, Based on the security key rate of the plurality of photons under high-dimensional quantum key distribution, the expression of the security key length of high-dimensional quantum key distribution under finite length effect is obtained; wherein, is the secure key length of the orbital angular momentum basis for high-dimensional quantum key distribution under finite length effect, is the lower bound of the number of single-photon pulses in the sifted key of the OAM basis, is the total amount of the sifted key of the OAM basis, is the upper bound of the phase error rate of the sifted key of the single-photon signal state SUP basis, is the upper bound of the quantum bit error rate of the sifted key of the signal state OAM basis, denotes the Shannon entropy of d dimensions.

5. The method of claim 4, wherein, Based on the security key length of high-dimensional quantum key distribution under finite length effect and the number of the plurality of photons, the expression of the security key rate of high-dimensional quantum key distribution under finite length effect is determined; wherein, The secure key rate of high-dimensional quantum key distribution under finite-length effect, is the number of photons.

6. The method of claim 1, wherein, After comparing the security key rate of 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 to determine 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 in determining the security key rate of high-dimensional quantum key distribution under 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 finite length effect; wherein the three parameters are 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.

7. A processor, comprising: The processor is configured to run a program, wherein the program performs the method of any one of claims 1 to 6 when the program is running.

8. A computer-readable storage medium, characterized in that, The computer readable storage medium comprises a stored program, wherein the program controls the device where the computer readable storage medium is located to perform the method of any one of claims 1 to 6 when the program is running.

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