Method for improving performance of airborne orbital angular momentum MDI-QKD by grey wolf-difference algorithm

Abstract

The invention discloses an airborne orbital angular momentum MDI-QKD link building device, which comprises a transmitting end Alice, a transmitting end Bob and a receiving end Charlie, and is characterized in that the transmitting end Alice comprises a first laser, a first spatial light modulator SLM1, a first attenuator ATT, a first reflector, a second reflector, a first intensity modulator IM and a first telescope; the Bob end comprises a second laser, a second spatial light modulator SLM2, a second attenuator, a third reflector, a fourth reflector, a second intensity modulator IM and a second telescope; the receiving end Charlie comprises a third telescope composed of a fifth lens and a sixth lens, a fourth telescope composed of a seventh lens and an eighth lens, first to third beam splitters BS, first and second polarization gratings PG, fifth to eighth reflectors, first to fourth mode sorters MS, and first to fourth detectors. The invention further provides an MDI-QKD performance improvement method of the unmanned aerial vehicle platform OAM code based on the grey wolf-differential evolution hybrid algorithm GWO-DE. According to the method, an efficient parameter optimization strategy is provided for an airborne OAM-MDI-QKD system of a fixed link, a data set obtaining scheme for machine learning prediction is provided for meeting the high real-time requirement of a mobile link, and an idea is provided for achieving a safer and more reliable quantum communication network in the future.

Description

Technical Field

[0001] The present invention belongs to the technical field of quantum cryptography, and specifically relates to a method for improving the performance of measurement-device-independent quantum key distribution (MDI-QKD) of orbital angular momentum (OAM) encoding on an unmanned aerial vehicle (UAV) platform based on a Grey Wolf Optimization-Differential Evolution (GWO-DE) hybrid algorithm. The method comprises OAM-MDI-QKD scenario design and key estimation for the UAV platform, and a QKD performance improvement method based on an improved GWO-DE algorithm. Background Art

[0002] With the rapid development of quantum communication technology, quantum key distribution (QKD), a technique that theoretically can provide unconditional secure communication, has attracted widespread attention. In particular, implementing QKD on unmanned aerial vehicle (UAV) platforms is considered a promising solution for quantum communication networks due to its high mobility, flexibility, and low cost. However, practical QKD systems face security risks due to the presence of non-ideal devices, such as single-photon sources and detectors, which can be exploited by eavesdroppers. To address these issues, decoy state protocols and measurement-device-independent quantum key distribution (MDI-QKD) have been proposed to enhance system security.

[0003] On drone platforms, due to their high-speed movement and vibration, reference frame alignment loss must be considered. Orbital angular momentum (OAM) can effectively circumvent this problem by leveraging its rotational invariance. The OAM-MDI-QKD protocol utilizes the OAM degree of freedom of photons as an information carrier, avoiding the reference frame alignment issue while employing decoy states to overcome the security vulnerabilities of weakly coherent pulse sources.

[0004] In QKD systems, parameter optimization is crucial for achieving optimal performance. This includes the strengths of the signal and decoy states, as well as the probabilities associated with these strengths and basis selection. While ideal, global parameter search is computationally challenging for high-dimensional functions. To address these issues, researchers have proposed a variety of optimization algorithms, including local search algorithms (LSAs), particle swarm optimization (PSOs), and genetic algorithms (GAs). However, these algorithms can become trapped in local optima when dealing with non-convex objective functions, and LSA requires the first-order derivative of the objective function to be continuous, which is unacceptable for the key rates of many QKD protocols. Summary of the Invention

[0005] To address this issue, the present invention studies methods for improving the OAM-MDI-QKD performance of unmanned aerial vehicle platforms. By optimizing parameters through a swarm intelligence optimization algorithm, an airborne orbital angular momentum MDI-QKD link establishment device is proposed. The device includes transmitters Alice and Bob and a receiver Charlie. After the transmitters Alice and Bob achieve beacon light alignment with the receiver Charlie, OAM optical signal transmission is performed. The details are as follows:

[0006] Alice end includes a first laser, a first spatial light modulator SLM1, a first attenuator ATT, a first reflecting mirror, a second reflecting mirror, a first intensity modulator IM, and a first telescope;

[0007] The first laser emits a first optical signal;

[0008] The first spatial light modulator SLM1 receives the first optical signal emitted by the first laser and modulates it into a first orbital angular momentum OAM state output;

[0009] The first attenuator receives the first orbital angular momentum OAM state output by the first spatial light modulator and attenuates it to a first weak coherent state WCS output;

[0010] a first reflecting mirror, which reflects the first weak coherent state WCS output by the first attenuator at 90 degrees;

[0011] A second reflector, which again reflects the first weak coherent state WCS output by the first reflector at 90 degrees, thereby reversing the direction of the first weak coherent state WCS output by the first attenuator by 180 degrees;

[0012] The first intensity modulator receives the first weak coherent state WCS output by the second reflecting mirror, modulates it, and generates corresponding first decoy state and first vacuum state outputs;

[0013] The first telescope includes a first lens L1 and a second lens L2. The first decoy state and the first vacuum state output by the first intensity modulator pass through the first lens L1 and the second lens L2 in sequence, and are magnified and transmitted by the first lens L1 and the second lens L2.

[0014] Bob's end is identical and symmetrical to Alice's end, and includes a second laser, a second spatial light modulator SLM2, a second attenuator, a third reflector, a fourth reflector, a second intensity modulator IM, and a second telescope;

[0015] The second laser emits a second optical signal;

[0016] The second spatial light modulator receives the second optical signal emitted by the second laser and modulates it into a second orbital angular momentum OAM state output;

[0017] The second attenuator receives the second orbital angular momentum OAM state output by the second spatial light modulator and attenuates it into a second weak coherent state WCS output;

[0018] a third reflecting mirror, which reflects the second weak coherent state WCS output by the second attenuator at 90 degrees;

[0019] a fourth reflector, which again reflects the second weak coherent state WCS output by the third reflector at 90 degrees, thereby reversing the direction of the second weak coherent state WCS output by the second attenuator by 180 degrees;

[0020] The second intensity modulator receives the second weak coherent state WCS output by the fourth reflector, modulates it, and generates corresponding second decoy state and second vacuum state outputs;

[0021] The second telescope includes a third lens L3 and a fourth lens L4. The second decoy state and the second vacuum state output by the second intensity modulator pass through the third lens L3 and the fourth lens L4 in sequence, and are magnified and transmitted by the third lens L3 and the fourth lens L4.

[0022] The photons output by Bob and Alice are then sent to the receiving end Charlie via a free-air space link for measurement;

[0023] The receiving end Charlie includes a third telescope composed of the fifth and sixth lenses, a fourth telescope composed of the seventh and eighth lenses, first to third beam splitters BS, first and second polarization gratings PG, fifth to eighth reflecting mirrors, first to fourth mode selectors MS, and first to fourth detectors;

[0024] The third telescope receives the first signal state, the first decoy state, and the first vacuum state;

[0025] The fourth telescope receives the second signal state, the second decoy state, and the second vacuum state;

[0026] The first beam splitter BS interferes with the two groups of light signals output by the third and fourth telescopes to generate a first group of photons and a second group of photons, which are output separately at an angle of 90 degrees.

[0027] The first polarization grating separates the first group of photons into left-handed polarized photons and right-handed circularly polarized photons and outputs them;

[0028] The second polarization grating separates the second group of photons, namely left-handed polarized photons and right-handed circularly polarized photons, and outputs the photons;

[0029] The fifth reflector reflects the left-handed polarized photons of the first group of photons emitted from the first polarization grating at 90 degrees;

[0030] The sixth reflector reflects the right-handed polarized photons of the first group of photons emitted from the first polarization grating at 90 degrees;

[0031] The seventh reflecting mirror reflects the right-handed polarized photons of the second group of photons emitted from the second polarization grating at 90 degrees;

[0032] The seventh reflecting mirror reflects the left-handed polarized photons of the second group of photons emitted from the second polarization grating at 90 degrees;

[0033] The second beam splitter receives the left-handed polarized photons and the right-handed polarized photons of the first group output by the fifth and sixth reflectors, interferes with the photons, and outputs a first OAM photon state and a second OAM photon state from two directions approximately 90 degrees apart, respectively.

[0034] The third beam splitter receives the left-handed polarized photons and the right-handed polarized photons of the second group output by the seventh and eighth reflectors, interferes with the photons, and outputs a third OAM photon state and a fourth OAM photon state from two directions approximately 90 degrees apart, respectively.

[0035] The first mode selector receives and outputs the first OAM photon state emitted after interference from the second beam splitter;

[0036] The second mode selector receives and outputs the second OAM photon state emitted after interference from the second beam splitter;

[0037] The third mode selector receives and outputs the third OAM photon state emitted after interference from the third beam splitter;

[0038] The fourth mode selector receives and outputs the fourth OAM photon state emitted after interference from the third beam splitter;

[0039] The first detector D0 detects the first OAM photon state output by the first mode selector;

[0040] The second detector D1 detects the second OAM photon state output by the first mode selector;

[0041] The third detector H0 detects the third OAM photon state output by the first mode selector;

[0042] The fourth detector H1 detects the fourth OAM photon state output by the first mode selector.

[0043] A method for improving the performance of airborne orbital angular momentum MDI-QKD using a Grey Wolf-differential algorithm is also provided. The method is based on the above-mentioned airborne orbital angular momentum MDI-QKD link establishment device and specifically includes the following steps:

[0044] Step 1: Construction of OAM-MDI-QKD scenario on UAV platform;

[0045] Building the airborne orbital angular momentum MDI-QKD link building device as claimed in claim 1;

[0046] Step 2, OAM-MDI-QKD security key rate analysis;

[0047] The OAM-MDI-QKD protocol with a finite code length of three-intensity decoy states is adopted; two mutually unbiased bases, the OAM basis and the SUP basis, are used, which are expressed as:

[0048]

[0049] in, Indicates the OAM base state is 0, Indicates an OAM basis with a state of 1, represents the SUP basis with state n, l is the topological charge, and n represents the state of 0 or 1. At this time, the SUP basis is in a superposition state and does not have rotation invariance. The reference frame alignment error needs to be considered. Alice and Bob modulate the received weak coherent light pulse into {μ i},i=2,1,0 and {v j}, j = 2, 1, 0, where μ2 represents the signal state strength sent by Alice, μ1 represents the decoy state strength sent by Alice, μ0 represents the vacuum state strength sent by Alice, v2 represents the signal state strength sent by Bob, v1 represents the decoy state strength sent by Bob, and v0 represents the vacuum state strength sent by Bob; the probabilities of Alice sending the signal state, decoy state, and vacuum state are respectively and at this time Then, Alice and Bob each choose a basis with a certain OAM probability and SUP base selection probability Independently select OAM or SUP base encoding information, then Since it is a symmetric channel, Alice and Bob’s decoy state strength, transmission probability, and basis selection probability are all equal;

[0050] Taking into account parameters such as the strength of the signal state and the decoy state, the probability of sending the signal state, the decoy state, and the signal state, and the basis selection probability, the key rate formula of the OAM-MDI-QKD protocol is:

[0051]

[0052] in, represents the system key rate, represents the probability of Bob sending a signal, represents the probability that Alice discovers the signal state and uses OAM basis coding, represents the probability that Bob finds the signal state and uses OAM basis encoding, is the gain when both Alice and Bob choose the OAM basis and send single photon states, Indicates that after considering the selection of OAM basis probability and signal probability The lower bound of is the quantum bit error rate (QBER) when both parties choose the SUP basis and send a single photon state, Indicates that after considering the SUP base probability and signal probability The upper bound of It represents the total gain when both parties choose the OAM basis to send the signal state after considering the probability of selecting the OAM basis and the probability of the signal state. is the total QBER when both parties choose the OAM basis to send signals; H(x) = -xlog2(x)-(1-x)log2(1-x) is the binary Shannon information entropy function, and f is the system error correction efficiency;

[0053] According to the three-intensity decoy state and finite code length restriction used in the protocol, the gain and QBER when Alice and Bob send OAM coded information are obtained:

[0054] When Alice and Bob both choose the SUP basis, the gain and QBER are expressed as:

[0055]

[0056] in, Indicates that Alice and Bob both choose the SUP basis and send strength μ i and v j Gain at s ij represents the square root coefficient of the photon intensity, I0(·) represents the first kind of modified Bessel function, represents the QBER when both Alice and Bob choose the SUP basis, e0 represents the initial error rate, e d Detection deflection error, y ij represents the photon detection efficiency factor;

[0057] When Alice and Bob both choose OAM basis, the gain is:

[0058]

[0059] in, Alice and Bob both choose OAM basis and transmit strength μ i and v j The gain when Indicates the correct gain, represents the bit error gain, η A and η B are the transmittances of Alice and Bob respectively, Pd is the dark count rate of the single-photon detector, and the parameter formula y ij , photon transmission intensity μ ij ′、s ij It is given by:

[0060]

[0061] μ ij ′=η A μ i +η B ν j (10)

[0062]

[0063] Considering the probability of signal transmission, the limits of statistical fluctuations are as follows:

[0064]

[0065] Among them, x represents the selection of OAM basis and SUP basis, Indicates that the x basis is selected and the sending strength is μ i and v j The gain when Select x basis and send strength μ i and v j QBER, After considering the probability After considering the probability is the volatility of the modified gain, is the fluctuation rate of the corrected bit error, expressed as:

[0066]

[0067] Among them, n α is the value of the standard deviation used for statistical fluctuation analysis, After considering the probability, Alice and Bob use μ i and v j When the signal strength is x, the number of pulses of the base is:

[0068]

[0069] Where N is the total number of pulses sent by Alice and Bob. Indicates the sending signal strength μ i The probability of using x-based coding when Send signal strength v j The probability of using x-based coding when ; Indicates the signal strength v sent by Bob j probability;

[0070] Lower bound on single-photon gain and the upper bound of the single-photon QBER The calculation is performed by setting the choice of x, where x is an OAM basis or a SUP basis:

[0071]

[0072] in, is the single-photon gain in the x-basis, represents the lower bound of the single-photon gain in the x-basis after considering the probability, represents the gain when the x basis is selected under probability and the sending strength is μ2 and v2, express The upper bound of represents the gain when the x basis is selected under probability and the sending strength is μ1 and v1, express The lower bound, represents the QBER when the x basis is selected with the transmission strength of μ1 and v1 under probability, express The upper bound of is the single-photon QBER in the x basis, represents the upper bound of the single-photon QBER in the x-basis after considering the probability, Represents the signal strength difference gain under probability The lower bound, Indicates the probability of adjusting the coefficient gain The lower bound, Represents another set of adjustment coefficient combination gains under probability The lower bound, represents the error rate adjustment gain under probability The lower bound of κ represents the system gain adjustment coefficient, and the parameter formula κ, is given by:

[0073]

[0074] in, represents the gain of signal strength 0 and ν2 in the x basis, represents the gain of the signal strength μ2 and 0 under the x basis, represents the gain of signal strength 0 and ν1 in the basis x, represents the gain of signal strength μ1 and 0 under x basis, represents the gain of signal strength μ2 and ν1 in the basis x, represents the gain of signal strength 0 and 0 under x basis, represents the gain of signal strength μ1 and ν2 in the basis x, represents the QBER of signal strength 0 and ν1 in the basis x, represents the QBER for signal strengths μ1 and 0 in the basis x, represents the QBER of signal strength 0 and 0 under x basis;

[0075] Therefore, the key rate of the UAV fixed link OAM-MDI-QKD protocol is related to the following seven independent parameters: the signal state strength μ2, the decoy state strength μ1, the probability of selecting the signal state The probability of choosing the decoy state Determine the signal state and the conditional probability of choosing SUP basis code Determine the conditional probability of the decoy state and choose the SUP base code and the conditional probability of determining the signal state and selecting the SUP basis code Setting variable sets

[0076] Step 3: Improved Grey Wolf Difference Algorithm

[0077] In the present invention, for the parameter optimization of the 7-dimensional non-convex nonlinear objective function R, traditional convex optimization algorithms have certain limitations; the common particle swarm optimization (PSO) algorithm is prone to premature convergence in the early stage of the search, and the global search efficiency is reduced for high-dimensional and nonlinear problems; the genetic (GA) algorithm has good global search capabilities, but the crossover and mutation may have large fluctuations, the solution is unstable, and for high-dimensional problems, it may even cause the destruction of the solution, and the computational cost is high; the DE algorithm performs well in multi-peak function search, but the performance depends on parameter selection, and the population diversity decreases during the iteration process, resulting in a decrease in the search capability in the later stage; the GWO algorithm can better handle high-dimensional nonlinear problems and has better convergence and search capabilities, but has poor stability and is prone to falling into near-optimal solutions; to address these limitations, the present invention proposes an improved gray wolf algorithm and differential evolution hybrid algorithm, which integrates the crossover, mutation and selection processes of the DE algorithm into the GWO algorithm, adopts population initialization based on Cubic chaos mapping and a convergence factor of nonlinear attenuation to balance the different requirements for the search area in the early and late stages of the algorithm, overcomes the defect of GWO easily falling into near-optimal solutions, and improves the algorithm search accuracy and efficiency;

[0078] a. Population initialization based on Cubic chaotic map;

[0079] Cubic chaos map is expressed as:

[0080]

[0081] Where: x i+1 is the chaos value of the next generation, xi is the contemporary chaos value. In a specific embodiment of the present invention, the chaos mapping parameter γ = 2.595;

[0082] b. Improvement of nonlinear convergence factor;

[0083] A nonlinear convergence factor a based on the cosine function is introduced. The convergence factor expression is:

[0084]

[0085] Where: a max and a min are the initial and final values ​​of a, m is the decreasing index, T is the maximum number of iterations, and t represents the current number of iterations;

[0086] c.GWO-DE algorithm process;

[0087] The details are as follows:

[0088] (1) Initialize the environment and define parameters: population NP, dimension d, upper and lower bounds of variables ub and lb, maximum number of iterations T, upper and lower bounds of convergence factor a max and a min , DE scaling factor F, DE crossover operator P CR ;

[0089] (2) Initialize the population based on the Cubic chaos map and calculate the current fitness according to formula (3) Select the first three individual positions and label them as α, β and δ wolves respectively; the distance D from the wolf pack to the prey is:

[0090] D=|C·X p (t)-X(t)| (24)

[0091] X(t+1)=X p (t)-A·D (25)

[0092] Where: X p (t) is the position of the prey, X(t) is the position of the wolf after the tth iteration, and C and A are the coordination coefficients:

[0093] A=2a·r1-a (26)

[0094] C=2·r2 (27)

[0095] Among them, r1 and r2 are random numbers between [0,1];

[0096] During the pursuit, the gray wolf updates its position as its prey moves as follows:

[0097]

[0098] Where D α 、D β and D δ Respectively represent the distances of α, β and δ wolves to other ω wolves, X α (t), X β (t) and X δ (t) represents the current position of α, β and δ wolves respectively, X1(t), X2(t) and X3(t) represent the distance that ω wolf moves to α, β and δ wolves respectively, X(t+1) is the updated position of gray wolf, C1, C2 and C3 are three coordination coefficients, and A1, A2 and A3 are the other three coordination coefficients;

[0099] (3) Calculate the current convergence factor a according to formula (32), calculate the coordination coefficients A and C according to formulas (26) and (27), and calculate the relative distance D between the remaining ω wolves in the population and X1(t), X2(t), and X3(t) according to formulas (28)-(30). α 、D β and D δ and update the wolf pack's location;

[0100] (4) According to the crossover operator P CR , perform crossover and mutation operations on α, β, δ and ω wolves, and use a greedy strategy to select the target individual;

[0101] (5) Update the wolf pack position and recalculate fitness Identify the new generation of alpha, beta, and delta wolves;

[0102] (6) Determine whether the output condition is met. If t = T, record the current global optimal fitness and optimal individual position; otherwise, return to step (3) and continue execution.

[0103] In step a of Step 3 of a specific embodiment of the present invention, the chaotic mapping parameter γ=2.595.

[0104] The present invention combines the flexibility of the UAV platform and the rotational invariance of OAM with the security of MDI technology and decoy state technology to build a relay transmission link; it uses chaotic mapping and nonlinear strategies to enhance the algorithm's ability to escape local optimality and improve its convergence, thereby achieving efficient transmission of the link, providing a theoretical basis for further realizing a safer and more reliable quantum communication network. This optimization algorithm is also applicable to parameter optimization problems of other QKD systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0105] Figure 1 It is the OAM-MDI-QKD scenario diagram of the UAV platform;

[0106] Figure 2is the key rate of the OAM-MDI-QKD system without parameter optimization;

[0107] Figure 3 is the relationship between the number of iterations and the key rate under different algorithms;

[0108] Figure 4 It is the key rate result under the optimization of PSO, GA and DE algorithms;

[0109] Figure 5 It is the key rate result under the optimization of DE, GWO, and GWO-DE algorithms. DETAILED DESCRIPTION

[0110] The present invention will be described in detail below with reference to the accompanying drawings and embodiments.

[0111] The present invention proposes an airborne orbital angular momentum MDI-QKD link establishment device, which is specifically as follows.

[0112] Fixed communication links and optical paths established for UAV platforms Figure 1 shown.

[0113] The Alice end includes a first laser, a first spatial light modulator SLM1, a first attenuator (ATT), a first reflecting mirror, a second reflecting mirror, a first intensity modulator (IM), and a first telescope.

[0114] The first laser emits a first optical signal;

[0115] The first spatial light modulator SLM1 receives the first optical signal emitted by the first laser and modulates it into a first orbital angular momentum (OAM) state output;

[0116] The first attenuator receives the first orbital angular momentum OAM state output by the first spatial light modulator and attenuates it to a first weak coherent state (WCS) output;

[0117] a first reflecting mirror, which reflects the first weak coherent state WCS output by the first attenuator at 90 degrees;

[0118] The second reflector reflects the first weak coherent state WCS output by the first reflector M1 at 90 degrees again, so that the direction of the first weak coherent state WCS output by the first attenuator is reversed by 180 degrees;

[0119] The first intensity modulator receives the first weak coherent state WCS output by the second reflector M2, modulates it, and generates corresponding first decoy state and first vacuum state outputs;

[0120] The first telescope includes a first lens L1 and a second lens L2. The first decoy state and the first vacuum state output by the first intensity modulator pass through the first lens L1 and the second lens L2 in sequence, and are magnified and transmitted by the first lens L1 and the second lens L2.

[0121] The Bob end is identical and symmetrical to the Alice end, and includes a second laser, a second spatial light modulator SLM2, a second attenuator, a third reflector, a fourth reflector, a second intensity modulator (IM), and a second telescope.

[0122] The second laser emits a second optical signal;

[0123] The second spatial light modulator receives the second optical signal emitted by the second laser and modulates the second optical signal into a second orbital angular momentum (OAM) state output;

[0124] The second attenuator receives the second orbital angular momentum OAM state output by the second spatial light modulator and attenuates it into a second weak coherent state (WCS) output;

[0125] a third reflecting mirror, which reflects the second weak coherent state WCS output by the second attenuator at 90 degrees;

[0126] a fourth reflector, which again reflects the second weak coherent state WCS output by the third reflector at 90 degrees, thereby reversing the direction of the second weak coherent state WCS output by the second attenuator by 180 degrees;

[0127] The second intensity modulator receives the second weak coherent state WCS output by the fourth reflector M4, modulates it, and generates corresponding second decoy state and second vacuum state outputs;

[0128] The second telescope includes a third lens L3 and a fourth lens L4. The second decoy state and the second vacuum state output by the second intensity modulator pass through the third lens L3 and the fourth lens L4 in sequence, and are magnified and transmitted by the two lenses.

[0129] The photons output by Bob and Alice are then sent to the receiving end Charlie via a free-air space link for measurement.

[0130] The receiving end Charlie includes a third telescope composed of the fifth and sixth lenses, a fourth telescope composed of the seventh and eighth lenses, first to third beam splitters (BS), first and second polarization gratings (PG), fifth to eighth mirrors, first to fourth mode selectors (MS), and first to fourth detectors.

[0131] The third telescope receives the first signal state, the first decoy state, and the first vacuum state;

[0132] The fourth telescope receives the second signal state, the second decoy state, and the second vacuum state;

[0133] The first beam splitter BS interferes with the two groups of light signals output by the third and fourth telescopes to generate a first group of photons and a second group of photons, which are output separately at an angle of 90 degrees.

[0134] The first polarization grating separates the first group of photons into left-handed polarized photons and right-handed circularly polarized photons and outputs them;

[0135] The second polarization grating separates the second group of photons, namely left-handed polarized photons and right-handed circularly polarized photons, and outputs the photons;

[0136] The fifth reflector reflects the left-handed polarized photons of the first group of photons emitted from the first polarization grating at 90 degrees;

[0137] The sixth reflector reflects the right-handed polarized photons of the first group of photons emitted from the first polarization grating at 90 degrees;

[0138] The seventh reflecting mirror reflects the right-handed polarized photons of the second group of photons emitted from the second polarization grating at 90 degrees;

[0139] The seventh reflecting mirror reflects the left-handed polarized photons of the second group of photons emitted from the second polarization grating at 90 degrees;

[0140] The second beam splitter receives the left-handed polarized photons and the right-handed polarized photons of the first group output by the fifth and sixth reflectors, interferes with the photons, and outputs a first OAM photon state and a second OAM photon state from two directions approximately 90 degrees apart, respectively.

[0141] The third beam splitter receives the left-handed polarized photons and the right-handed polarized photons of the second group output by the seventh and eighth reflectors, interferes with the photons, and outputs a third OAM photon state and a fourth OAM photon state from two directions approximately 90 degrees apart, respectively.

[0142] The first mode selector receives and outputs the first OAM photon state emitted after interference from the second beam splitter;

[0143] The second mode selector receives and outputs the second OAM photon state emitted after interference from the second beam splitter;

[0144] The third mode selector receives and outputs the third OAM photon state emitted after interference from the third beam splitter;

[0145] The fourth mode selector receives and outputs the fourth OAM photon state emitted after interference from the third beam splitter;

[0146] The first detector D0 detects the first OAM photon state output by the first mode selector;

[0147] The second detector D1 detects the second OAM photon state output by the first mode selector;

[0148] The third detector H0 detects the third OAM photon state output by the first mode selector;

[0149] The fourth detector H1 detects the fourth OAM photon state output by the first mode selector;

[0150] The system uses the unmanned aerial vehicle (UAV) platform Charlie as the receiving and processing end, hovering at a fixed point in the air. Alice and Bob serve as the transmitting ends, located at ground stations on either side. Different system parameter selections for different transmission distances will result in different key rates. Therefore, a key rate function optimization algorithm can be used to determine the optimal parameter values ​​for the current transmission distance. These parameters can be pre-entered when establishing the link, maximizing the transmission key rate and improving system performance.

[0151] The present invention also proposes a method for improving the performance of airborne orbital angular momentum MDI-QKD based on the Grey Wolf-Differential Algorithm, which specifically includes the following steps.

[0152] Step 1: Construction of OAM-MDI-QKD scenario on UAV platform;

[0153] Build the airborne orbital angular momentum MDI-QKD link construction device as described above.

[0154] Step 2, OAM-MDI-QKD security key rate analysis;

[0155] The OAM-MDI-QKD protocol with three-intensity decoy states (signal state, decoy state, and vacuum state) and finite code length is adopted. Two mutually unbiased bases, the OAM basis and the SUP basis, are used, which are expressed as:

[0156]

[0157] in, Indicates the OAM base state is 0, Indicates an OAM basis with a state of 1, represents the SUP basis with state n, l is the topological charge, and n represents the state of 0 or 1. At this time, the SUP basis is in a superposition state and does not have rotation invariance. The reference frame alignment error needs to be considered. Alice and Bob modulate the received weak coherent light pulse into {μ i},i=2,1,0 and {v j}, j = 2, 1, 0, where μ2 represents the signal state strength sent by Alice, μ1 represents the decoy state strength sent by Alice, μ0 represents the vacuum state strength sent by Alice, v2 represents the signal state strength sent by Bob, v1 represents the decoy state strength sent by Bob, and v0 represents the vacuum state strength sent by Bob; the probabilities of Alice sending the signal state, decoy state, and vacuum state are respectively and at this time Then, Alice and Bob each choose a basis with a certain OAM probability and SUP base selection probability Independently select OAM or SUP base encoding information, then Since it is a symmetric channel, Alice and Bob's decoy state strength, transmission probability and basis selection probability are equal.

[0158] Taking into account parameters such as the strength of the signal state and the decoy state, the probability of sending the signal state, the decoy state, and the signal state, and the basis selection probability, the key rate formula of the OAM-MDI-QKD protocol is:

[0159]

[0160] in, represents the system key rate (i.e., current fitness), represents the probability of Bob sending a signal, represents the probability that Bob finds the signal state and uses OAM basis encoding, is the gain when both Alice and Bob choose the OAM basis and send single photon states, Indicates that after considering the selection of OAM basis probability and signal probability The lower bound of is the quantum bit error rate (QBER) when both parties choose the SUP basis and send a single photon state, Indicates that after considering the SUP base probability and signal probability The upper bound of . It represents the total gain when both parties choose the OAM basis to send the signal state after considering the probability of selecting the OAM basis and the probability of the signal state. is the total QBER when both parties choose the OAM basis to send signals. In addition, H(x) = -xlog2(x)-(1-x)log2(1-x) is the binary Shannon information entropy function, and f is the system error correction efficiency.

[0161] According to the three-intensity decoy state and finite code length limit used in the protocol, the gain and QBER when Alice and Bob send OAM coded information can be obtained:

[0162] When Alice and Bob both choose the SUP basis, the gain and QBER are expressed as:

[0163]

[0164] in, Indicates that Alice and Bob both choose the SUP basis and send strength μ i and v j Gain at time, I0(s ij ) represents the modified Bessel function of the first kind, represents the QBER when both Alice and Bob choose the SUP basis, e0 represents the initial error rate, e d Detection deflection error, photon detection efficiency factor y ij and the square root coefficient of photon intensity s ij .

[0165] When Alice and Bob both choose OAM basis, the gain is:

[0166]

[0167] in, Alice and Bob both choose OAM basis and transmit strength μ i and v j The gain when Indicates the correct gain, represents the bit error gain, η A and η B are the transmittances of Alice and Bob respectively, P d is the dark count rate of the single-photon detector, and the parameter formula y ij , photon transmission intensity μ ij ′、s ij It is given by:

[0168]

[0169] μ ij ′ =η A μ i +η B ν j (10)

[0170]

[0171] Considering the probability of signal transmission, the limits of statistical fluctuations are as follows:

[0172]

[0173] Among them, x represents the selection of OAM basis and SUP basis, Indicates that the x basis is selected and the sending strength is μ i and v j The gain when Select x basis and send strength μ i and v j QBER, After considering the probability After considering the probability is the volatility of the modified gain, is the fluctuation rate of the corrected bit error, expressed as:

[0174]

[0175] Among them, n α is the value of the standard deviation used for statistical fluctuation analysis, After considering the probability, Alice and Bob use μ i and v j When the signal strength is x, the number of pulses of the base is:

[0176]

[0177] Where N is the total number of pulses sent by Alice and Bob. Indicates the sending signal strength μ i The probability of using x-based coding when Send signal strength v j The probability of using x-based coding when .

[0178] Lower bound on single-photon gain and the upper bound of the single-photon QBER The calculation can be performed by setting the choice of x, where x is an OAM basis or a SUP basis:

[0179]

[0180] in, is the single-photon gain in the x-basis, represents the lower bound of the single-photon gain in the x-basis after considering the probability, represents the gain when the x basis is selected under probability and the sending strength is μ2 and v2, express The upper bound of represents the gain when the x basis is selected under probability and the sending strength is μ1 and v1, express The lower bound, represents the QBER when the x basis is selected with the transmission strength of μ1 and v1 under probability, express The upper bound of is the single-photon QBER in the x basis, represents the upper bound of the single-photon QBER in the x-basis after considering the probability, Represents the signal strength difference gain under probability The lower bound, Indicates the probability of adjusting the coefficient gain The lower bound, Represents another set of adjustment coefficient combination gains under probability The lower bound, represents the error rate adjustment gain under probability The lower bound of κ represents the system gain adjustment coefficient, and the parameter formula κ, is given by:

[0181]

[0182] in, represents the gain of signal strength 0 and ν2 in the x basis, represents the gain of the signal strength μ2 and 0 under the x basis, represents the gain of signal strength 0 and ν1 in the basis x, represents the gain of signal strength μ1 and 0 under x basis, represents the gain of signal strength μ2 and ν1 in the basis x, represents the gain of signal strength 0 and 0 under x basis, represents the gain of signal strength μ1 and ν2 in the basis x, represents the gain of signal strength 0 and ν2 in the x basis, represents the QBER of signal strength 0 and ν1 in the basis x, represents the QBER for signal strengths μ1 and 0 in the basis x, Indicates the QBER of signal strength 0 and 0 in the basis x.

[0183] Therefore, the key rate of the UAV fixed link OAM-MDI-QKD protocol is related to the following seven independent parameters: the signal state strength μ2, the decoy state strength μ1, the probability of selecting the signal state The probability of choosing the decoy state Determine the signal state and the conditional probability of choosing SUP basis code Determine the conditional probability of the decoy state and choose the SUP base code and the conditional probability of determining the signal state and selecting the SUP basis code Setting variable sets

[0184] Step 3: Improved Grey Wolf Difference Algorithm

[0185] a. Differential Evolution (DE)

[0186] Assume K i For the i-th individual in the N population, the DE algorithm randomly selects two individuals and performs a mutation operation on the third individual using weighted difference:

[0187]

[0188] Where: t is the number of iterations, W i (t+1) is the i-th individual that mutated in the t+1-th evolution, is the r1th individual (target individual) after the tth evolution, r1, r2 and r3 are random numbers in [1, N] that are different from i and are not equal to each other, and F is the scaling factor that controls the impact of the mutation, which is usually a positive number between 0 and 2.

[0189] In order to increase individual diversity, the crossover operator and the random number are compared to determine whether to perform a crossover operation. The experimental individuals generated by the crossover operation are:

[0190] Z(t+1)=(z1(t+1),z2(t+1),…z d (t+1)) (21)

[0191]

[0192] Where: Z(t+1) is the experimental individual of the t+1 evolution, z j (t+1) is the value of the jth dimension in Z(t+1), w j (t+1) is the individual W after the mutation operation i The value of the jth dimension in (t+1), K i (t+1) is the target individual, k j (t+1) is K i The value of the jth dimension in (t+1), rand is a random number between [0,1], Cr is the crossover operator, the subscript d indicates the dimension, rand d is a randomly chosen dimension.

[0193] After the mutation and crossover process, the DE algorithm uses a greedy selection strategy to compare the fitness of the test individual and the target individual and select the better one as the new target individual.

[0194]

[0195] Where: Z i(t+1) represents the experimental individual of the t-th evolution, f(x) represents the fitness of the objective function, and the key selection rate is the fitness of the objective function.

[0196] b. Grey Wolf Optimization (GWO)

[0197] The social hierarchy is divided into four layers: the first layer is the leader, called α wolf; the second layer is responsible for assisting α wolf, called β wolf; the third layer is responsible for following the orders and decisions of α and β, called δ wolf; and the fourth layer is the lowest-ranking follower, called ω wolf. Through fitness calculation, the top three optimal solutions are selected as α, β, and δ wolf, and the rest are ω wolf.

[0198] The wolf pack takes action to surround the prey. Assume that the distance D between the wolf pack and the prey is:

[0199] D=|C·X p (t)-X(t)| (24)

[0200] X(t+1)=X p (t)-A·D (25)

[0201] Where: X p (t) is the position of the prey, X(t) is the position of the wolf after the tth iteration, t is the current iteration number, and C and A are the coordination coefficients:

[0202] A=2a·r1-a (26)

[0203] C=2·r2 (27)

[0204] in, is a linearly decreasing convergence factor, T is the maximum number of iterations, and r1 and r2 are random numbers between [0,1].

[0205] During the pursuit, the gray wolf updates its position as its prey moves as follows:

[0206]

[0207] Where D α 、D β and D δ Respectively represent the distances of α, β and δ wolves to other ω wolves, X α (t), X β (t) and X δ(t) represents the current position of α, β and δ wolves respectively, X1(t), X2(t) and X3(t) represent the distance that ω wolf moves to α, β and δ wolves respectively, X(t+1) is the updated position of gray wolf, C1, C2 and C3 are three coordination coefficients, and A1, A2 and A3 are the other three coordination coefficients.

[0208] c. Improved Grey Wolf-Difference Hybrid Algorithm

[0209] In the present invention, for the parameter optimization of the 7-dimensional non-convex nonlinear objective function R, traditional convex optimization algorithms have certain limitations. The common particle swarm optimization (PSO) algorithm is prone to premature convergence in the early stage of the search, and the global search efficiency is reduced for high-dimensional and nonlinear problems; the genetic (GA) algorithm has good global search capabilities, but the crossover and mutation may have large fluctuations, the solution is unstable, and for high-dimensional problems it may even lead to the destruction of the solution, and the computational cost is high; the DE algorithm performs well in multi-peak function search, but the performance depends on parameter selection, and the population diversity decreases during the iteration process, resulting in a decrease in the later search capability; the GWO algorithm can better handle high-dimensional nonlinear problems, with better convergence and search capabilities, but poor stability and easy to fall into the approximate optimal solution. In response to these limitations, the present invention proposes an improved gray wolf algorithm and differential evolution hybrid algorithm, which integrates the crossover, mutation and selection processes of the DE algorithm into the GWO, adopts the population initialization based on the Cubic chaos map and the convergence factor of nonlinear attenuation to balance the different requirements for the search area in the early and late stages of the algorithm, overcomes the defect of the GWO easily falling into the approximate optimal solution, and improves the algorithm search accuracy and search efficiency.

[0210] (1) Population initialization based on Cubic chaotic map

[0211] Cubic chaos mapping is a mapping method proposed by Robert M. May to simulate the dynamic changes of biological populations. It has a relatively simple mathematical form and can introduce chaotic values ​​into the search space to increase the population diversity of the algorithm, enhance the global search capability and accuracy, while not using too much computing resources. Cubic chaos mapping can be expressed as:

[0212]

[0213] Where: x i+1 is the chaos value of the next generation, x i is the contemporary chaos value. In a specific embodiment of the present invention, the chaos mapping parameter γ=2.595.

[0214] (2) Improvement of nonlinear convergence factor

[0215] The convergence factor a directly affects the search dynamics and convergence behavior of GWO. The search strategy of a gray wolf group is closely related to the cooperation coefficient A. When |A|>1, the gray wolf group tends to expand the search range to achieve rapid global search and convergence; when |A|<1, the group narrows the search range and focuses on a detailed search for potential optimal solutions, namely local search, which converges relatively slowly. However, in traditional GWO algorithms, the convergence factor a typically decreases linearly, which may not accurately reflect the complexity of the algorithm in the actual search process. The linearly decreasing convergence factor a may cause the algorithm to lack the necessary flexibility in the later convergence stage and fail to effectively balance the needs of global and local search.

[0216] Therefore, the present invention introduces a nonlinear convergence factor based on the cosine function. This convergence factor dynamically adjusts the search intensity according to the number of algorithm iterations by using the periodic variation of the cosine function to adapt to the search requirements at different stages and improve the algorithm performance. The convergence factor is expressed as:

[0217]

[0218] Where: a max and a min are the initial and final values ​​of a, m is the decreasing index, T is the maximum number of iterations, and t represents the current number of iterations.

[0219] (3) GWO-DE algorithm flow

[0220] The basic process of the GWO-DE algorithm of the present invention is as follows:

[0221] (1) Initialize the environment and define parameters: population NP, dimension d, upper and lower bounds of variables ub and lb, maximum number of iterations T, upper and lower bounds of convergence factor a max and a min , DE scaling factor F, DE crossover operator P CR ;

[0222] (2) Initialize the population based on the Cubic chaotic map, calculate the individual fitness, and select the first three individual positions and mark them as α, β, and δ wolves respectively;

[0223] (3) Calculate the current convergence factor a, calculate the coordination coefficients A, C, and the relative distance D between the remaining ω wolves in the population and X1(t), X2(t), and X3(t) α 、D β and D δ and update the wolf pack's location;

[0224] (4) According to the dynamic crossover operator P CR , perform crossover and mutation operations, and use a greedy strategy to select the target individual;

[0225] (5) Update the wolf pack, re-evaluate individual fitness, and determine the new generation of α, β, and δ wolves;

[0226] (6) Determine whether the output condition is met. If t = T, record the current global optimal fitness and optimal individual position; otherwise, return to step (3) and continue execution.

[0227] Step 4: Simulation Analysis

[0228] a. Test function optimization

[0229] Four test functions are used to test the performance of different optimization algorithms. The relevant parameter settings of the test functions are shown in Table 1.

[0230] Table 1 Test function parameter settings

[0231]

[0232] The PSO, GA, DE, GWO, and GWO-DE algorithms were tested using the measurement function. Core TM The simulations were conducted using an Intel Core i7-11800H 2.30 GHz processor and Windows 10. Matlab 2020a was used for simulations. The parameters for each optimization algorithm were set as follows: dimension d = 10, population size NP = 50, and number of iterations T = 500. The specific parameters are shown in Table 2, and the parameter settings for the improved GWO-DE algorithm are shown in Table 3.

[0233] Table 2 PSO, GA, DE parameter settings

[0234]

[0235]

[0236] Table 3 GWO-DE parameter settings

[0237]

[0238] To enhance the credibility of the test results and mitigate potential optimization errors, the five algorithms were each run 30 times using four test functions. The optimal values, averages, and standard deviations of the five algorithms were compared, as shown in Tables 4 and 5. This comparison of the test function performance reveals that the PSO and GA algorithms perform poorly for optimizing high-dimensional functions and are prone to falling into local minima. The DE algorithm exhibits slightly better optimization and stability than the PSO and GA algorithms. The GWO and GWO-DE algorithms significantly outperform the other algorithms, demonstrating superior global search capabilities and stability regardless of the test function. Furthermore, the GWO-DE algorithm exhibits several orders of magnitude higher optimization and stability than the GWO algorithm.

[0239] Table 4 Comparison of the effects of PSO, GA, and DE algorithms on test functions

[0240]

[0241]

[0242] Table 5. Comparison of the performance of GWO and GWO-DE algorithms on test functions

[0243]

[0244] b. System performance optimization

[0245] The present invention uses different algorithms to simulate and optimize the OAM-MDI-QKD performance of fixed-link UAVs. The protocol parameters are derived from experimental data as shown in Table 6.

[0246] Table 6 Protocol parameters

[0247]

[0248] Figure 2 The key rate of the OAM-MDI-QKD protocol under multiple channel influencing factors such as atmospheric turbulence, SDD, weather visibility, and drone pointing error is demonstrated. The basis coding probability is not considered at this time. and The probability of sending a pulse signal state and Only a certain number of signaling, decoy, and vacuum states are considered, with transmission intensities of μ2 = 0.36, μ1 = 0.1, and μ0 = 0, respectively. As shown in the figure, under the predetermined parameters, the maximum transmission distance of a single link in the protocol is approximately 4.2 km. Adjusting the altitude of the drone yields the distance between Alice and Bob.

[0249] Figure 3The figure shows the optimization accuracy of different algorithms. The relevant parameters are set as follows: transmission distance L = 3 km, population size NP = 50, and maximum number of iterations T = 500. As can be seen from the figure, the GA algorithm tends to converge prematurely, falling into local optimal values, and has low optimization accuracy. The PSO algorithm is greatly affected by the initial value and has weak global search capabilities, and it also has the problem of being unable to escape the local optimal point. The DE algorithm has strong global search capabilities and has the potential to escape the local optimal point as the number of iterations increases, and the optimization accuracy is acceptable. The GWO algorithm has strong global search capabilities and good optimization accuracy. The improved GWO-DE algorithm combines the advantages of the GWO and DE algorithms, showing excellent global search capabilities and algorithm optimization accuracy, which are superior to both the GWO and DE algorithms.

[0250] Table 7 shows the optimal computation speed and key rate for different algorithms under specified parameters. As can be seen from the table, PSO has the fastest computation speed, followed by DE, while GWO-DE is computationally complex and slower. However, for airborne OAM-MDI-QKD systems with fixed links, where real-time performance is less critical, algorithm accuracy is the primary consideration in this section. For system models with high real-time requirements, such as mobile links, machine learning prediction can be used for parameter optimization.

[0251] Table 7 Comparison of calculation time and accuracy of five algorithms

[0252]

[0253] Figure 4 The results of three different algorithms after parameter optimization are compared with those without optimization. It can be seen that the PSO, GA, and DE algorithms all achieve optimization results, with key rate results approximately one order of magnitude better than the original data, and can also appropriately extend the communication distance. The GA algorithm is less stable and prone to premature convergence and falling into a local optimum. The PSO algorithm has good convergence but lacks the ability to escape local optimal points. The DE algorithm has better global search capabilities than the PSO and GA algorithms and can escape local optimal points, but the optimization results are unstable at close distances. As the transmission distance increases, the optimization results gradually stabilize.

[0254] Depend on Figure 5 It can be seen that the optimization performance of DE algorithm is better than that of PSO and GA algorithms. Figure 5Using the DE algorithm as a comparison, the performance of the GWO and GWO-DE algorithms was analyzed. The GWO algorithm has stronger global search and optimization capabilities, resulting in higher optimization accuracy than the DE algorithm. Under close-range transmission, the GWO algorithm outperforms the DE algorithm by approximately 1-2 orders of magnitude; as the transmission distance increases, the GWO algorithm outperforms the DE algorithm by approximately 3-4 orders of magnitude. However, GWO suffers from insufficient stability, exhibits significant numerical drift, and still suffers from the tendency to become trapped in local optimal points. The improved GWO-DE algorithm effectively addresses this numerical drift issue, exhibits significant convergence, and achieves higher optimization accuracy than the GWO algorithm, meeting the requirements for fixed-link OAM-MDI-QKD parameter optimization and significantly improving system performance.

Claims

1. An airborne orbital angular momentum MDI-QKD link establishment device, comprising transmitting ends Alice and Bob and a receiving end Charlie, wherein the transmitting ends Alice and Bob perform OAM optical signal transmission after achieving beacon light alignment with the receiving end Charlie; characterized in that: The details are as follows: Alice end includes a first laser, a first spatial light modulator SLM1, a first attenuator ATT, a first reflecting mirror, a second reflecting mirror, a first intensity modulator IM, and a first telescope; The first laser emits a first optical signal; The first spatial light modulator SLM1 receives the first optical signal emitted by the first laser and modulates it into a first orbital angular momentum OAM state output; The first attenuator receives the first orbital angular momentum OAM state output by the first spatial light modulator and attenuates it to a first weak coherent state WCS output; a first reflecting mirror, which reflects the first weak coherent state WCS output by the first attenuator at 90 degrees; A second reflector, which again reflects the first weak coherent state WCS output by the first reflector at 90 degrees, thereby reversing the direction of the first weak coherent state WCS output by the first attenuator by 180 degrees; The first intensity modulator receives the first weak coherent state WCS output by the second reflecting mirror, modulates it, and generates corresponding first decoy state and first vacuum state outputs; The first telescope includes a first lens L1 and a second lens L2. The first decoy state and the first vacuum state output by the first intensity modulator pass through the first lens L1 and the second lens L2 in sequence, and are magnified and transmitted by the first lens L1 and the second lens L2. Bob's end is identical and symmetrical to Alice's end, and includes a second laser, a second spatial light modulator SLM2, a second attenuator, a third reflector, a fourth reflector, a second intensity modulator IM, and a second telescope; The second laser emits a second optical signal; The second spatial light modulator receives the second optical signal emitted by the second laser and modulates it into a second orbital angular momentum OAM state output; The second attenuator receives the second orbital angular momentum OAM state output by the second spatial light modulator and attenuates it into a second weak coherent state WCS output; a third reflecting mirror, which reflects the second weak coherent state WCS output by the second attenuator at 90 degrees; a fourth reflector, which again reflects the second weak coherent state WCS output by the third reflector at 90 degrees, thereby reversing the direction of the second weak coherent state WCS output by the second attenuator by 180 degrees; The second intensity modulator receives the second weak coherent state WCS output by the fourth reflector, modulates it, and generates corresponding second decoy state and second vacuum state outputs; The second telescope includes a third lens L3 and a fourth lens L4. The second decoy state and the second vacuum state output by the second intensity modulator pass through the third lens L3 and the fourth lens L4 in sequence, and are magnified and transmitted by the third lens L3 and the fourth lens L4. The photons output by Bob and Alice are then sent to the receiving end Charlie via a free-air space link for measurement; The receiving end Charlie includes a third telescope composed of the fifth and sixth lenses, a fourth telescope composed of the seventh and eighth lenses, first to third beam splitters BS, first and second polarization gratings PG, fifth to eighth reflecting mirrors, first to fourth mode selectors MS, and first to fourth detectors; The third telescope receives the first signal state, the first decoy state, and the first vacuum state; The fourth telescope receives the second signal state, the second decoy state, and the second vacuum state; The first beam splitter BS interferes with the two groups of light signals output by the third and fourth telescopes to generate a first group of photons and a second group of photons, which are output separately at an angle of 90 degrees. The first polarization grating separates the first group of photons into left-handed polarized photons and right-handed circularly polarized photons and outputs them; The second polarization grating separates the second group of photons, namely left-handed polarized photons and right-handed circularly polarized photons, and outputs the photons; The fifth reflector reflects the left-handed polarized photons of the first group of photons emitted from the first polarization grating at 90 degrees; The sixth reflector reflects the right-handed polarized photons of the first group of photons emitted from the first polarization grating at 90 degrees; The seventh reflecting mirror reflects the right-handed polarized photons of the second group of photons emitted from the second polarization grating at 90 degrees; The seventh reflecting mirror reflects the left-handed polarized photons of the second group of photons emitted from the second polarization grating at 90 degrees; The second beam splitter receives the left-handed polarized photons and the right-handed polarized photons of the first group output by the fifth and sixth reflectors, interferes with the photons, and outputs a first OAM photon state and a second OAM photon state from two directions approximately 90 degrees apart, respectively. The third beam splitter receives the left-handed polarized photons and the right-handed polarized photons of the second group output by the seventh and eighth reflectors, interferes with the photons, and outputs a third OAM photon state and a fourth OAM photon state from two directions approximately 90 degrees apart, respectively. The first mode selector receives and outputs the first OAM photon state emitted after interference from the second beam splitter; The second mode selector receives and outputs the second OAM photon state emitted after interference from the second beam splitter; The third mode selector receives and outputs the third OAM photon state emitted after interference from the third beam splitter; The fourth mode selector receives and outputs the fourth OAM photon state emitted after interference from the third beam splitter; The first detector D0 detects the first OAM photon state output by the first mode selector; The second detector D1 detects the second OAM photon state output by the first mode selector; The third detector H0 detects the third OAM photon state output by the first mode selector; The fourth detector H1 detects the fourth OAM photon state output by the first mode selector.

2. A method for improving the performance of airborne orbital angular momentum MDI-QKD using the Grey Wolf-Differential algorithm, based on the airborne orbital angular momentum MDI-QKD link establishment device according to claim 1, characterized in that: Specifically include the following steps: Step 1: Construction of OAM-MDI-QKD scenario on UAV platform; Building the airborne orbital angular momentum MDI-QKD link building device as claimed in claim 1; Step 2, OAM-MDI-QKD security key rate analysis; The OAM-MDI-QKD protocol with a finite code length of three-intensity decoy states is adopted; two mutually unbiased bases, the OAM basis and the SUP basis, are used, which are expressed as: in, Indicates the OAM base state is 0, Indicates an OAM basis with a state of 1, represents the SUP basis with state n, l is the topological charge, and n represents the state of 0 or 1. At this time, the SUP basis is in a superposition state and does not have rotation invariance. The reference frame alignment error needs to be considered. Alice and Bob modulate the received weak coherent light pulse into {μ i },i=2,1,0 and {v j }, j = 2, 1, 0, where μ2 represents the signal state strength sent by Alice, μ1 represents the decoy state strength sent by Alice, μ0 represents the vacuum state strength sent by Alice, v2 represents the signal state strength sent by Bob, v1 represents the decoy state strength sent by Bob, and v0 represents the vacuum state strength sent by Bob; the probabilities of Alice sending the signal state, decoy state, and vacuum state are respectively and at this time Then, Alice and Bob each choose a basis with a certain OAM probability and SUP base selection probability Independently select OAM or SUP base encoding information, then Since it is a symmetric channel, Alice and Bob’s decoy state strength, transmission probability, and basis selection probability are all equal; Taking into account parameters such as the strength of the signal state and the decoy state, the probability of sending the signal state, the decoy state, and the signal state, and the basis selection probability, the key rate formula of the OAM-MDI-QKD protocol is: in, represents the system key rate, represents the probability of Bob sending a signal, represents the probability that Alice discovers the signal state and uses OAM basis coding, represents the probability that Bob finds the signal state and uses OAM basis encoding, is the gain when both Alice and Bob choose the OAM basis and send single photon states, Indicates that after considering the selection of OAM basis probability and signal probability The lower bound of is the quantum bit error rate (QBER) when both parties choose the SUP basis and send a single photon state, Indicates that after considering the SUP base probability and signal probability The upper bound of It represents the total gain when both parties choose the OAM basis to send the signal state after considering the probability of selecting the OAM basis and the probability of the signal state. is the total QBER when both parties choose the OAM basis to send signals; H(x) = -xlog2(x)-(1-x)log2(1-x) is the binary Shannon information entropy function, and f is the system error correction efficiency; According to the three-intensity decoy state and finite code length restriction used in the protocol, the gain and QBER when Alice and Bob send OAM coded information are obtained: When Alice and Bob both choose the SUP basis, the gain and QBER are expressed as: in, Indicates that Alice and Bob both choose the SUP basis and send strength μ i and v j Gain at s ij represents the square root coefficient of the photon intensity, I0(·) represents the first kind of modified Bessel function, represents the QBER when both Alice and Bob choose the SUP basis, e0 represents the initial error rate, e d Detection deflection error, y ij represents the photon detection efficiency factor; When Alice and Bob both choose OAM basis, the gain is: in, Alice and Bob both choose OAM basis and transmit strength μ i and v j The gain when Indicates the correct gain, represents the bit error gain, η A and η B They represent the transmittance of Alice and Bob respectively, P d is the dark count rate of the single-photon detector, and the parameter formula y ij , photon transmission intensity μ ij ′、s ij It is given by: m ij ′=η A m i +n B n j (10) Considering the probability of signal transmission, the limits of statistical fluctuations are as follows: Among them, x represents the selection of OAM basis and SUP basis, Indicates that the x basis is selected and the sending strength is μ i and v j The gain when Select x basis and send strength μ i and v j QBER, After considering the probability After considering the probability is the volatility of the modified gain, is the fluctuation rate of the corrected bit error, expressed as: Among them, n α is the value of the standard deviation used for statistical fluctuation analysis, After considering the probability, Alice and Bob use μ i and v j When the signal strength is x, the number of pulses of the base is: Where N is the total number of pulses sent by Alice and Bob. Indicates the sending signal strength μ i The probability of using x-based coding when Send signal strength v j The probability of using x-based coding when ; Indicates the signal strength v sent by Bob j probability; Lower bound on single-photon gain and the upper bound of the single-photon QBER The calculation is performed by setting the choice of x, where x is an OAM basis or a SUP basis: in, is the single-photon gain in the x-basis, represents the lower bound of the single-photon gain in the x-basis after considering the probability, represents the gain when the x basis is selected under probability and the sending strength is μ2 and v2, express The upper bound of represents the gain when the x basis is selected under probability and the sending strength is μ1 and v1, express The lower bound, represents the QBER when the x basis is selected with the transmission strength of μ1 and v1 under probability, express The upper bound of is the single-photon QBER in the x basis, represents the upper bound of the single-photon QBER in the x-basis after considering the probability, Represents the signal strength difference gain under probability The lower bound, Indicates the probability of adjusting the coefficient gain The lower bound, Represents another set of adjustment coefficient combination gains under probability The lower bound, represents the error rate adjustment gain under probability The lower bound of κ represents the system gain adjustment coefficient, and the parameter formula κ, is given by: in, represents the gain of signal strength 0 and ν2 in the x basis, represents the gain of signal strength μ2 and 0 under x basis, represents the gain of signal strength 0 and ν1 in the x basis, represents the gain of signal strength μ1 and 0 in the basis x, represents the gain of signal strength μ2 and ν1 in the basis x, represents the gain of signal strength 0 and 0 under x basis, represents the gain of signal strength μ1 and ν2 in the basis x, represents the QBER of signal strength 0 and ν1 in the basis x, represents the QBER for signal strengths μ1 and 0 in the basis x, represents the QBER of signal strength 0 and 0 under x basis; Therefore, the key rate of the UAV fixed link OAM-MDI-QKD protocol is related to the following seven independent parameters: the signal state strength μ2, the decoy state strength μ1, the probability of selecting the signal state The probability of choosing the decoy state Determine the signal state and the conditional probability of choosing SUP basis code Determine the conditional probability of the decoy state and choose the SUP base code and the conditional probability of determining the signal state and selecting the SUP basis code Setting variable sets Step 3: Improved Grey Wolf Difference Algorithm In the present invention, for the parameter optimization of the 7-dimensional non-convex nonlinear objective function R, traditional convex optimization algorithms have certain limitations; the common particle swarm optimization (PSO) algorithm is prone to premature convergence in the early stage of the search, and the global search efficiency is reduced for high-dimensional and nonlinear problems; the genetic (GA) algorithm has good global search capabilities, but the crossover and mutation may have large fluctuations, the solution is unstable, and for high-dimensional problems, it may even cause the destruction of the solution, and the computational cost is high; the DE algorithm performs well in multi-peak function search, but the performance depends on parameter selection, and the population diversity decreases during the iteration process, resulting in a decrease in the search capability in the later stage; the GWO algorithm can better handle high-dimensional nonlinear problems and has better convergence and search capabilities, but has poor stability and is prone to falling into near-optimal solutions; to address these limitations, the present invention proposes an improved gray wolf algorithm and differential evolution hybrid algorithm, which integrates the crossover, mutation and selection processes of the DE algorithm into the GWO algorithm, adopts population initialization based on Cubic chaos mapping and a convergence factor of nonlinear attenuation to balance the different requirements for the search area in the early and late stages of the algorithm, overcomes the defect of GWO easily falling into near-optimal solutions, and improves the algorithm search accuracy and efficiency; a. Population initialization based on Cubic chaotic map; Cubic chaos map is expressed as: Where: x i+1 is the chaos value of the next generation, x i is the contemporary chaos value. In a specific embodiment of the present invention, the chaos mapping parameter γ = 2.595; b. Improvement of nonlinear convergence factor; A nonlinear convergence factor a based on the cosine function is introduced. The convergence factor expression is: Where: a max and a min are the initial and final values ​​of a, m is the decreasing index, T is the maximum number of iterations, and t represents the current number of iterations; c.GWO-DE algorithm process; The details are as follows: (1) Initialize the environment and define parameters: population NP, dimension d, upper and lower bounds of variables ub and lb, maximum number of iterations T, upper and lower bounds of convergence factor a max and a min , DE scaling factor F, DE crossover operator P CR ; (2) Initialize the population based on the Cubic chaos map and calculate the current fitness according to formula (3) Select the first three individual positions and label them as α, β and δ wolves respectively; the distance D from the wolf pack to the prey is: D=|C·X p (t)-X(t)| (24) X(t+1)=X p (t)-A·D (25) Where: X p (t) is the position of the prey, X(t) is the position of the wolf after the tth iteration, and C and A are the coordination coefficients: A=2a·r1-a (26) C＝2·r2 (27) Among them, r1 and r2 are random numbers between [0,1]; During the pursuit, the gray wolf updates its position as its prey moves as follows: Where D α 、D β and D δ Respectively represent the distances between α, β and δ wolves and other ω wolves, X α (t), X β (t) and X δ (t) represents the current position of α, β and δ wolves respectively, X1(t), X2(t) and X3(t) represent the distance that ω wolf moves to α, β and δ wolves respectively, X(t+1) is the updated position of gray wolf, C1, C2 and C3 are three coordination coefficients, and A1, A2 and A3 are the other three coordination coefficients; (3) Calculate the current convergence factor a according to formula (32), calculate the coordination coefficients A and C according to formulas (26) and (27), and calculate the relative distance D between the remaining ω wolves in the population and X1(t), X2(t), and X3(t) according to formulas (28)-(30). α 、D β and D δ and update the wolf pack's location; (4) According to the crossover operator P CR , perform crossover and mutation operations on α, β, δ and ω wolves, and use a greedy strategy to select the target individual; (5) Update the wolf pack position and recalculate fitness Identify the new generation of alpha, beta, and delta wolves; (6) Determine whether the output condition is met. If t = T, record the current global optimal fitness and optimal individual position; otherwise, return to step (3) and continue execution.

3. The method for improving the performance of the Grey Wolf-Differential Algorithm Airborne Orbital Angular Momentum MDI-QKD according to claim 2, wherein: In Step 3, step a, the chaotic mapping parameter γ = 2.595.

Images