AI-based frequency bin encoding measurement-device-independent quantum key distribution method

Abstract

The application discloses a kind of measurement equipment independent quantum key distribution methods based on AI's frequency bin coding, including computer system executes following steps: input quantum signal sent by communication both sides, relative radial velocity between communication node and infeasible relay node and historical quantum interference statistical characteristic data;Quantum channel observation and frequency bin quantum state construction, the dynamic evolution of frequency bin caused by relative motion, frequency compensation decision based on reinforcement learning, the influence of residual frequency error on quantum interference performance, frequency bin utilization rate and error propagation caused by interference degradation and security key rate generation.The application can effectively improve the adaptability and operation reliability of MDI-QKD system based on frequency bin in dynamic, multi-noise environment, and provides an intelligent solution for security key distribution in high-capacity quantum communication network.

Description

AI-based frequency bin coding measurement device-independent quantum key distribution method Technical Field

[0001] This invention relates to the fields of quantum communication and quantum information security, and specifically to a measurement device-independent quantum key distribution method based on AI-based frequency bin coding. Background Technology

[0002] With the continuous development of quantum communication technology, quantum key distribution (QKD), as an important means of achieving information-theoretic secure communication, has been widely studied in application scenarios such as metropolitan quantum networks, satellite-to-ground quantum communication, and multi-user quantum access networks. Among them, measurement-device-independent quantum key distribution (MDI-QKD), by completing the measurement process through an untrusted relay, eliminates the risk of detector side-channel attacks and has become an important technical solution for building large-scale secure quantum networks. To further improve the capacity and spectral efficiency of quantum key distribution systems, frequency-bin encoding has been introduced into QKD systems, achieving high-dimensional parallel transmission by dividing the spectral domain into multiple orthogonal frequency modes. However, in this process, frequency-bin-based QKD systems are susceptible to factors such as channel noise, spectral drift, phase mismatch, and multi-user interference, leading to decreased interference visibility and increased qubit error rate (QBER), thereby limiting the secure key generation rate and system operational stability.

[0003] Existing optimization methods for frequency bin MDI-QKD mostly rely on static parameter configuration or channel compensation strategies based on empirical models. They typically assume that channel conditions remain stable over a certain time scale, making it difficult to effectively cope with dynamic disturbances in complex quantum channels that change with time, spectrum, and link state.

[0004] Meanwhile, traditional channel modeling methods have limited accuracy in predicting system performance degradation in high-noise regions or under multi-user interference conditions. They also lack the ability to jointly sense and adaptively adjust key quantum characteristic parameters (such as interference visibility, bit error distribution, and frequency-related noise), leading to a significant decline in system performance in long-distance transmission or dynamic network environments.

[0005] In summary, there is an urgent need for a quantum key distribution method that can precisely sense the quantum channel state at frequency bins and dynamically optimize system parameters based on channel changes, in order to improve the key generation efficiency and operational robustness of MDI-QKD systems in complex environments. Summary of the Invention

[0006] The main objective of this invention is to provide an AI-based frequency bin coding measurement device-independent quantum key distribution method, which aims to solve the problems of decreased interference visibility, static parameter configuration, and limited key generation efficiency faced by existing technologies under complex quantum channel conditions.

[0007] Based on a first key aspect of the present invention, a measurement device-independent quantum key distribution method based on AI frequency bin coding is provided, comprising a computer system performing the following steps:

[0008] The computer system is input with quantum signals sent by both communicating parties, the relative radial velocity between the communication node and the untrusted relay node, and historical quantum interference statistical data; the quantum signals include weakly coherent optical pulses and frequency bins;

[0009] A measurement device-independent quantum key distribution system model based on frequency bin coding is constructed to uniformly describe the quantum signals sent by both communicating parties in the frequency domain and obtain the frequency bin-coded quantum states;

[0010] Based on the relative radial velocity between the communication node and the untrusted relay node, the frequency bin-encoded quantum state generates a time-dependent Doppler frequency shift, and the resulting overall frequency drift is analyzed.

[0011] Based on relative radial velocity and historical quantum interference statistical data, a frequency calibration control quantity is dynamically generated through a learning-driven frequency compensation mechanism to form a residual frequency error after compensating for the Doppler frequency shift.

[0012] Based on the frequency domain two-photon interference model, we analyze how residual frequency error affects the interference quality of frequency bins, and further obtain the effective interference visibility;

[0013] The effective interference visibility is mapped to the number of available frequency bins and quantum error characteristics to obtain the number of effective frequency bins and the total error rate. The final secure key generation rate is calculated and output.

[0014] As a further preferred embodiment, in the aforementioned method, the execution steps for constructing the measurement device-independent quantum key distribution system model based on frequency bin coding are as follows:

[0015] The phase-randomized weakly coherent state obtained by phase randomization of the weakly coherent light pulse is used as a quantum carrier to obtain the corresponding optical field quantum state;

[0016] By using electro-optic modulation and narrowband frequency domain filtering, the single-photon subspace is mapped to an orthogonal frequency domain ground state composed of multiple discrete frequency bins;

[0017] Under single-photon conditions, the frequency bin-encoded quantum state is:

[0018]

[0019]

[0020] in, Represents the quantum state encoded by frequency bin. Indicates the total number of frequency bins. Index representing a single frequency bin. Indicates the first The complex amplitude of a frequency bin. Indicates the first The orthogonal frequency domain ground state corresponding to each frequency bin This represents the center carrier frequency of the quantum signal. Indicates the first The center frequency of each frequency bin Indicates the spacing width between adjacent frequency bins;

[0021] Meanwhile, a uniform distribution strategy is adopted for the probability weights of the complex amplitude of each frequency bin.

[0022] As a further preferred embodiment, in the aforementioned method, the steps for performing the overall frequency drift caused by the analysis are as follows:

[0023] The Doppler frequency shift is expressed as:

[0024]

[0025] in, The speed of light is constant. Represents relative radial velocity, This represents the center carrier frequency of the quantum signal. Indicates the discrete time step index. Indicates different communication links or node pairs;

[0026] Meanwhile, the initial spectral envelope function of each frequency bin is modeled as a Gaussian form;

[0027] Under the influence of the Doppler frequency shift, the spectrum of frequency bin does not change shape, but only causes the overall spectral envelope to shift over time;

[0028] Specifically, the overall evolution of the spectral envelope over time is as follows:

[0029]

[0030] in, Indicates Doppler frequency shift, Represents frequency variables. Indicates the discrete time step index. Indicates different communication links or node pairs. Denotes the initial spectral envelope function. Index representing a single frequency bin.

[0031] As a further preferred embodiment, in the aforementioned method, the execution steps for dynamically generating the frequency calibration control quantity are as follows:

[0032] The learning-driven frequency compensation mechanism includes a reinforcement learning agent;

[0033] At each discrete time step, a state vector is constructed; the state vector includes the relative radial velocity between the communication node and the relay node and the effective visibility estimate obtained based on historical quantum interference statistical property data;

[0034] The reinforcement learning agent selects a frequency compensation amount from a preset range based on the state vector, as the frequency calibration control amount;

[0035] Meanwhile, the residual frequency error after compensation is defined as:

[0036]

[0037] in, Indicates Doppler frequency shift, Indicates the compensation execution coefficient. This indicates the frequency calibration control quantity. Indicates different communication links or node pairs. This represents the discrete time step index.

[0038] As a further preferred embodiment, in the aforementioned method, the steps for obtaining effective interference visibility are as follows:

[0039] First, based on the frequency domain two-photon interference model, the success probability of Bell states at different frequency bins is calculated to obtain the interference probability corresponding to the frequency bin;

[0040] Under the Gaussian spectrum assumption, the interference probability is simplified to a frequency interference visibility function;

[0041] Finally, a minimum visibility parameter is introduced to obtain the modified visibility model, and the effective visibility is defined at the same time.

[0042] Specifically, the visibility model is:

[0043]

[0044] in, Indicates the minimum degree of visibility parameter. Indicates residual frequency error. This represents the effective spectral width of a single frequency bin. This represents an exponential function.

[0045] As a further preferred embodiment, in the aforementioned method, the steps for obtaining the effective frequency bin number and the total bit error rate are as follows:

[0046] First, an effective frequency bin number is introduced to quantify the number of parallel frequency channels that can participate in key generation under the current channel conditions;

[0047] Meanwhile, the interference degradation caused by Doppler frequency shift leads to an increase in the probability of bit error, and a corresponding bit error term is obtained;

[0048] Finally, the total bit error rate under single-photon conditions is obtained based on the bit error rate items, and the total bit error rate does not exceed a set threshold.

[0049] As a further preferred embodiment, in the aforementioned method, the steps for calculating the final security key generation rate are as follows:

[0050] The single-photon yield is calculated based on the effective frequency bin number; and the security key rate is calculated based on the single-photon yield.

[0051]

[0052] in, Indicates single-photon yield. Represents the binary entropy function. Represents the total bit error rate under single-photon conditions. Indicates the total gain. This represents the error correction efficiency factor. This represents the overall bit error rate, including contributions from multiple photons and noise.

[0053] Based on a second key aspect of the present invention, a measurement device-independent quantum key distribution system based on AI frequency bin coding is provided, which applies the aforementioned measurement device-independent quantum key distribution method based on AI frequency bin coding, including:

[0054] The information input module is used to input the quantum signals sent by both communicating parties, the relative radial velocity between the communication node and the relay node, and historical quantum interference statistical characteristic data;

[0055] The frequency domain quantum state construction module is used to construct a measurement device-independent quantum key distribution system model based on frequency bin encoding, and to provide a unified description of the quantum signals sent by the two communicating parties in the frequency domain;

[0056] The relative motion frequency shift evolution module is used to consider the influence of the relative motion between the communication node and the relay node on the frequency bin quantum state and to analyze the overall frequency drift caused by the Doppler effect.

[0057] The reinforcement learning frequency compensation module has a built-in reinforcement learning agent, which dynamically generates frequency calibration control quantity through a learning-driven frequency compensation mechanism to form residual frequency error after compensating for the Doppler frequency shift.

[0058] The interferometric visibility analysis module is used to analyze the influence of residual frequency error on frequency bin interferometric visibility based on the frequency domain two-photon interferometry model.

[0059] The frequency bin utilization and bit error statistics module is used to map the effective interference visibility to the number of available frequency bin resources and quantum bit error characteristics, and to obtain the number of effective frequency bins and the total bit error rate.

[0060] The security key generation module is used to calculate the final security key generation rate based on the effective frequency bin number and output the security key generation rate.

[0061] According to a third key aspect of the present invention, an electronic device is provided, comprising: a processor, a communication interface, a memory, and a communication bus, wherein the processor, the communication interface, and the memory communicate with each other through the communication bus;

[0062] The memory stores a computer program that, when executed by the processor, causes the processor to perform the aforementioned AI-based frequency bin coding measurement device-independent quantum key distribution method.

[0063] Based on a fourth key aspect of the present invention, a computer-readable storage medium is provided having a computer program stored thereon that, when executed, implements the aforementioned AI-based frequency bin-encoded measurement device-independent quantum key distribution method.

[0064] Compared with existing technologies, this invention provides an AI-based frequency bin coding measurement device-independent quantum key distribution method. First, this invention integrates frequency bin quantum state evolution, Doppler shift, interference statistics, and secure key generation performance into a single feedback loop for joint modeling and optimization. This overcomes the shortcomings of existing frequency bin coding measurement device-independent quantum key distribution schemes, where each step is processed independently and lacks a collaborative optimization mechanism, resulting in low spectral utilization, poor interference stability, and difficulty in comprehensively improving key generation performance. It achieves synergistic linkage between quantum dynamic evolution, frequency shift compensation, interference quality, and key generation, providing a unified and efficient technical framework for optimizing overall system performance.

[0065] Secondly, this invention embeds the reinforcement learning decision-making process into the execution flow of the quantum key distribution protocol. Without relying on a precise prior channel model, it can autonomously adjust frequency compensation and frequency bin configuration strategies based on real-time observed interference performance and key generation feedback, thereby achieving continuous tracking and stable control of rapidly time-varying channel conditions. This overcomes the problems of decreased interference visibility and increased quantum bit error rate (QBER) in existing schemes, achieving continuous tracking and stable control of highly dynamic channel environments and improving adaptability to complex communication scenarios.

[0066] Finally, the reinforcement learning process in this invention only operates on the protocol parameters and frequency control level, and does not participate in the generation and processing of the key content itself. This ensures that the confidentiality and integrity of the quantum key distribution protocol are not affected under the measurement device-independent security framework. At the same time, this invention integrates frequency bin quantum coding, Doppler dynamic modeling and reinforcement learning adaptive control mechanism under a unified framework. Without introducing additional security assumptions, it significantly improves the interference stability, spectral efficiency and secure key generation rate of the measurement device-independent quantum key distribution system in high dynamic scenarios. It is suitable for application scenarios such as satellite quantum communication, high-speed mobile platforms and future large-scale quantum networks. Attached Figure Description

[0067] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, obtaining other drawings based on these drawings without creative effort still falls within the scope of the present invention.

[0068] Figure 1 shows an execution flowchart of a measurement device-independent quantum key distribution method based on AI frequency bin coding in one embodiment of the present invention;

[0069] Figure 2 shows a diagram of a stand-alone QKD system with a trusted source and an untrusted central measurement node provided in one embodiment of the present invention;

[0070] Figure 3 shows a diagram of an AI-controlled frequency reuse MDI-QKD system (single user) provided in one embodiment of the present invention;

[0071] Figure 4 shows a Doppler compensation flowchart based on reinforcement learning for a measurement device-independent quantum key distribution method based on AI-based frequency bin coding, according to one embodiment of the present invention. Detailed Implementation

[0072] The preferred embodiments of the present invention will be described in detail below to provide a clearer understanding of the purpose, features, and advantages of the invention. It should be understood that the following embodiments are not intended to limit the scope of the invention, but are merely illustrative of the essential spirit of the technical solution of the invention.

[0073] In the following description, certain specific details are set forth for the purpose of illustrating various disclosed embodiments in order to provide a thorough understanding of the various disclosed embodiments. However, those skilled in the art will recognize that embodiments may be practiced without one or more of these specific details. In other instances, well-known techniques associated with the invention may not have been shown or described in detail to avoid unnecessarily obscuring the description of the embodiments.

[0074] Throughout this specification, references to "an embodiment" or "an embodiment" indicate that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment. Therefore, the appearance of "in an embodiment" or "an embodiment" in various places throughout the specification does not necessarily refer to the same embodiment. Furthermore, a particular feature, structure, or characteristic may be combined in any manner in one or more embodiments.

[0075] The following is a description of the specific meanings of technical terms, English abbreviations, and formula parameters that may be used in this invention:

[0076] Frequency bin: A discrete, independent frequency domain channel or interval unit divided in the frequency domain dimension, which is the basic carrier of frequency domain parallel coding.

[0077] Frequency bin coding: A signal coding method based on frequency bins. Through modulation and filtering techniques, information is modulated onto different frequency bins to achieve parallel information carrying in the frequency domain.

[0078] Weakly coherent optical pulses are optical pulses formed by pulse modulation and intensity attenuation of continuous coherent laser light. Their average number of photons is much less than 1, the optical field is in a single-mode coherent state, and the photons follow a Poisson distribution.

[0079] Phase-random weakly coherent state: A quantum state formed by uniformly randomizing the light field based on a weakly coherent light pulse.

[0080] Frequency-domain two-photon interference model: A photon interference theoretical model based on frequency domain analysis, which quantifies the intensity and quality of two-photon interference by calculating the spectral overlap of the two-transmit single-photon signals in the frequency domain.

[0081] Bell state measurement (BSM): A core joint measurement operation in quantum processing that measures the quantum state after two-photon interference to determine the quantum state correlation of two photons.

[0082] Doppler shift: When there is relative motion between the wave source and the observer, the frequency of the wave received by the observer shifts, and the amount of shift is proportional to the relative velocity.

[0083] Communication node: In a communication system, a terminal device responsible for generating, sending, receiving, and processing signals is the endpoint of the communication link.

[0084] Untrusted relay node: A device located in the middle of a communication link, used to forward, amplify, or process secondary signals, which can extend the communication distance or implement specific functions.

[0085] Quantum error characteristics: The statistical patterns of bit errors caused by factors such as channel noise, interference degradation, and measurement errors during quantum key distribution, including bit error rate, bit error distribution, and sources of errors.

[0086] Electro-optic modulation: a technique that uses the electro-optic effect to modulate the amplitude, phase, frequency, and other parameters of an optical signal by changing the refractive index of an optical medium through an applied electric field.

[0087] Narrowband frequency domain filtering: a filtering technique that allows only optical signals within a specific narrow frequency range to pass through while suppressing other frequency components, enabling selective extraction of frequency domain signals.

[0088] Reinforcement Learning (RL): A machine learning paradigm whose core principle is to enable an agent to learn the optimal decision-making strategy through continuous interaction with a dynamic environment and trial and error, in order to maximize long-term cumulative rewards.

[0089] Reinforcement learning agent: The core decision-making unit in reinforcement learning algorithms. It continuously interacts with the dynamic environment, perceives the state of the environment, executes decision-making actions, and obtains feedback rewards. With the goal of maximizing long-term cumulative rewards, it autonomously iterates and optimizes its own decision-making strategy, thereby achieving adaptive control in unknown or time-varying complex environments.

[0090] Gaussian spectrum: A spectrum of a signal whose energy distribution in the frequency domain follows a Gaussian function. Its energy is concentrated near the center frequency, and although the frequency deviation decreases exponentially, it is the standard spectral form for describing narrowband, low crosstalk frequency domain channels in quantum communication and signal processing.

[0091] As shown in Figure 1, in one embodiment, a measurement device-independent quantum key distribution method based on AI frequency bin coding according to the present invention includes the following steps S1-S6:

[0092] S1, input the quantum signals sent by the two communicating parties, the relative radial velocity between the communication node and the untrusted relay node, and historical quantum interference statistical characteristic data into the computer system; the quantum signals include weakly coherent optical pulses and frequency bin;

[0093] S2, Construct a measurement device-independent quantum key distribution system model based on frequency bin coding, perform a unified description of the quantum signals sent by both communicating parties in the frequency domain, and obtain the frequency bin-coded quantum state;

[0094] S3, based on the relative radial velocity between the communication node and the untrusted relay node, the frequency bin-encoded quantum state generates a time-related Doppler frequency shift, and the resulting overall frequency drift is analyzed;

[0095] S4, based on relative radial velocity and historical quantum interference statistical characteristics data, a frequency calibration control quantity is dynamically generated through a learning-driven frequency compensation mechanism to form a residual frequency error after compensating for the Doppler frequency shift;

[0096] S5, based on the frequency domain two-photon interference model, analyzes how residual frequency error affects the interference quality of frequency bins, and further obtains effective interference visibility;

[0097] S6. Map the effective interference visibility to the number of available frequency bins and quantum error characteristics to obtain the number of effective frequency bins and the total error rate, calculate the final secure key generation rate, and output the secure key generation rate.

[0098] In one feasible implementation, step S2 is described in detail:

[0099] Step S2 specifically involves the quantum channel observation and frequency bin quantum state construction stage, where a unified frequency domain quantum model is first performed on the quantum signals sent by both communicating parties based on a measurement device-independent quantum key distribution architecture with frequency bin encoding.

[0100] Specifically, the transmitting end uses weakly coherent optical pulses to perform phase randomization to obtain the center carrier frequency. The phase-random weakly coherent state is used as a quantum carrier, and its corresponding optical field quantum state can be expressed as:

[0101]

[0102] in, The complex amplitude of the coherent state is represented by its squared magnitude. The corresponding average photon number is used to control the single-photon emission probability and suppress the risk of multiphoton leakage; Represents the photon number state basis. Represents an exponential function. Represents the number of photons.

[0103] By using electro-optic modulation and narrowband frequency domain filtering, the single-photon subspace is mapped to a matrix composed of... The orthogonal frequency domain ground state is composed of discrete frequency bins. Its inner product satisfies ,in This represents the Kronecker delta, thus ensuring the orthogonality and distinguishability of different frequency bins under ideal conditions.

[0104] Under single-photon conditions, the frequency bin-encoded quantum state can be represented as:

[0105]

[0106]

[0107] in, Represents the quantum state encoded by frequency bin. Indicates the total number of frequency bins; An index representing a single frequency bin; Indicates the first The complex amplitude of each frequency bin; Indicates the first The orthogonal frequency domain ground states corresponding to each frequency bin; This indicates the center carrier frequency of the quantum signal; Indicates the first The center frequency of each frequency bin; This indicates the spacing width between adjacent frequency bins.

[0108] To maximize spectral parallelism and simplify subsequent statistical modeling, this invention employs a uniform distribution strategy:

[0109]

[0110] in, Indicates the first The complex amplitude of each frequency bin; This represents the probability weight, used to characterize the proportion of photons occupied in that frequency channel. Indicates the total number of frequency bins;

[0111] Thus, frequency bin numbers are established. Spectrum spacing A clear correspondence between this and the ability to generate parallel keys.

[0112] This frequency-domain quantum state modeling provides a unified state description basis for subsequent Doppler perturbation analysis and adaptive compensation.

[0113] Figure 2 is a diagram of a measurement device-independent QKD system with a trusted source and an untrusted central measurement node provided in an embodiment of the present invention. This figure illustrates the complete quantum flow of frequency-bin multiplexed measurement device-independent quantum key distribution in a single-user scenario, where the user... and Quantum pulses encoded with frequency bins are generated separately and transmitted to the central MDI relay via a frequency-multiplexed quantum channel in the same optical fiber. At the relay node, the quantum states from both sides first interfere at the beam splitter, and then the different frequency bins are mapped to the corresponding measurement channels by the frequency demultiplexer, and the detection is completed by a single-photon detector.

[0114] In one feasible implementation, step S3 is described in detail:

[0115] In the frequency bin dynamic evolution stage caused by relative motion, this invention considers the relative radial velocity between the communication node (transmitter or receiver) and the untrusted relay node. , where subscript Used to distinguish different communication links or node pairs. This represents the discrete-time evolution step.

[0116] The instantaneous Doppler frequency shift caused by relative motion can be expressed as:

[0117]

[0118] in, The speed of light is constant. Represents relative radial velocity, This represents the center carrier frequency of the quantum signal. Indicates the discrete time step index. Indicates different communication links or node pairs;

[0119] This expression describes the linear frequency shift relationship of the center frequency under relative motion conditions.

[0120] In the frequency domain description, the first The initial spectral envelope function of each frequency bin is modeled in Gaussian form:

[0121]

[0122] in, Represents the initial spectral envelope function; The effective spectral width of a single frequency bin is used to describe the degree of concentration of the spectrum after modulation and filtering. Indicates the first The center frequency of each frequency bin; Represents frequency variables. This represents an exponential function.

[0123] Under the influence of Doppler frequency shift, the entire spectral envelope is shifted, and its time... The evolution of time is as follows:

[0124]

[0125] in, Indicates Doppler frequency shift, Represents frequency variables. Indicates the discrete time step index. Indicates different communication links or node pairs. Denotes the initial spectral envelope function. Index representing a single frequency bin.

[0126] Therefore, the Doppler effect does not change the shape of the spectrum itself, but it causes a continuous drift of the frequency center, resulting in a change in the degree of spectral overlap between different communicating parties over time. This dynamic evolution mechanism provides a direct physical basis for subsequent two-photon interference degradation and bit error rate increase.

[0127] Figure 3 is a diagram of the AI-controlled frequency multiplexing MDI-QKD system (single user) provided in an embodiment of the present invention. This diagram illustrates the complete quantum process of frequency-bin multiplexing measurement device-independent quantum key distribution in a single-user scenario, where the user... and Quantum pulses encoded with frequency bins are generated separately and transmitted to the central MDI relay via a frequency-multiplexed quantum channel in the same optical fiber. At the relay node, the quantum states from both sides first interfere at the beam splitter, and then the different frequency bins are mapped to the corresponding measurement channels by a frequency demultiplexer, and detected by a single-photon detector. The detection event corresponds to the projection of partial Bell states on the frequency degrees of freedom, and its statistical results serve as the classical measurement output, providing the physical basis for secure key distribution in measurement device-independent protocols.

[0128] In a multi-user scenario, multiple users, Alice and Bob, each prepare weakly coherent quantum states encoded with frequency bins using narrow-linewidth laser sources and transmit them to an untrusted central node, Charlie, via independent quantum channels. At the central node, the quantum states from different users undergo two-photon interference at a beam splitter after frequency and phase matching, and the joint quantum state is projected through frequency-domain Bell state measurements. A single-photon detector array times-frequency labels the interference results and outputs classical measurement results, thereby establishing a quantum correlation between Alice and Bob without requiring trusted measurement equipment, providing a quantum basis for subsequent key generation.

[0129] In one feasible implementation, step S4 is described in detail:

[0130] In the frequency compensation decision-making stage based on reinforcement learning, as shown in Figure 4, this figure illustrates how the Doppler effect caused by relative motion propagates step by step and ultimately degrades the performance of the quantum communication system, and how reinforcement learning actively breaks this degradation chain at a critical stage: The time-varying relative velocity of the two communicating parties first generates a continuously changing Doppler frequency shift. This frequency shift forms a residual frequency offset when traditional compensation is insufficient, which in turn leads to spectral energy diffusion, enhanced phase noise, and mode instability, ultimately manifesting as an increase in QBER and a decrease in SKR. To address this, the system introduces an adaptive frequency compensation mechanism based on reinforcement learning. Through the perception of the velocity state and policy inference, the optimal compensation action is output in real time, compressing the residual Doppler frequency offset within a controllable range, refocusing the spectrum, and restoring physical layer stability. This significantly reduces the bit error rate, increases the security key rate, and enhances the overall robustness at the system level.

[0131] As shown in Figure 4, the time-varying relative velocity between the two communicating parties first produces a continuously changing Doppler frequency shift. This frequency shift forms a residual frequency offset when traditional compensation is insufficient, which in turn leads to spectral energy diffusion, phase noise enhancement, and mode instability, ultimately manifesting as an increase in QBER and a decrease in SKR.

[0132] To address this, the present invention introduces an adaptive frequency compensation mechanism based on reinforcement learning. By sensing the velocity state and inferring the policy, the optimal compensation action is output in real time, compressing the residual Doppler frequency offset within a controllable range, refocusing the spectrum and restoring physical layer stability, thereby significantly reducing the bit error rate, improving the security key rate and enhancing overall robustness at the system level.

[0133] Specifically, this invention introduces a frequency calibration control quantity. It is used for active correction of real-time Doppler frequency shift.

[0134] Considering the limitations of actual hardware execution efficiency and control precision, the compensated residual frequency error is defined as:

[0135]

[0136] in, Indicates Doppler frequency shift; This represents the compensation execution coefficient, used to model the response attenuation between control commands and actual frequency adjustments; Indicates the frequency calibration control quantity; Indicates the discrete time step index; This indicates different communication links or node pairs.

[0137] This invention, at each discrete time step Construct the state vector:

[0138]

[0139] in, Represents communication node With another communication node At any moment The relative radial velocity; This represents the effective visibility estimate obtained based on historical interference statistical characteristics data; This represents the discrete time step index.

[0140] The reinforcement learning agent adjusts its behavior according to the current state. Select action:

[0141]

[0142] in, This indicates that reinforcement learning occurs at time steps. The action, i.e., the frequency compensation amount; Indicates at time step Frequency calibration control quantity; Indicates the maximum permissible amplitude of frequency compensation control; This represents the discrete time step index.

[0143] This allows for adaptive adjustment of the compensation amplitude within the permissible frequency adjustment range, and indirectly reshapes the probability distribution of the residual frequency error. .

[0144] This decision-making process lays the foundation for subsequent optimization of interference performance.

[0145] In one feasible implementation, step S5 is described in detail:

[0146] In the stage where residual frequency error affects the visibility of quantum interference, this invention calculates the success probability of Bell state measurement (BSM) at different frequency bins based on a frequency domain two-photon interference model.

[0147] No. The interference probabilities corresponding to each frequency bin satisfy:

[0148]

[0149] in, Indicates the first The interference probability corresponding to each frequency bin; , representing the relevant proportionality constant; and These represent the time steps of the two communicating parties. spectral envelope function; Represents a frequency variable.

[0150] Under the Gaussian spectrum assumption, the above integral can be analytically simplified to a frequency interference visibility function:

[0151]

[0152] in, This represents the frequency interference visibility function determined by the residual frequency error; Indicates residual frequency error; Represents an exponential function; This represents the effective spectral width of a single frequency bin.

[0153] This function quantitatively characterizes the exponential decay effect of residual frequency error on interference quality.

[0154] To further consider non-ideal factors such as detection efficiency mismatch, time jitter, and system noise, a minimum visibility parameter is introduced. The corrected visibility model is obtained as follows:

[0155] Specifically, the visibility model is as follows:

[0156]

[0157] in, This represents the frequency interference visibility function determined by the residual frequency error; Indicates the minimum visibility parameter; Indicates residual frequency error; Indicates the effective spectral width of a single frequency bin; This represents an exponential function.

[0158] Ultimately, the effective interference visibility is defined as:

[0159]

[0160] in, Indicates effective visibility; This represents the baseline visibility under ideal frequency matching conditions. This represents the frequency interference visibility function determined by the residual frequency error. This indicates the residual frequency error.

[0161] In one feasible implementation, step S6 is described in detail:

[0162] In the stage of frequency bin utilization and bit error propagation caused by interference degradation, this invention further maps the effective interference visibility to the availability of spectrum resources, introducing the effective frequency bin number. The number of parallel frequency channels that can participate in key generation under the current channel conditions is quantified and defined as follows:

[0163]

[0164] in, This represents the total number of bins used in parallel within the system. An index representing a single frequency bin; Indicates the first Effective interference visibility per frequency bin; Indicates effective visibility; This represents the visibility threshold, used to determine whether the frequency bin has effective interference capability; This represents the minimum value function.

[0165] Meanwhile, the interference degradation caused by the Doppler frequency shift will directly lead to an increase in the bit error probability, and the corresponding bit error term can be approximated as:

[0166]

[0167] in, This represents the total number of bins used in parallel within the system. An index representing a single frequency bin; Indicates the first Frequency interference visibility of each frequency bin; Indicates the visibility of frequency interference.

[0168] This expression reflects the average contribution of frequency mismatch to the bit flip probability.

[0169] Finally, the total bit error rate under single-photon conditions is obtained:

[0170]

[0171]

[0172] in, This represents the total bit error rate under single-photon conditions. This represents the fundamental bit error rate term caused by channel loss and probe noise; Indicates an error item.

[0173] This step also includes, during the key post-processing and secure key generation stage, using the effective frequency bin number obtained in the previous stage. Calculate single-photon yield:

[0174]

[0175] in, Indicates the first The probability of successful single-photon detection in each frequency bin; Indicates the number of effective frequency bins; An index representing a single frequency bin; This represents the baseline single-photon yield for a single frequency bin.

[0176] Therefore, the security key rate can be expressed as:

[0177]

[0178] in, Indicates single-photon yield; Represents the binary entropy function; This represents the total bit error rate under single-photon conditions. Indicates total gain; This represents the error correction efficiency factor; This represents the overall bit error rate, including contributions from multiple photons and noise.

[0179] Secure key rate Mapped to the reward function of reinforcement learning:

[0180]

[0181] in, Indicates at time step The security key generation rate is optimized through a policy process: By continuously updating the frequency compensation strategy, the frequency bin utilization rate, interference visibility and security key generation rate are jointly optimized in the dynamic Doppler environment, thereby forming a stable adaptive optimization closed loop.

[0182] In the strategy optimization process This represents the reinforcement learning policy function; Indicates at time step Reward discount factor; Represents the expectation symbol. This indicates that reinforcement learning occurs at time steps. The instant reward value.

[0183] The technical terms, principles, or means related to the technical solutions of the present invention mentioned in the above embodiments, which are not described in detail above, are all well-known technologies or common practices that are known to those skilled in the art.

[0184] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of this invention is defined by the appended claims and their equivalents.

Claims

1. A measurement device-independent quantum key distribution method based on AI frequency bin coding, characterized in that, The computer system performs the following steps: inputting quantum signals sent by both communicating parties, the relative radial velocity between the communicating node and the untrusted relay node, and historical quantum interference statistical characteristic data into the computer system; the quantum signals include weakly coherent optical pulses and frequency bins; constructing a measurement device-independent quantum key distribution system model based on frequency bin encoding, uniformly describing the quantum signals sent by both communicating parties in the frequency domain, and obtaining frequency bin-encoded quantum states; based on the relative radial velocity between the communicating node and the untrusted relay node, the frequency bin-encoded quantum states generate time-dependent Doppler frequency shifts, and analyzing the resulting overall frequency drift; based on the relative radial velocity and historical quantum interference statistical characteristic data, dynamically generating frequency calibration control quantities through a learning-driven frequency compensation mechanism to compensate for the Doppler frequency shifts and form residual frequency errors; based on a frequency-domain two-photon interference model, analyzing how the residual frequency errors affect the interference quality of the frequency bins, and further obtaining effective interference visibility; The effective interference visibility is mapped to the number of available frequency bins and quantum error characteristics to obtain the number of effective frequency bins and the total error rate. The final secure key generation rate is calculated and output. The execution steps of dynamically generating the frequency calibration control quantity are as follows: The learning-driven frequency compensation mechanism includes a reinforcement learning agent. At each discrete time step, a state vector is constructed. The state vector includes the relative radial velocity between the communication node and the relay node and the effective visibility estimate obtained based on historical quantum interference statistical characteristic data. The reinforcement learning agent selects a frequency compensation quantity from a preset range according to the state vector as the frequency calibration control quantity. At the same time, the residual frequency error after compensation is defined as: in, Indicates Doppler frequency shift, Indicates the compensation execution coefficient. This indicates the frequency calibration control quantity. Indicates different communication links or node pairs. This represents the discrete time step index.

2. The measurement device-independent quantum key distribution method based on AI frequency bin coding according to claim 1, characterized in that, The execution steps for constructing the measurement device-independent quantum key distribution system model based on frequency bin encoding are as follows: The phase-randomized weakly coherent state obtained after phase randomization of the weakly coherent optical pulse is used as the quantum carrier to obtain the corresponding optical field quantum state; through electro-optic modulation and narrowband frequency domain filtering, the single-photon subspace is mapped to an orthogonal frequency domain ground state composed of multiple discrete frequency bins; under single-photon conditions, the frequency bin-encoded quantum state is: in, Represents the frequency bin-encoded quantum state. Indicates the total number of frequency bins. Index representing a single frequency bin. Indicates the first The complex amplitude of a frequency bin. Indicates the first The orthogonal frequency domain ground state corresponding to each frequency bin This represents the center carrier frequency of the quantum signal. Indicates the first The center frequency of each frequency bin This represents the spacing width between adjacent frequency bins; meanwhile, a uniform distribution strategy is adopted for the probability weights of the complex amplitude of each frequency bin.

3. The measurement device-independent quantum key distribution method based on AI frequency bin coding according to claim 1, characterized in that, The steps for performing the overall frequency drift caused by the analysis are as follows: The Doppler frequency shift is expressed as: in, The speed of light is constant. Represents relative radial velocity, This represents the center carrier frequency of the quantum signal. Indicates the discrete time step index. This represents different communication links or node pairs; simultaneously, the initial spectral envelope function of each frequency bin is modeled as a Gaussian form; under the influence of the Doppler frequency shift, the spectrum of the frequency bin does not change shape, only causing the overall spectral envelope to shift over time; specifically, the evolution of the overall spectral envelope over time is as follows: in, Indicates Doppler frequency shift, Represents frequency variables. Indicates the discrete time step index. Indicates different communication links or node pairs. Denotes the initial spectral envelope function. Index representing a single frequency bin.

4. The measurement device-independent quantum key distribution method based on AI frequency bin coding according to claim 1, characterized in that, The steps for obtaining effective interferometric visibility are as follows: First, based on the frequency-domain two-photon interferometry model, the success probability of Bell states at different frequency bins is calculated to obtain the interferometric probability corresponding to the frequency bin; under the Gaussian spectrum assumption, the interferometric probability is simplified into a frequency interferometric visibility function; finally, a minimum visibility parameter is introduced to obtain the corrected visibility model, and the effective visibility is defined; specifically, the visibility model is: in, Indicates the minimum visibility parameter. Indicates residual frequency error. This represents the effective spectral width of a single frequency bin. This represents an exponential function.

5. The measurement device-independent quantum key distribution method based on AI frequency bin coding according to claim 1, characterized in that, The execution steps for obtaining the effective frequency bin number and the total bit error rate are as follows: First, the effective frequency bin number is introduced to quantify the number of parallel frequency channels that can participate in key generation under the current channel state; at the same time, the interference degradation caused by Doppler frequency shift leads to an increase in the bit error probability, and the corresponding bit error term is obtained; finally, the total bit error rate under single-photon conditions is obtained based on the bit error term, and the total bit error rate does not exceed a set threshold.

6. The measurement device-independent quantum key distribution method based on AI frequency bin coding according to claim 1, characterized in that, The steps for calculating the final secure key generation rate are as follows: calculate the single-photon yield based on the effective frequency bin number; and calculate the secure key rate based on the single-photon yield. in, Indicates single-photon yield. Represents the binary entropy function. Represents the total bit error rate under single-photon conditions. Indicates the total gain. This represents the error correction efficiency factor. This represents the overall bit error rate, including contributions from multiple photons and noise.

7. A measurement device-independent quantum key distribution system based on AI-based frequency bin encoding, employing the measurement device-independent quantum key distribution method based on AI-based frequency bin encoding as described in any one of claims 1-6, characterized in that, include: The information input module is used to input the quantum signals sent by both communicating parties, the relative radial velocity between the communication node and the relay node, and historical quantum interference statistical characteristics data; the frequency domain quantum state construction module is used to construct a measurement device-independent quantum key distribution system model based on frequency bin encoding, and to uniformly describe the quantum signals sent by both communicating parties in the frequency domain; the relative motion frequency shift evolution module is used to consider the influence of the relative motion between the communication node and the relay node on the frequency bin quantum state, and to analyze the overall frequency drift caused by the Doppler effect; The reinforcement learning frequency compensation module incorporates a reinforcement learning agent to dynamically generate frequency calibration control quantities through a learning-driven frequency compensation mechanism, thereby compensating for the Doppler frequency shift and forming a residual frequency error. The interference visibility analysis module analyzes the impact of the residual frequency error on the frequency bin interference visibility based on a frequency-domain two-photon interference model. The frequency bin utilization and bit error statistics module maps the effective interference visibility to the number of available frequency bin resources and quantum bit error characteristics, obtaining the effective number of frequency bins and the total bit error rate. The security key generation module is used to calculate the final security key generation rate based on the effective frequency bin number and output the security key generation rate.

8. An electronic device, comprising: The system comprises a processor, a communication interface, a memory, and a communication bus, wherein the processor, the communication interface, and the memory communicate with each other via the communication bus; characterized in that the memory stores a computer program, which, when executed by the processor, causes the processor to perform the measurement device-independent quantum key distribution method based on AI frequency bin coding as described in any one of claims 1-7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed, it implements the measurement device-independent quantum key distribution method based on AI frequency bin encoding as described in any one of claims 1 to 7.

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