A Bayesian parameter estimation method for free-space continuous variable quantum communication systems

Abstract

The present invention discloses a Bayesian parameter estimation method for a free-space continuous-variable quantum communication system. First, a priori information of the free-space channel is constructed using a Bayesian random-effect model. Second, channel state information is obtained through pilot information. Due to the sparsity of the free-space channel, compressed sensing technology is used to achieve efficient design and accurate reconstruction of the pilot signal. Finally, system parameter estimation is achieved in the free-space channel using the priori information and channel state information. Therefore, the Bayesian estimation method proposed in the present invention takes into account the overall characteristics of the channel and is applicable to free-space channels with fluctuating characteristics, providing a post-processing solution for realizing a free-space continuous-variable quantum secure communication system.

Description

Technical Field

[0001] The present invention relates to a parameter estimation method, in particular to a Bayesian parameter estimation method for a free space continuous variable quantum communication system. Background Art

[0002] In quantum communication technology, the physical components of a continuous-variable quantum key distribution (CVQKD) system include quantum state preparation, transmission, and measurement, as well as post-processing, including parameter estimation, information negotiation, and confidentiality enhancement. Parameter estimation is a critical link between the quantum state transmission phase and data post-processing in a continuous-variable quantum communication system. It not only assesses the security of quantum states during quantum channel transmission, but also provides parameters for subsequent post-processing by evaluating various parameters of information during channel transmission, thus influencing the final key rate. Therefore, effective and accurate parameter estimation is essential.

[0003] In free-space channels, transmission effects such as atmospheric turbulence can cause transmission distortion of quantum signals, severely degrading system performance and worsening communication quality. Therefore, it is urgent and necessary to develop data post-processing technologies suitable for free space. The implementation of post-processing technologies can fully leverage the advantages of free-space channels while avoiding the impact of channel fluctuations on system performance, thereby promoting the further development of quantum communication in free-space channels. Recently, free-space parameter estimation schemes have been proposed one after another. For example, G. Chai et al. proposed an atmospheric link parameter estimation method based on maximum likelihood estimation and subchannel theory, R. Laszlo et al. proposed an estimation scheme for clustering large amounts of transmitted data, and G. Chai et al. studied blind parameter estimation in free space.

[0004] While these existing methods have been effectively applied in free-space CVQKD systems, their fundamental principle is to divide the free-space channel into a series of stable sub-channels. This process can result in non-standard or erroneous divisions, and they also fail to systematically consider the overall characteristics of the channel. Therefore, there is an urgent need to develop a robust parameter estimation method for free-space channels that comprehensively considers the impact of channel fluctuations on system transmission and achieves both robustness and high accuracy in free-space channels. Summary of the Invention

[0005] The purpose of the present invention is to provide a Bayesian parameter estimation method for a free-space continuous variable quantum communication system, so as to solve technical problems such as the need to enhance the robustness and accuracy of existing free-space channels and the need to consider the overall volatility of the channel.

[0006] In order to achieve the above tasks, the present invention adopts the following technical solutions:

[0007] A Bayesian parameter estimation method for a free-space continuous variable quantum communication system comprises the following steps:

[0008] Step 1: Use the Bayesian random effect model to construct the prior information P(T) of the free space channel;

[0009] Step 2: Design a pilot signal using compressed sensing, and obtain channel state information P(y|T) through the pilot signal;

[0010] Step 3: Based on the robust prior information P(T) obtained in step 1 and the channel state information P(y|T) obtained in step 2, Bayesian estimation is used to estimate the system parameters in the free space channel.

[0011] Furthermore, in step 1, the prior information P(T) of the system parameters under the free space channel is a joint distribution of the probability distribution of the channel transmittance T under the elliptical model and the probability distribution of the channel transmittance T under the scintillation model.

[0012] Furthermore, the specific operations of step 2 are as follows:

[0013] Step 2.1: Generate a pilot signal at the sender Alice and transmit it to the receiver Bob.

[0014] Step 2.2: The receiving end, Bob, uses compressed sensing technology to reconstruct the received pilot signal and obtain a reconstructed pilot signal.

[0015] Step 2.3: Use the statistical characteristics of the reconstructed pilot signal obtained in step 2.2 to estimate the channel state information P(y|T).

[0016] Furthermore, in step 2.1, a continuous wave laser is used to generate weak coherent light at the sender Alice, which is processed into a pulse signal by an amplitude modulator. An unbalanced beam splitter is used to split the pulse signal into a quantum signal and a pilot signal. Polarization multiplexing and time division multiplexing are used to transmit the quantum signal and the pilot signal through a free space channel to the receiver Bob.

[0017] Furthermore, step 3 includes the following operations:

[0018] System parameters The Bayesian estimate is obtained as follows:

[0019]

[0020]

[0021] Where P(T|y) represents the posterior information of T.

[0022] Compared with the prior art, the present invention has the following technical features:

[0023] The present invention implements a Bayesian parameter estimation method for continuous variable quantum communication for free-space quantum channels. The method of the present invention uses pilot signals to complete parameter estimation, which can effectively save quantum resources. The design of the position and length of the pilot signal can fully utilize the pilot resources while ensuring accuracy, so that a balance is achieved between the two aspects. The estimated value of the parameter under the existing technology is easily affected by the amplitude attenuation and phase fluctuation of the quantum signal. The method of the present invention completes the construction of prior information by comprehensively considering the influence of amplitude attenuation and phase fluctuation, and then uses the channel state to correct the prior information, and finally obtains more accurate posterior information. System parameter estimation under free-space channels is realized. Therefore, the Bayesian estimation method proposed by the present invention takes into account the overall characteristics of the channel, is applicable to free-space channels with fluctuating characteristics, and provides a post-processing solution for realizing free-space quantum secure communication systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 This is a flow chart of the parameter estimation method of the free-space continuous variable quantum communication system based on Bayesian estimation of the present invention.

[0025] Figure 2 Schematic diagram for comparing system key rates under different parameter estimation conditions. DETAILED DESCRIPTION

[0026] like Figure 1 As shown, the present invention provides a Bayesian parameter estimation method for a free-space continuous-variable quantum communication system. The method's concept is as follows: First, a Bayesian random-effect model is used to construct robust prior information for the free-space channel. Second, due to the sparsity of the free-space channel, compressed sensing technology is used to efficiently design and accurately reconstruct the receiving Bob pilot signal. The channel state information P(y|T) is estimated from the pilot signal. Finally, the prior information and channel state information are used to estimate the system parameters in the free-space channel.

[0027] Step 1: Use the Bayesian random effect model to construct the prior information P(T) of the free space channel.

[0028] The Bayesian random effects model is defined below. The Bayesian random effects model is a classic linear model. The Bayesian random effects model shown in Formula 2 is an extension of the classic linear model. It regards the regression coefficients of the original (fixed effect model) as random variables and expresses the output as the sum of the random effect vector (used to represent the difference) and the random error vector. It is usually assumed that the two are independent and obey the normal distribution.

[0029] yij =v i +e ij (i=1,2,...,k; j=1,2,...,m), (2)

[0030] where v represents the random effect vector of differences, e ij is a random error vector, and n and m are both constants. It is usually assumed The two are independent of each other.

[0031] Therefore, the Bayesian random effects model can be used to combine the elliptical beam model and the scintillation model, comprehensively considering the various negative effects of atmospheric turbulence to construct more robust and complete prior information and establish a complete probability distribution of the atmospheric channel transmittance T. Furthermore, the prior information P(T) of the system parameters in the free-space channel can be comprehensively considered by the elliptical model and the scintillation model. Specifically, P(T) can be the joint distribution of the probability distribution of the channel transmittance T under the elliptical model and the probability distribution of the channel transmittance T under the scintillation model.

[0032] Step 2: Use compressed sensing to design a pilot signal and estimate the channel state information through the pilot signal.

[0033] A continuous-wave laser is used to generate weak coherent light at the sender Alice. This light is then processed into a pulse signal using an amplitude modulator. An unbalanced beam splitter is then used to split the pulse signal into a quantum signal and a pilot signal. The quantum signal and pilot signal are then transmitted to the receiver Bob via a free-space channel.

[0034] Due to the sparse nature of free-space channels, the design of the pilot signal at the receiving end, Bob, requires the use of compressed sensing technology to efficiently design and accurately reconstruct the pilot signal. The receiving end, Bob, uses the statistical properties of the reconstructed pilot signal to estimate the channel state information P(y|T).

[0035] Step 3: Based on the prior information P(T) obtained in step 1 and the channel state information P(y|T) obtained in step 2, Bayesian estimation is used to estimate the system parameters in the free space channel.

[0036] According to the Bayesian formula, the posterior information of T is described as:

[0037]

[0038] Therefore, the system parameters The Bayesian estimate is obtained as follows:

[0039]

[0040] In order to verify the feasibility and effectiveness of the method of the present invention, the following experiments were carried out:

[0041] 1. Results and mean square error of estimated transmittance T under different conditions

[0042] The estimation results and mean square errors of transmittance under different conditions were calculated and compared using different estimation methods (wherein Bayesian estimation is the parameter estimation method proposed in the present invention), as shown in Table 1:

[0043] Table 1 Comparison of two different estimation methods

[0044]

[0045] As shown in Table 1, the experiments show that even for fluctuating channels, such as free space channels, Bayesian estimation can still maintain good estimation results. Compared with the maximum likelihood estimation results, the estimation accuracy is improved by an order of magnitude.

[0046] 2. Method performance analysis

[0047] The key rate under quantum key distribution can effectively represent the performance of the system. The following key rate simulation is used to analyze the system performance by comparing the key rates under different parameter estimation conditions. The simulation results are as follows Figure 1 As shown, Figure 2 From top to bottom in the figure, the first line (dashed line) represents the PLOB bound, the second line (solid line) represents the system key rate under Bayesian estimation, the third line (dashed line) represents the key rate under maximum likelihood estimation (MLE) estimation when the estimator is 0.1 times the total data volume, the fourth line (dashed line) represents the key rate under MLE estimation when the estimator is 0.5 times the total data volume, and the fifth line (dashed line) represents the key rate under MLE estimation when the estimator is 0.9 times the total data volume.

[0048] like Figure 2 As shown in the figure, it can be seen that maximum likelihood estimation consumes quantum resources during the estimation process, which leads to an overall reduction in the system's key rate. In contrast, the Bayesian estimation of the present invention utilizes pilot signals to avoid quantum signal loss. From this perspective, the Bayesian estimation of the present invention not only provides more stable and accurate parameter estimation results, but also fully utilizes quantum signals to improve system performance.

Claims

1. A Bayesian parameter estimation method for a free-space continuous variable quantum communication system, characterized in that: The steps include: Step 1: Use the Bayesian random effect model to construct the prior information of the free space channel ; Prior information of system parameters under the free space channel is the channel transmittance under the elliptical model T The probability distribution of channel transmittance under the scintillation model T The joint distribution of the probability distribution of ; Step 2: Use compressed sensing to design a pilot signal and obtain channel state information through the pilot signal ; The specific operations are as follows: Step 2.1: Generate a pilot signal at the sender, Alice, and transmit it to the receiver, Bob. Specifically, a continuous-wave laser is used to generate weak coherent light at the sender, Alice, which is then processed into a pulse signal using an amplitude modulator. An unbalanced beam splitter is used to split the pulse signal into a quantum signal and a pilot signal. Polarization multiplexing and time division multiplexing are used to transmit the quantum signal and pilot signal over a free-space channel to the receiver, Bob. Step 2.2: The receiving end, Bob, uses compressed sensing technology to reconstruct the received pilot signal and obtain a reconstructed pilot signal. Step 2.3: Use the statistical characteristics of the reconstructed pilot signal obtained in step 2.2 to complete the channel state information estimates; Step 3: Based on the robust prior information obtained in step 1 and the channel state information obtained in step 2 , using Bayesian estimation, the system parameters are estimated under free space channel.

2. The Bayesian parameter estimation method for free-space continuous variable quantum communication according to claim 1, wherein: Step 3 includes the following operations: System parameters The Bayesian estimate is obtained as follows: Where, represents the posterior information of T.

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