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Physical Review Applied

Bayesian Parameter Estimation for Continuous-Variable Quantum Key Distribution

Kexin Liang, Geng Chai, Zhengwen Cao, Yuan Yang, Xinlei Chen, Yuan Lu, Jinye Peng

Published Nov 23, 2022• 8 citations
Publisher

Abstract

The effectiveness and accuracy of parameter estimation are guarantees for the high-performance and high-safety operation of practical continuous-variable quantum key distribution systems. A scheme based on Bayesian estimation is proposed to tackle the fluctuations of channels. In free-space channel, the Bayesian random-effects model is employed to construct complete prior information, and the channel state information extracted through pilot signals is applied to rectify the prior information. Compressed sensing technology is applied due to the sparsity of the free-space channel to reduce the cost of the system. Experimental results show that the proposed scheme has higher estimation accuracy under the free space, and the system performance is also enhanced. Moreover, the results under fiber show higher estimation accuracy and better stability than that of traditional methods. In conclusion, the scheme can create practical conditions for the construction of future global quantum networks.

DOI
10.1103/physrevapplied.18.054077

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The effectiveness and accuracy of parameter estimation are guarantees for the high-performance and high-safety operation of practical continuous-variable quantum key distribution systems. A scheme based on Bayesian estimation is proposed to tackle the fluctuations of channels. In free-space channel, the Bayesian random-effects model is employed to construct complete prior information, and the channel state information extracted through pilot signals is applied to rectify the prior information. Compressed sensing technology is applied due to the sparsity of the free-space channel to reduce the cost of the system. Experimental results show that the proposed scheme has higher estimation accuracy under the free space, and the system performance is also enhanced. Moreover, the results under fiber show higher estimation accuracy and better stability than that of traditional methods. In conclusion, the scheme can create practical conditions for the construction of future global quantum networks.
In satellite-based free-space continuous-variable QKD (CV-QKD), the parameter estimation for the atmospheric channel fluctuations due to the turbulence effects and attenuation is crucial for analyzing and improving the protocol performance. However, the partial key data usually need to be sacrificed for the parameter estimation leading to the secret key reduction and the possible information leakage, especially when the channel is varying. In this paper, compressive sensing (CS) theory is applied to free-space CV-QKD to achieve the channel parameter estimation with small amount of key data sacrifice and low computational complexity. According to CS theory, the possibility of the sparse representation for free-space channel is analyzed and the two types of sparse reconstruction models for the channel parameters are constructed combining with the stability of the sub-channels. The most part of key data for parameter estimation is saved by using the model constructed by the variables in the quantum signals, while all the key data can be saved and be used to generate the secret key by using the model constructed by the second-order statistics of the variables. Thus, the methods can generate more secret key, improve the secret key rate, and be well adapted for the cases with the limited communication time since fewer or no key data (variables) is sacrificed for parameter estimation. Finally, simulation results are given to verify the effectiveness of the proposed methods.
In satellite-based free-space continuous-variable QKD (CV-QKD), the parameter estimation for the atmospheric channel fluctuations due to the turbulence effects and attenuation is crucial for analyzing and improving the protocol performance. In this paper, compressive sensing (CS) theory is applied to free-space CV-QKD to achieve the channel parameter estimation with low computational complexity and small amount of data. According to CS theory, the possibility of the sparse representation for free-space channel is analyzed and the two types of sparse reconstruction models for the channel parameters are constructed combining with the stability of the sub-channels. The most part of variable for parameter estimation is saved by using the model relying on the variables in the quantum signals, while all the variables can be used to generate the secret key by using the model relying on the second-order statistics of the variables. The methods are well adapted for the cases with the limited communication time since a little or no variable is sacrificed for parameter estimation. Finally, simulation results are given to verify the effectiveness of the proposed methods.
For the maximum-likelihood parameter estimation (MPE) of continuous-variable quantum key distribution (CVQKD), it sacrifices partial key when estimating the channel parameters, and when the channel is varying, even slowly, legitimate communication parties must constantly exchange partial input signal and output signal to update the channel estimation. Therefore, the MPE leads to the following problems in practical application: (a) MPE achieved by randomly sampling the states can not accurately reflect the dynamic channel; (b) there exist a trade-off between the secret key rate (SKR) and the accuracy of parameter estimation in the finite-size regime; and (c) information leakage may be caused by the correlation between key variables. In this article, a novel parameter estimation method for CVQKD is proposed without affecting the security, and the consistency between the method and the physical model is given. Experimental simulation results show that the method can effectively improve the SKR and secure propagation distance. The experimental verification of the proposed method is given through the fiber system. Besides, the security analysis demonstrates that the method is secure against entanglement-distillation attack.
Atmospheric effects are the chief threats to the quantum properties of propagating quantum signals and may degrade the performance of quantum key distribution seriously. As one of the most important parts of continuous-variable quantum key distribution (CVQKD), a parameter estimation method has not been specially proposed in an atmospheric channel, and usually the security analysis is based on the assumption that the relevant parameters, especially the excess noise, have been previously obtained. Here we propose a parameter estimation method for Gaussian modulated coherent state continuous-variable quantum key distribution over the atmospheric link, and we investigate the impact of the atmospheric channel on the estimated values of the parameters. Based on this method, we study theoretically the effect of link fluctuations on the achievable secret key rate of CVQKD under different practical transmitted conditions. The results show that this method is unified with the physical model and can effectively resist entanglement-distillation attack. The proposed method fills in the blank of parameter estimation for implementation of practical atmospheric CVQKD.
Free-space continuous variable quantum key distribution has attracted attention due to its ability to provide a more widely available transmission channel. However, the key rate of free-space continuous variable quantum key distribution itself is not high, and a portion of the original key needs to be allocated for parameter estimation. In this article, we analyze the spatial correlation of free-space continuous variable quantum key distribution and propose the use of a nearby system to transmit an inexpensive signal. Parameter estimation is performed using a deep learning model to predict and reduce the amount of original key used for parameter estimation, thereby improving the key rate.
Quantum key distribution can be used to share secret keys with information-theoretic security between two legitimate partners for secure communication. In the case of satellite communication, free-space channel is the only way to transmit information, thus research on its properties is of great significance to quantum cryptographic communication. In this paper, we thoroughly analyze the influence of free-space channel fading effects on continuous variable quantum key distribution and for the first time prove that random distribution (such as Rayleigh distribution, Rice distribution and et al.) of free-space channel fading coefficients can be used to increase secret information rates and improve system stability against excess noises. Our results offer academic reference for practical applications of ground-space and space-space quantum communication and global quantum communication network.