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Rate-adaptive reconciliation with polar coding for continuous-variable quantum key distribution

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Abstract

Quantum key distribution (QKD) enables two authenticated parties to share secret keys with the ability to detect any attempts to eavesdrop the keys theoretically. As a crucial step, information reconciliation protocol has a significant effect on the secret key rate and maximal transmission distance of continuous-variable quantum key distribution (CV-QKD) systems. To improve the secret key rate in practical CV-QKD systems with time-varying quantum channel, we propose an efficient rate-adaptive multidimensional information reconciliation protocol based on polar codes. Simulation results verify that our proposed rate-adaptive reconciliation protocol can enhance the secret key rate compared to that of the conventional reconciliation protocol.

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Notes

  1. We denote \(K_{\ell }\) as the length of information at the \(\ell \)th retransmission, and take the first transmission as the 0th retransmission, thereby \(K_0 = K = NR_{\mathrm{max}}\). With the estimated channel reliability \(\varvec{\mathcal {\omega }}=[\omega _0, \omega _1, \cdots , \omega _{N-1}]\) in an ascending order, channel-bit index in \(A = \{\omega _{N-1}, \omega _{N-2}, \cdots , \omega _{N-K_{\ell }}\}\) and \(A^c = \{0,1, \cdots , N-1\}-A\) are used to send information bits \(\mathbf{u }_\mathcal {I}\) and frozen bits \(\mathbf{u }_\mathcal {F}\), respectively.

  2. \(K_{\mathrm{step}}\) channel-bits in \(\mathcal {F'} = \{\omega _{N-K_{\ell -1}}, \cdots , \omega _{N-K_{\ell -1}+K_{\mathrm{step}}-1} \}\) are removed from A and added to \(A^c\) simultaneously. That is, \(A = A - \mathcal {F'}\), \(A^c = A^c + \mathcal {F'}\); information bits denoted by \(\mathbf{u }_\mathcal {F'}\) become frozen bits.

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Acknowledgements

This research was supported by the National Natural Science Foundation of China (Grant No. 61601403), Shanghai Municipal Science and Technology Major Project (Grant No. 2019SHZDZX01), the Fundamental Research Funds for the Central Universities and Graduate Student Innovation Fund of Donghua University (Grant No. CUSF-DH-D-2020084) and the State Key Laboratory of Advanced Optical Communication Systems and Networks (Grant No. 2020GZKF002), China.

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Authors and Affiliations

  1. School of Information Engineering, Yangzhou University, Yangzhou, 225127, China

    Meixiang Zhang

  2. School of Information Science and Technology, Donghua University, Shanghai, 201620, China

    Han Hai, Yan Feng & Xue-Qin Jiang

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  1. Meixiang Zhang
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Zhang, M., Hai, H., Feng, Y. et al. Rate-adaptive reconciliation with polar coding for continuous-variable quantum key distribution. Quantum Inf Process 20, 318 (2021). https://doi.org/10.1007/s11128-021-03248-0

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