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Improved information reconciliation with systematic polar codes for continuous variable quantum key distribution

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Abstract

Quantum key distribution (QKD) enables two authenticated parties to share secret key and can detect any attack that attempts to eavesdrop on the key. Information reconciliation is an important part of QKD. The secret key between two communication parties can be extracted by correcting errors caused by quantum channel noise. To improve the efficiency of information reconciliation and secret key rate, this paper proposes an improved multidimensional information reconciliation protocol based on systematic polar codes. Moreover, we have demonstrated and analyzed the security of the proposed protocol. Simulation results show that the proposed protocol achieves the reconciliation efficiency of around 97% in a wider range of signal-to-noise ratio range \(\left( 0,0.18\right) \) and a quite low frame error rate (\(P_e<0.001\)). As a result, the improved multidimensional information reconciliation protocol based on the systematic polar codes can achieve a longer quantum communication transmission distance.

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References

  1. Gao, C., Jiang, D., Lu, L., Guo, Y., Chen, L.: Multi-matrix post-processing for quantum key distribution. Opt. Express 27, 14545 (2019)

    Article  ADS  Google Scholar 

  2. Jouguet, P., Kunz, J., Sébastien, L.A.: Long distance continuous-variable quantum key distribution with a gaussian modulation. Phys. Rev. A 84, 6 (2011)

    Article  Google Scholar 

  3. Frédéric, G., Cerf, N.J., Jérme, W., et al.: Virtual entanglement and reconciliation protocols for quantum cryptography with continuous variables. Quant. Inf. Comput. (2003)

  4. Van Assche, G., Cardinal, J., Cerf, N.J.: Reconciliation of a quantum-distributed gaussian key. IEEE Trans. Inf. Theory 50, 394 (2012)

    MathSciNet  MATH  Google Scholar 

  5. Deutsch, D., Ekert, A., Jozsa, R., et al.: Quantum privacy amplification and the security of quantum cryptography over noisy channels. Phys. Rev. Lett. 9, 77 (1996)

    Google Scholar 

  6. Mink, A., Nakassis, A.: LDPC for QKD reconciliation. Comput. Sci. F. 2, 2 (2012)

    Google Scholar 

  7. Wang, X., Zhang, Y., et al.: Efficient rate-adaptive reconciliation for continuous-variable quantum key distribution. Quant Inf Comput 17, 13–14 (2017)

    MathSciNet  Google Scholar 

  8. Jiang, X.Q., Yang, S., Peng, H., et al.: High speed reconciliation for cvqkd based on spatially coupled ldpc codes. IEEE Photon. J. 10(4), 1–10 (2018)

    Article  Google Scholar 

  9. Wen, X., et al.: Novel reconciliation protocol based on spinal code for continuous-variable quantum key distribution. Quant. Inf. Process. 19(10) (2020)

  10. Arikan, E.: Channel polarization: a method for constructing capacity-achieving codes for symmetric binary-input memoryless channels. IEEE Trans. Inf. Theory 55(7), 3051 (2009)

    Article  MathSciNet  Google Scholar 

  11. Nakassis, A., Mink, A.: Polar codes in a QKD environment. Int Soc Opt Photon Quant Inf Comput 12 (2014)

  12. Lee, S., Park, J, Heo, J.: Improved reconciliation with polar codes in quantum key distribution. Quant. Inf. Comput. (2018)

  13. Jouguet, P., Kunz, J., Sébastien, L.M.: High performance error correction for quantum key distribution using polar codes. Quant. Inf. Comput. 14, 3 (2013)

    MathSciNet  Google Scholar 

  14. Kim, Y., Suh, C., Rhee, J.: Reconciliation with polar codes constructed using Gaussian approximation for long-distance continuous-variable quantum key distribution. In: International Conference on Information and Communication Technology Convergence (2017)

  15. Arikan, E.: Systematic polar coding. IEEE Commun. Lett. 15(8), 860 (2011)

    Article  Google Scholar 

  16. Silberhorn, C., Ralph, T.C., Lütkenhaus, N., Leuchs, G.: Continuous variable quantum cryptography-beating the 3 dB loss limit. Phys. Rev. Lett. 89(16), 167901 (2002)

    Article  ADS  Google Scholar 

  17. Grosshans, F., Assche, G.V., Wenger, J., et al.: Quantum key distribution using gaussian-modulated coherent states. Nature 421(6920), 238 (2003)

    Article  ADS  Google Scholar 

  18. Sarkis, G., Tal, I., Giard, P., et al.: Flexible and low-complexity encoding and decoding of systematic polar codes. IEEE Trans. Commun. 64(7), 2732 (2015)

    Article  Google Scholar 

  19. Li, L., Zhang, W.: On the encoding complexity of systematic polar codes. In: IEEE International System-on-Chip Conference (2015)

  20. Li, L., Xu, Z., Hu, Y.: Channel estimation with systematic polar codes. IEEE Trans. Veh. Technol. 67(6), 1 (2018)

    Article  Google Scholar 

  21. Li, L. , Zhang, W.: On the encoding complexity of systematic polar codes. In: IEEE International System-on-Chip Conference. IEEE (2015)

  22. Ye, M., Li, H.: A performance comparison of systematic polar codes and non-systematic polar codes. In: International Conference on Mathematics, Modelling, Simulation and Algorithms (2018)

  23. Leverrier, A., Alléaume, R., Boutros, J., et al.: Multidimensional reconciliation for continuous-variable quantum key distribution. Phys. Rev. A 77, 042325 (2008)

    Article  ADS  Google Scholar 

  24. He, G., Belfiore, J.C., Land, I., Yang, G., Wen, T.: \(\beta \)-expansion: a theoretical framework for fast and recursive construction of polar codes. In: GLOBECOM 2017 - 2017 IEEE Global Communications (2017)

  25. Ma, X.C., Sun, S.H., Jiang, M.S., et al.: Local oscillator fluctuation opens a loophole for eve in practical continuous-variable quantum-key-distribution systems. Phys. Rev. A 88(2), 290–296 (2013)

    Article  Google Scholar 

  26. Hillery, M.: Quantum cryptography with squeezed states. Phys. Rev. A 61(2), 022309 (1999)

    Article  MathSciNet  ADS  Google Scholar 

  27. Frédéric, G., Grangier, P.: Continuous variable quantum cryptography using coherent states. Phys. Rev. Lett. 88(5), 057902 (2002)

    Article  Google Scholar 

  28. Afisiadis, O. , Balatsoukas-Stimming, A. , Burg, A.P.: A low-complexity improved successive cancellation decoder for polar codes. In: Asilomar Conference on Signals, Systems and Computers. IEEE (2014)

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Acknowledgements

This research was supported by the National Natural Science Foundation of China (Grant No. 61601403), the Young Backbone Teachers Project of Yangzhou University, the National Natural Science Foundation of Shanghai (Grant No. 20ZR1400700), and the Shanghai Municipal Science and Technology Major Project (Grant No. 2019SHZDZX01).

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Authors and Affiliations

  1. Yangzhou University, Yangzhou, 225127, China

    Meixiang Zhang, Yin Dou & Yuting Huang

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

    Xue-Qin Jiang & Yan Feng

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  1. Meixiang Zhang
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  2. Yin Dou
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  3. Yuting Huang
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  4. Xue-Qin Jiang
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  5. Yan Feng
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Correspondence to Meixiang Zhang.

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Zhang, M., Dou, Y., Huang, Y. et al. Improved information reconciliation with systematic polar codes for continuous variable quantum key distribution. Quantum Inf Process 20, 327 (2021). https://doi.org/10.1007/s11128-021-03265-z

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