An improved multidimensional reconciliation algorithm for continuous-variable quantum key distribution

  • Qiong LiEmail author
  • Xuan Wen
  • Haokun Mao
  • Xiaojun Wen


Reconciliation is a crucial procedure for continuous-variable quantum key distribution (CV-QKD) systems since it directly affects the performance of practical system including processing speed, secret key rate, and maximal transmission distance. In this paper, we proposed a novel initial decoding message computation method for multidimensional reconciliation with low density parity check code, which does not need the norm information from the encoder. Both theoretical analysis and simulation results demonstrate that the improved scheme can greatly decrease the communication traffic and storage resource consumption of the reconciliation procedure almost without degradation in the reconciliation efficiency. What is more, the improved scheme can decrease the secure key consumption for classical channel authentication, then increase the secure key rate, and also be conducive to the realization of high-speed CV-QKD systems.


Continuous-variable quantum key distribution Multidimensional reconciliation Quantization Low density parity check code Reconciliation efficiency 



This work is supported by the NSFC No. 61471141 and No. 61771168, Key Technology Program of Shenzhen, China, (No. JSGG20160427185010977), Space Science and Technology Advance Research Joint Funds (6141B06110105). 2018 Shenzhen Discipline Layout Project (No. JCYJ20170815145900474), and Shenzhen Basic Research Project (No. JCYJ20170818115704188). Many thanks are extended to Prof. H. Guo’s group of Peking university and Prof. S. Yu’s group of Beijing University of Post and Telecommunications for the helpful discussion on the experimental results.


  1. 1.
    Bennett, C.H., Brassard, G.: Quantum cryptography: public key distribution and coin tossing. In: Proceedings of IEEE International Conference on Computers, Systems and Signal Processing, pp. 175–179 (1984)Google Scholar
  2. 2.
    Bennett, C.H.: Quantum cryptography using any two nonorthogonal states. Phys. Rev. Lett. 68, 3121–3124 (1992)ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    Gisin, G., Ribordy, G., Tittel, W., Zbinden, H.: Quantum cryptography. Rev. Mod. Phys. 74, 145–195 (2002)ADSCrossRefGoogle Scholar
  4. 4.
    Weedbrook, C., Pirandola, S., Cerf, N.J., et al.: Gaussian quantum information. Rev. Mod. Phys. 84, 621 (2012)ADSCrossRefGoogle Scholar
  5. 5.
    Lo, H.K., Curty, M., Qi, B.: Measurement-device-independent quantum key distribution. Phys. Rev. Lett. 108(13), 130503 (2012)ADSCrossRefGoogle Scholar
  6. 6.
    Shen, D.S., Ma, W.P., Wang, L.L.: Two-party quantum key agreement with four-qubit cluster states. Quantum Inf. Process. 13(10), 2313–2324 (2014)ADSMathSciNetCrossRefGoogle Scholar
  7. 7.
    Grosshans, F., Grangier, P.: Continuous variable quantum cryptography using coherent states. Phys. Rev. Lett. 88(5), 057902 (2002)ADSCrossRefGoogle Scholar
  8. 8.
    Lodewyck, J., Bloch, M., Fossier, S., Karpov, E., Diamanti, E., et al.: Quantum key distribution over 25 km with an all-fiber continuous-variable system. Phys. Rev. A. 76(4), 538–538 (2007)CrossRefGoogle Scholar
  9. 9.
    Fossier, S., Diamanti, E., Debuisschert, T., Villing, A., Grangier, P.: Field test of a continuous-variable quantum key distribution prototype. New J. Phys. 11(4), 045023 (2009)ADSCrossRefGoogle Scholar
  10. 10.
    Asp, H., Bengtsson, B., Jensen, P.: Long distance continuous-variable quantum key distribution with a Gaussian modulation. Phys. Rev. A. 84(6), 062317 (2011)CrossRefGoogle Scholar
  11. 11.
    Guo, H., Peng, X., Li, Z.: Continuous-variable measurement-device-independent quantum key distribution with imperfect detectors. IEEE Lasers Electro Opt 90, 1–2 (2014)Google Scholar
  12. 12.
    Huang, D., Huang, P., Lin, D., Zeng, G.: Long-distance continuous-variable quantum key distribution by controlling excess noise. Sci. Rep. 6, 19201 (2015)ADSCrossRefGoogle Scholar
  13. 13.
    Wang, C., Huang, D., Huang, P., Lin, D., Peng, J., Zeng, G.: 25 MHz clock continuous-variable quantum key distribution system over 50 km fiber channel. Sci. Rep. 5(4), 102–108 (2015)Google Scholar
  14. 14.
    García-Patrón, R., Cerf, N.J.: Unconditional optimality of gaussian attacks against continuous-variable quantum key distribution. Phys. Rev. Lett. 97(19), 190503 (2006)ADSCrossRefGoogle Scholar
  15. 15.
    Becir, A., Wahiddin, M.R.B.: Tight bounds for the eavesdropping collective attacks on general CV-QKD protocols that involve non-maximally entanglement. Quantum Inf. Process. 12(2), 1155–1171 (2012)ADSMathSciNetCrossRefGoogle Scholar
  16. 16.
    Renner, R.: De finetti representation theorem for infinite-dimensional quantum systems and applications to quantum cryptography. Phys. Rev. Lett. 102(11), 110504 (2009)ADSCrossRefGoogle Scholar
  17. 17.
    Furrer, F., Franz, T., Berta, M., Leverrier, A., Scholz, V.B., Tomamichel, M., et al.: Continuous variable quantum key distribution: finite-key analysis of composable security against coherent attacks. Phys. Rev. Lett. 109(10), 100502 (2012)ADSCrossRefGoogle Scholar
  18. 18.
    Kraus, B., Gisin, N., Renner, R.: Lower and upper bounds on the secret-key rate for quantum key distribution protocols using one-way classical communication. Phys. Rev. Lett. 95(95), 080501 (2005)ADSCrossRefGoogle Scholar
  19. 19.
    Dixon, A.R., Sato, H.: High speed and adaptable error correction for megabit/s rate quantum key distribution. Sci. Rep. 4, 7275 (2014)ADSCrossRefGoogle Scholar
  20. 20.
    Gallager, R.G.: Low-density parity-check codes. IEEE Commun. Surv. Tutor. 13(1), 3–26 (1962)zbMATHGoogle Scholar
  21. 21.
    Brassard, G., Salvail, L.: Secret-key reconciliation by public discussion. Adv. Cryptol. Eurocrypt 93(765), 410–423 (1993)zbMATHGoogle Scholar
  22. 22.
    Buttler, W.T., Lamoreaux, S.K., Torgerson, J.R., et al.: Fast, efficient error reconciliation for quantum cryptography. Phys. Rev. A 67(5), 052303 (2003)ADSCrossRefGoogle Scholar
  23. 23.
    Yan, H., Ren, T., Peng, X., Lin, X., Jiang, W., Liu, T., et al.: Information reconciliation protocol in quantum key distribution system. Proc. IEEE Int. Conf. Nat. Comput. 3, 637–641 (2008)Google Scholar
  24. 24.
    Ch, S., Korolkova, N., Leuchs, G.: Quantum key distribution with bright entangled beams. Phys. Rev. Lett. 88(16), 167902 (2002)ADSCrossRefGoogle Scholar
  25. 25.
    Ch, S., Ralph, T.C., Lütkenhaus, N., Leuchs, G.: Continuous variable quantum cryptography: beating the 3 db loss limit. Phys. Rev. Lett. 89(16), 167901 (2002)ADSCrossRefGoogle Scholar
  26. 26.
    Van, A.G., Cardinal, J., Cerf, N.J.: Reconciliation of a quantum-distributed gaussian key. IEEE Trans. Inf. Theory. 50(2), 394–400 (2004)MathSciNetCrossRefGoogle Scholar
  27. 27.
    Bloch, M., Thangaraj, A., Mclaughlin, S.W., Merolla, J.M.: LDPC-based Gaussian key reconciliation. In: 2006 IEEE Information Theory Workshop, ITW ’06 Punta del Este. IEEE, pp. 116–120 (2006)Google Scholar
  28. 28.
    Leverrier, A., Alléaume, R., Boutros, J., Zémor, G., Grangier, P.: Multidimensional reconciliation for a continuous-variable quantum key distribution. Phys. Rev. A 77(4), 140–140 (2008)CrossRefGoogle Scholar
  29. 29.
    Jouguet, P., Kunzjacques, S., Leverrier, A., Grangier, P., Diamanti, E.: Experimental demonstration of long-distance continuous-variable quantum key distribution. Nat. Photonics 7(5), 378–381 (2013)ADSCrossRefGoogle Scholar
  30. 30.
    Jouguet, P., Kunzjacques, S.: High performance error correction for quantum key distribution using polar codes. Quantum Inf. Comput. 14(3), 329–338 (2012)MathSciNetGoogle Scholar
  31. 31.
    Leverrier, A., Grangier, P.: Continuous-variable quantum key distribution protocols with a non-Gaussian modulation. Phys. Rev. A 83(83), 3182–3182 (2011)Google Scholar
  32. 32.
    Lin, D., Huang, D., Huang, P., Peng, J., Zeng, G.: High performance reconciliation for continuous-variable quantum key distribution with LDPC code. Int. J. Quantum Inf. 13(02), 1550010 (2015)MathSciNetCrossRefGoogle Scholar
  33. 33.
    Wang, X., Zhang, Y.C., Li, Z. et al.: Efficient rate-adaptive reconciliation for continuous-variable quantum key distribution. arXiv:1703.04916 (2017)
  34. 34.
    Jiang, X.Q., Huang, P., Huang, D., Lin, D., Zeng, G.: Secret information reconciliation based on punctured low-density parity-check codes for continuous-variable quantum key distribution. Phys. Rev. A 95(2), 022318 (2017)ADSCrossRefGoogle Scholar
  35. 35.
    Walenta, N., Burg, A., Caselunghe, D., Constantin, J., Gisin, N., Guinnard, O., Houlmann, R., Junod, P., Korzh, B., Kulesza, N., et al.: A fast and versatile quantum key distribution system with hardware key distillation and wavelength multiplexing. New J. Phys. 16(1), 013047 (2014)ADSCrossRefGoogle Scholar
  36. 36.
    Mink, A.: Custom hardware to eliminate bottlenecks in QKD throughput performance. In: Proceedings of SPIE The International Society for Optical Engineering, p. 6780 (2007)Google Scholar
  37. 37.
    Chung, S.Y., Richardson, T.J., Urbanke, R.L.: Analysis of sum-product decoding of low-density parity-check codes using a Gaussian approximation. IEEE Trans. Inf. Theory 47(2), 657–670 (2000)MathSciNetCrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.Department of Computer Science and TechnologyHarbin Institute of TechnologyHarbinChina
  2. 2.Shenzhen PolytechnicShenzhenChina

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