International Journal of Theoretical Physics

, Volume 57, Issue 9, pp 2775–2786 | Cite as

A Hierarchical Modulation Coherent Communication Scheme for Simultaneous Four-State Continuous-Variable Quantum Key Distribution and Classical Communication

  • Can Yang
  • Cheng Ma
  • Linxi Hu
  • Guangqiang HeEmail author


We present a hierarchical modulation coherent communication protocol, which simultaneously achieves classical optical communication and continuous-variable quantum key distribution. Our hierarchical modulation scheme consists of a quadrature phase-shifting keying modulation for classical communication and a four-state discrete modulation for continuous-variable quantum key distribution. The simulation results based on practical parameters show that it is feasible to transmit both quantum information and classical information on a single carrier. We obtained a secure key rate of \(10^{-3}\) bits/pulse to \(10^{-1}\) bits/pulse within 40 kilometers, and in the meantime the maximum bit error rate for classical information is about \(10^{-7}\). Because continuous-variable quantum key distribution protocol is compatible with standard telecommunication technology, we think our hierarchical modulation scheme can be used to upgrade the digital communication systems to extend system function in the future.


Quantum key distribution Hierarchical modulation Simultaneous transmission Coherent state 



We would like to thank anyone who made suggestions for this paper. We also acknowledge support from the National Natural Science Foundation of China(Grants No.61475099 and No.61102053), Program of State Key Laboratory of Quantum Optics and Quantum Optics Devices (KF201405), Open Fund of IPOC(BUPT) (IPOC2015B004) and Program of State Key Information Security (2016-MS-05).


  1. 1.
    Lo, H.-K., Curty, M., Tamaki, K.: Nat. Photonics 8, 595 (2014)ADSCrossRefGoogle Scholar
  2. 2.
    Ekert, A.K.: Phys. Rev. Lett. 67, 661 (1991)ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    Diamanti, E., Leverrier, A.: Entropy 17, 6072 (2015)ADSMathSciNetCrossRefGoogle Scholar
  4. 4.
    Grosshans, F., Assche, G.V., Wenger, J., Brouri, R., Cerf, N.J., Grangier, P.: Nature 421, 238 (2003)ADSCrossRefGoogle Scholar
  5. 5.
    Ralph, T.C.: Phys. Rev. A 61, 010303 (1999)CrossRefGoogle Scholar
  6. 6.
    García-Patrón, R., Cerf, N.J.: Phys. Rev. Lett. 97, 190503 (2006)ADSCrossRefGoogle Scholar
  7. 7.
    Renner, R., Cirac, J.I.: Phys. Rev. Lett. 102, 110504 (2009)ADSCrossRefGoogle Scholar
  8. 8.
    Leverrier, A.: Phys. Rev. Lett. 114, 070501 (2015)ADSCrossRefGoogle Scholar
  9. 9.
    Leverrier, A., Alléaume, R., Boutros, J., Zémor, G., Grangier, P.: Phys. Rev. A 77, 042325 (2008)ADSCrossRefGoogle Scholar
  10. 10.
    Leverrier, A., Grangier, P.: Phys. Rev. Lett. 102, 180504 (2009)ADSCrossRefGoogle Scholar
  11. 11.
    Braunstein, S.L., Loock, P.: Rev. Mod. Phys. 77, 513 (2005)ADSCrossRefGoogle Scholar
  12. 12.
    Kumar, R., Qin, H., Alléaume, R.: New J. Phys. 17, 043027 (2015)ADSCrossRefGoogle Scholar
  13. 13.
    Qi, B.: Phys. Rev. A 94, 042340 (2016)ADSCrossRefGoogle Scholar
  14. 14.
    Maurer, U.M.: IEEE Trans. Inf. Theory 39, 733 (1993)CrossRefGoogle Scholar
  15. 15.
    Bennett, C.H., Brassard, G., Crépeau, C., Maurer, U.M.: IEEE Trans. Inf. Theory 41, 1915 (1995)CrossRefGoogle Scholar
  16. 16.
    Kunz-Jacques, S., Jouguet, P.: Phys. Rev. A 91, 022307 (2015)ADSCrossRefGoogle Scholar
  17. 17.
    Jiang, H., Wilford, P.A.: IEEE Trans. Broadcast. 51, 223 (2005)CrossRefGoogle Scholar
  18. 18.
    Vitthaladevuni, P.K., Alouini, M.S.: IEEE Trans. Broadcast. 47, 228 (2001)CrossRefGoogle Scholar
  19. 19.
    Navascués, M., Grosshans, F., Acín, A.: Phys. Rev. Lett. 97, 190502 (2006)ADSCrossRefGoogle Scholar
  20. 20.
    Wolf, M.M., Giedke, G., Cirac, J.I.: Phys. Rev. Lett. 96, 080502 (2006)ADSMathSciNetCrossRefGoogle Scholar
  21. 21.
    Lodewyck, J., Bloch, M., García-Patrón, R., Fossier, S., Karpov, E., Diamanti, E., Debuisschert, T., Cerf, N.J., Tualle-Brouri, R., McLaughlin, S.W., Grangier, P.: Phys. Rev. A 76, 042305 (2007)ADSCrossRefGoogle Scholar
  22. 22.
    Leverrier, A., Grangier, P.: Phys. Rev. A 83, 042312 (2011)ADSCrossRefGoogle Scholar
  23. 23.
    Devetak, I., Winter, A.: Proc. R. Soc. A 461, 207 (2005)ADSCrossRefGoogle Scholar
  24. 24.
    Cover, T.M., Thomas, J.A.: Elements of Information Theory. Wiley (2006)Google Scholar
  25. 25.
    Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press (2000)Google Scholar
  26. 26.
    Zhang, H., Fang, J., He, G.: Phys. Rev. A 86, 022338 (2012)ADSCrossRefGoogle Scholar
  27. 27.
    Fossier, S., Diamanti, E., Debuisschert, T., Tuallebrouri, R., Grangier, P.: J. Phys. B 42, 114014 (2009)ADSCrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.State Key Laboratory of Advanced Optical Communication Systems and Networks, Department of Electronic EngineeringShanghai Jiao Tong UniversityShanghaiChina

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