Sequential quantum secret sharing in noisy environments

Abstract

Sequential quantum secret sharing (QSS) schemes do not use entangled states for secret sharing, rather they rely on sequential operations of the players on a single state which is circulated between the players. In order to check the viability of these schemes under imperfect operations and noise in the channels, we consider one such scheme in detail and show that under moderate conditions it is still possible to extract viable secure shared keys in this scheme. Although we specifically consider only one type of sequential scheme and three different noise models, our method is fairly general to be applied to other QSS schemes and noise models as well.

This is a preview of subscription content, log in to check access.

Fig. 1

References

  1. 1.

    Bennett, C.H., Brassard, G.: Quantum cryptography: public keydistribution and coin tossing. In: Proceedings of IEEEInternational Conference on Computers, Systems and SignalProcessing, vol. 175, pp. 8. New York (1984)

  2. 2.

    Ekert, A.: Quantum cryptography based on Bell’s theorem. Phys. Rev. Lett. 67, 661–663 (1991)

    ADS  MathSciNet  Article  Google Scholar 

  3. 3.

    Hillery, M., Buzek, V., Berthiaume, A.: Quantum secret sharing. Phys. Rev. A 59, 1829 (1999)

    ADS  MathSciNet  Article  Google Scholar 

  4. 4.

    De Sen, A., Sen, U., Zukowski, M.: Multiqubit W states lead to stronger nonclassicality than Greenberger–Horne–Zeilinger states. Phys. Rev. A 68, 032309 (2003)

    ADS  MathSciNet  Article  Google Scholar 

  5. 5.

    Xiao, L., Long, G.L., Deng, F.-G., Pan, J.-W.: Efficient multiparty quantum-secret-sharing schemes. Phys. Rev. A 59, 1829 (1999)

    MathSciNet  Article  Google Scholar 

  6. 6.

    Karlsson, A., Koashi, M., Imoto, N.: Quantum entanglement for secret sharing and secret splitting. Phys. Rev. A 59, 162 (1999)

    ADS  Article  Google Scholar 

  7. 7.

    Xiao, L., Lu Long, G., Deng, F.-G., Pan, J.-W.: Efficient multiparty quantum-secret-sharing schemes. Phys. Rev. A 69, 052307 (2004)

    ADS  Article  Google Scholar 

  8. 8.

    Zhang, Z-j, Man, Z-x: Multiparty quantum secret sharing of classical messages based on entanglement swapping. Phys. Rev. A 72, 022303 (2005)

    ADS  MathSciNet  Article  Google Scholar 

  9. 9.

    Deng, F.-G., Long, G.L., Zhou, H.-Y.: Probabilistic teleportation of an arbitrary GHZ-class state with a pure entangled two-particle quantum channel and its application in quantum state sharing. Phys. Lett. A 340, 43 (2005)

    ADS  Article  Google Scholar 

  10. 10.

    Bagherinezhad, S., Karimipour, V.: Quantum secret sharing based on reusable Greenberger–Horne–Zeilinger states as secure carriers. Phys. Rev. A 67, 044302 (2003)

    ADS  Article  Google Scholar 

  11. 11.

    Chen, Y.-A., et al.: Experimental quantum secret sharing and third-man quantum cryptography. Phys. Rev. Lett. 95, 200502 (2005)

    ADS  Article  Google Scholar 

  12. 12.

    Gaertner, S., Kurtsiefer, C., Bourennane, M., Weinfurter, H.: Experimental demonstration of four-party quantum secret sharing. Phys. Rev. Lett. 98, 020503 (2007)

    ADS  Article  Google Scholar 

  13. 13.

    Tyc, T., Sanders, B.C.: How to share a continuous-variable quantum secret by optical interferometry. Phys. Rev. A 65, 042310 (2002)

    ADS  Article  Google Scholar 

  14. 14.

    Lance, A.M., Symul, T., Bowen, W.P., Tyc, T., Sanders, B.C., Lam, P.K.: Continuous variable (2,3) threshold quantum secret sharing schemes. New J. Phys. 5, 4 (2003)

    ADS  MathSciNet  Article  Google Scholar 

  15. 15.

    Lance, A.M., Symul, T., Bowen, W.P., Sanders, B.C., Lam, P.K.: Tripartite quantum state sharing. Phys. Rev. Lett. 92, 177903 (2004)

    ADS  Article  Google Scholar 

  16. 16.

    Grosshans, F., Van Assche, G., Wenger, J., Brouri, R., Cerf, N.J., Grangiera, P.: Quantum key distribution using gaussian-modulated coherent states. Nature 421, 238–241 (2003)

    ADS  Article  Google Scholar 

  17. 17.

    Grosshans, F., Grangier, P.: Continuous variable quantum cryptography using coherent states. Phys. Rev. Lett. 88, 057902 (2002)

    ADS  Article  Google Scholar 

  18. 18.

    Schmid, C., Trojek, P., Bourennane, M., Kurtsiefer, C., Zukowski, M., Weinfurter, H.: Single qubit quantum secret sharing. Phys. Rev. Lett. 95, 230505 (2005)

    ADS  Article  Google Scholar 

  19. 19.

    Yan, F.-L., Gao, T.: Quantum secret sharing between multiparty and multiparty without entanglement. Phys. Rev. A 72, 012304 (2005)

    ADS  Article  Google Scholar 

  20. 20.

    He, G.-P.: Secret sharing without monitoring signal disturbance. Phys. Rev. Lett. 98, 028901 (2007)

    ADS  Article  Google Scholar 

  21. 21.

    Karimipour, V., Asoudeh, M.: Quantum secret sharing and random hopping; using single states instead of entanglement. Phys. Rev. A 92, 030301 (2015). (Rapid Communications)

    ADS  MathSciNet  Article  Google Scholar 

  22. 22.

    Tavakoli, A., Herbauts, I., Zukowski, M., Bourennane, M.: Sequential quantum secret sharing in noisy environments (preprint). arXiv:1501.05582

  23. 23.

    Chen, K., Lo, H.-K.: Multi-partite quantum cryptographic protocols with noisy GHZ states. Quantum Inf. Comput. 7, 689 (2007)

    MathSciNet  MATH  Google Scholar 

  24. 24.

    Kogias, I., Xiang, Y., He, Q., Adesso, G.: Unconditional security of entanglement-based continuous-variable quantum secret sharing. Phys. Rev. A 95, 012315 (2017)

    ADS  Article  Google Scholar 

  25. 25.

    Ray, M., Chatterjee, S., Chakrabarty, I.: Sequential quantum secret sharing in a noisy environment aided with weak measurements. Phys. J. D 70, 114 (2016)

    ADS  Google Scholar 

  26. 26.

    Adhikari, S., Chakrabarty, I., Agrawal, P.: Probabilistic secret sharing through noisy quantum channels. Quantum Inf. Comput. 12, 0253 (2012)

    MathSciNet  MATH  Google Scholar 

  27. 27.

    Bohmann, M., Sperling, J., Vogel, W.: Entanglement and phase properties of noisy NOON states. Phys. Rev. A 91, 042332 (2015)

    ADS  Article  Google Scholar 

  28. 28.

    Bohmann, M., Sperling, J., Vogel, W.: Entanglement verification ofnoisy NOON states. Phys. Rev. A 96, 012321 (2017)

    ADS  Article  Google Scholar 

  29. 29.

    Zhang, Z-j, Li, Y., Man, Z-x: Multiparty quantum secret sharing. Phys. Rev. A 71, 044301 (2005)

    ADS  MathSciNet  Article  Google Scholar 

  30. 30.

    Zhu, X., Fan, Z.: Secure direct communication based on secret transmitting order of particles. Phys. Rev. A 73, 022338 (2006)

    ADS  Article  Google Scholar 

  31. 31.

    Deng, F.-G., Li, X.-H., Zhou, H.-Y., Zhang, Z-j: Improving the security of multiparty quantum secret sharing against Trojan horse attack. Phys. Rev. A 72, 044302 (2005)

    ADS  Article  Google Scholar 

  32. 32.

    Li, X.-H., Deng, F.-G., Zhou, H.-Y.: Improving the security of secure direct communication based on the secret transmitting order of particles. Phys. Rev. A 74, 054302 (2006)

    ADS  Article  Google Scholar 

  33. 33.

    Schmid, C., et al.: Reply to comment on experimental single qubit quantum secret sharing. Phys. Rev. Lett. 98, 028902 (2007)

    ADS  Article  Google Scholar 

  34. 34.

    He, G.P., Wang, Z.D.: Single qubit quantum secret sharing with improved security. Quantum Inf. Comput. 10, 28 (2010)

    MathSciNet  MATH  Google Scholar 

  35. 35.

    Lance, A.M., Symul, T., Bowen, W.P., Tyc, T., Sanders, B.C., Lam, P.K.: Continuous variable (2, 3) threshold quantum secret sharing schemes. New J. Phys. 5, 4 (2003)

    ADS  MathSciNet  Article  Google Scholar 

  36. 36.

    Markham, D., Sanders, B.C.: Graph states for quantum secret sharing. Phys. Rev. A 78, 042309 (2008)

    ADS  MathSciNet  Article  Google Scholar 

  37. 37.

    Lau, H.-K., Weedbrook, C.: Quantum secret sharing with continuous-variable cluster states. Phys. Rev. A 88, 042313 (2013)

    ADS  Article  Google Scholar 

  38. 38.

    Wu, Y., Cai, R., He, G., Zhang, J.: Quantum secret sharing with continuous variable graph state. Quantum Inf. Proc. 13, 1085 (2014)

    ADS  MathSciNet  Article  Google Scholar 

Download references

Acknowledgements

This work was financially supported by the Grant no. 96011347 from Iran National Science Foundation (INSF). M. A. would like to thank Abdus Salam International Center for Theoretical Physics (ICTP), where part of this research was carried out. She also thanked V. Karimipour for many discussions and Fabio Benatti for his valuable comments.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Marzieh Asoudeh.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Khakbiz, P., Asoudeh, M. Sequential quantum secret sharing in noisy environments. Quantum Inf Process 18, 11 (2019). https://doi.org/10.1007/s11128-018-2123-3

Download citation

Keywords

  • Quantum secret sharing
  • Noise
  • Sequential