Three-party quantum secret sharing against collective noise

  • Yu-Guang YangEmail author
  • Shang Gao
  • Dan Li
  • Yi-Hua Zhou
  • Wei-Min Shi


In this paper, based on logical GHZ states and logical χ-states, we present four three-party quantum secret sharing protocols immune to the collective-dephasing noise and the collective-rotation noise, respectively. They make full use of the measurement correlation property of multi-particle entangled states and local unitary operations. Compared with existing three-party quantum secret sharing protocols against collective noise, our protocols are the most efficient. Furthermore, these protocols are congenitally free from the Trojan horse attacks.


Quantum cryptography Quantum secret sharing Collective noise Qubit efficiency 



This work was supported by the National Natural Science Foundation of China (Grant Nos. 61572053, 61671087, U1636106, 61602019, 61571226, 61701229, 61702367); Beijing Natural Science Foundation (Grant No. 4182006); Natural Science Foundation of Jiangsu Province, China (Grant No. BK20170802); Jiangsu Postdoctoral Science Foundation; Guangxi Key Laboratory of Cryptography and Information Security.


  1. 1.
    Bennett, C. H., Brassard, G.: Quantum cryptography: public-key distribution and coin tossing. In: Proceedings of the IEEE International Conference on Computers, Systems and Signal Processing. New York: IEEE, pp. 175–179 (1984)Google Scholar
  2. 2.
    Ekert, A.: Quantum cryptography based on Bell’s theorem. Phys. Rev. Lett. 67, 661–664 (1991)ADSMathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Bennett, C.H.: Quantum cryptography using any two nonorthogonal states. Phys. Rev. Lett. 68, 3121–3124 (1992)ADSMathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Boström, K., Felbinger, T.: Deterministic secure direct communication using entanglement. Phys. Rev. Lett. 89, 187902 (2002)ADSCrossRefGoogle Scholar
  5. 5.
    Deng, F.G., Long, G.L., Liu, X.S.: Two-step quantum direct communication protocol using the Einstein-Podolsky-Rosen pair block. Phys. Rev. A 68, 042317 (2003)ADSCrossRefGoogle Scholar
  6. 6.
    Dušek, M., Haderka, O., Hendrych, M., Myska, R.: Quantum identification system. Phys. Rev. A 60, 149–156 (1999)ADSCrossRefGoogle Scholar
  7. 7.
    Yang, Y.G., Wen, Q.Y.: An efficient two-party quantum private comparison protocol with decoy photons and two-photon entanglement. J. Phys. A: Math. Theor. 42(5), 055305 (2009)ADSMathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Yang, Y.G., Cao, W.F., Wen, Q.Y.: Secure quantum private comparison. Phys. Scr. 80(6), 065002 (2009)ADSzbMATHCrossRefGoogle Scholar
  9. 9.
    Chen, X.B., Xu, G., Niu, X.X., Wen, Q.Y., Yang, Y.X.: An efficient protocol for the private comparison of equal information based on the triplet entangled state and single particle measurement. Opt. Commun. 283(7), 1561–1565 (2010)ADSCrossRefGoogle Scholar
  10. 10.
    Yang, Y.-G., Liu, Z.-C., Li, J., Chen, X.-B., Zuo, H.-J., Zhou, Y.-H., Shi, W.-M.: Theoretically extensible quantum digital signature with starlike cluster states. Quantum Inf. Process. 16(1), 1–15 (2017)zbMATHCrossRefGoogle Scholar
  11. 11.
    Yang, Y.-G., Lei, H., Liu, Z.-C., Zhou, Y.-H., Shi, W.-M.: Arbitrated quantum signature scheme based on cluster states. Quantum Inf. Process. 15(6), 2487–2497 (2016)ADSMathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Gao, F., Liu, B., Huang, W., Wen, Q.Y.: Postprocessing of the oblivious key in quantum private query. IEEE. J. Sel. Top. Quant. 21, 6600111 (2015)CrossRefGoogle Scholar
  13. 13.
    Wei, C.Y., Wang, T.Y., Gao, F.: Practical quantum private query with better performance in resisting joint-measurement attack. Phys. Rev. A 93, 042318 (2016)ADSCrossRefGoogle Scholar
  14. 14.
    Yang, Y.-G., Liu, Z.-C., Chen, X.-B., Zhou, Y.-H., Shi, W.-M.: Robust QKD-based private database queries based on alternative sequences of single-qubit measurements. Sci. Chin. Phys. Mech. Astron. 60(12), 120311 (2017)ADSCrossRefGoogle Scholar
  15. 15.
    Yang, Y.-G., Liu, Z.-C., Li, J., Chen, X.-B., Zuo, H.-J., Zhou, Y.-H., Shi, W.-M.: Quantum private query with perfect user privacy against a joint-measurement attack. Phys. Lett. A 380(48), 4033–4038 (2016)ADSzbMATHCrossRefGoogle Scholar
  16. 16.
    Yang, Y.-G., Liu, Z.C., Chen, X.B., Cao, W.F., Zhou, Y.H., Shi, W.M.: Novel classical post-processing for quantum key distribution-based quantum private query. Quantum Inf. Process. 15, 3833–3840 (2016)ADSMathSciNetzbMATHCrossRefGoogle Scholar
  17. 17.
    Gao, F., Liu, B., Wen, Q.-Y.: Flexible quantum private queries based on quantum key distribution. Opt. Exp. 20, 17411–17420 (2012)ADSCrossRefGoogle Scholar
  18. 18.
    Yang, Y.-G., Sun, S.-J., Xu, P., Tian, J.: Flexible protocol for quantum private query based on B92 protocol. Quantum Inf. Process. 13, 805–813 (2014)ADSMathSciNetCrossRefGoogle Scholar
  19. 19.
    Gao, F., Qin, S.J., Huang, W., Wen, Q.Y.: Quantum private query: a new kind of practical quantum cryptographic protocols. Sci. China-Phys. Mech. Astron. 62, 070301 (2019)CrossRefGoogle Scholar
  20. 20.
    Yang, Y.-G., Guo, X.-P., Xu, G., Chen, X.-B., Li, J., Zhou, Y.-H., Shi, W.-M.: Reducing the communication complexity of quantum private database queries by subtle classical post-processing with relaxed quantum ability. Computers & Security 81, 15–24 (2019)CrossRefGoogle Scholar
  21. 21.
    Hillery, M., Bužek, V., Berthiaume, A.: Quantum secret sharing. Phys. Rev. A 59, 1829–1834 (1999)ADSMathSciNetzbMATHCrossRefGoogle Scholar
  22. 22.
    Karlsson, A., Koashi, M., Imoto, N.: Quantum entanglement for secret sharing and secret splitting. Phys. Rev. A 59, 162–168 (1999)ADSCrossRefGoogle Scholar
  23. 23.
    Guo, G.P., Guo, G.C.: Quantum secret sharing without entanglement. Phys. Rev. A 310, 247–251 (2003)MathSciNetzbMATHGoogle Scholar
  24. 24.
    Xiao, L., Long, G.L., Deng, F.G., Pan, J.W.: Efficient multiparty quantum-secret-sharing schemes. Phys. Rev. A 69, 052307 (2004)ADSCrossRefGoogle Scholar
  25. 25.
    Zhang, Z., Liu, W., Li, C.: Quantum secret sharing based on quantum error-correcting codes. Chin. Phys. B 20(5), 050309 (2011)ADSCrossRefGoogle Scholar
  26. 26.
    Jia, H.Y., Wen, Q.Y., Gao, F., Qin, S.J., Guo, F.Z.: Dynamic quantum secret sharing. Phys. Lett. A 376, 1035–1041 (2012)ADSMathSciNetzbMATHCrossRefGoogle Scholar
  27. 27.
    Cleve, R., Gottesman, D., Lo, H.-K.: How to share a quantum secret. Phys. Rev. Lett. 83, 648 (1999)ADSCrossRefGoogle Scholar
  28. 28.
    Gottesman, D.: Theory of quantum secret sharing. Phys. Rev. A 61, 042311 (2000)ADSMathSciNetCrossRefGoogle Scholar
  29. 29.
    Lance, A.M., Symul, T., Bowen, W.P., Sanders, B.C., Lam, P.K.: Tripartite quantum state sharing. Phys. Rev. Lett. 92, 177903 (2004)ADSCrossRefGoogle Scholar
  30. 30.
    Yang, C.P., Chu, S.I., Han, S.: Efficient many-party controlled teleportation of multiqubit quantum information via entanglement. Phys. Rev. A 70, 022329 (2004)ADSCrossRefGoogle Scholar
  31. 31.
    Ray, M., Chatterjee, S., Chakrabarty, I.: Sequential quantum secret sharing in a noisy environment aided with weak measurements. Eur. Phys. J. D 70, 1–11 (2016)CrossRefGoogle Scholar
  32. 32.
    Yang, Y.-G., Xia, J., Jia, X., Shi, L., Zhang, H.: Economical five-party quantum state sharing of an arbitrary m-atom with five-atom cluster state in cavity QED. Eur. Phys. J. D 67(3), 59–61 (2013)ADSCrossRefGoogle Scholar
  33. 33.
    Gordon, G., Rigolin, G.: Generalized quantum-state sharing. Phys. Rev. A 73, 062316 (2006)ADSCrossRefGoogle Scholar
  34. 34.
    Bai, C.M., Li, Z.H., Xu, T.T., Li, Y.M.: A generalized information theoretical model for quantum secret sharing. Int. J. Theor. Phys. 55, 4972–4986 (2016)zbMATHCrossRefGoogle Scholar
  35. 35.
    Karimipour, V., Asoudeh, M.: Quantum secret sharing and random hopping: using single states instead of entanglement. Phys. Rev. A 92, 030301(R) (2015)ADSMathSciNetCrossRefGoogle Scholar
  36. 36.
    Gheorghiu, V., Sanders, B.C.: Accessing quantum secrets via local operations and classical communication. Phys. Rev. A 88(2), 022340 (2013)ADSCrossRefGoogle Scholar
  37. 37.
    Tavakoli, A., Herbauts, I., Zukowski, M., Bourennane, M.: Secret sharing with a single d-level quantum system. Phys. Rev. A 92, 030302(R) (2015)ADSCrossRefGoogle Scholar
  38. 38.
    Maitra, A., De, S.J., Paul, G., Pal, A.K.: Proposal for quantum rational secret sharing. Phys. Rev. A 92, 022305 (2015)ADSCrossRefGoogle Scholar
  39. 39.
    Rahaman, R., Parker, M.G.: Quantum scheme for secret sharing based on local distinguishability. Phys. Rev. A 91, 022330 (2015)ADSCrossRefGoogle Scholar
  40. 40.
    Wang, J., Li, L., Peng, H., Yang, Y.: Quantum-secret-sharing scheme based on local distinguishability of orthogonal multiqudit entangled states. Phys. Rev. A 95(2), 022320 (2017)ADSCrossRefGoogle Scholar
  41. 41.
    Zanardi, P., Rasetti, M.: Noiseless quantum codes. Phys. Rev. Lett. 79(17), 3306 (1997)ADSCrossRefGoogle Scholar
  42. 42.
    Kwiat, P.G., Berglund, A.J., Altepeter, J.B., White, A.G.: Experimental verification of decoherence-free subspaces. Science (New York, N.Y.) 290(5491), pp. 498–501 (2000)ADSCrossRefGoogle Scholar
  43. 43.
    Gu, B., Mu, L., Ding, L., et al.: Fault tolerant three-party quantum secret sharing against collective noise. Opt. Commun. 283(15), 3099–3103 (2010)ADSCrossRefGoogle Scholar
  44. 44.
    Li, C.-Y., Li, Y.-S.: Fault-tolerate three-party quantum secret sharing over a collective-noise channel. Chin. Phys. Lett. 28, 020304 (2011)ADSCrossRefGoogle Scholar
  45. 45.
    Yang, Y.G., Teng, Y.W., Chai, H.P., Wen, Q.Y.: Fault-tolerant quantum secret sharing against collective noise. Phys. Scr. 83, 025003 (2011)ADSzbMATHCrossRefGoogle Scholar
  46. 46.
    Cai, Q.Y.: Eavesdropping on the two-way quantum communication protocols with invisible photons. Phys. Lett. A 351, 23–25 (2006)ADSzbMATHCrossRefGoogle Scholar
  47. 47.
    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)ADSCrossRefGoogle Scholar
  48. 48.
    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)ADSCrossRefGoogle Scholar
  49. 49.
    Cabello, A.: Quantum key distribution in the Holevo limit. Phys. Rev. Lett. 85, 5635–5638 (2000)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Yu-Guang Yang
    • 1
    • 2
    • 3
    Email author
  • Shang Gao
    • 1
    • 3
  • Dan Li
    • 2
    • 3
  • Yi-Hua Zhou
    • 1
    • 3
  • Wei-Min Shi
    • 1
    • 3
  1. 1.Faculty of Information TechnologyBeijing University of TechnologyBeijingChina
  2. 2.Beijing Key Laboratory of Trusted ComputingBeijingChina
  3. 3.College of Computer Science and TechnologyNanjing University of Aeronautics and AstronauticsNanjingChina

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