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Quantum secret sharing using orthogonal multiqudit entangled states

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Abstract

In this work, we investigate the distinguishability of orthogonal multiqudit entangled states under restricted local operations and classical communication. According to these properties, we propose a quantum secret sharing scheme to realize three types of access structures, i.e., the (n, n)-threshold, the restricted (3, n)-threshold and restricted (4, n)-threshold schemes (called LOCC-QSS scheme). All cooperating players in the restricted threshold schemes are from two disjoint groups. In the proposed protocol, the participants use the computational basis measurement and classical communication to distinguish between those orthogonal states and reconstruct the original secret. Furthermore, we also analyze the security of our scheme in four primary quantum attacks and give a simple encoding method in order to better prevent the participant conspiracy attack.

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References

  1. Shamir, A.: How to share a secret. Commun. ACM 22(11), 612 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  2. Blakley, G.R. In: Proceedings of the National Computer Conference (AFIPS, 1979), pp. 313–317 (1979)

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

    Article  ADS  MathSciNet  MATH  Google Scholar 

  4. Cleve, R., Gottesman, D., Lo, H.-K.: How to share a quantum secret. Phys. Rev. Lett. 83, 648 (1999)

    Article  ADS  Google Scholar 

  5. Gottesman, D.: Theory of quantum secret sharing. Phys. Rev. A 61, 042311 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  6. Deng, F.G., Zhou, H.Y., Long, G.L.: Circular quantum secret sharing. J. Phys. A Math. Gen. 39, 14089–14099 (2006)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  7. Zukowski, M., Zeilinger, A., Horne, M.A., et al.: Quest for GHZ states. Acta Phys. Pol. A 93, 187 (1998)

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  10. Zhang, Z., Liu, W., Li, C.: Quantum secret sharing based on quantum error-correcting codes. Chin. Phys. B 20(5), 050309 (2011)

    Article  ADS  Google Scholar 

  11. Hsu, L.Y., Li, C.M.: Quantum secret sharing using product states. Phys. Rev. A 71, 022321 (2005)

    Article  ADS  Google Scholar 

  12. Deng, F.G., Long, G.L.: Secure direct communication with a quantum one-time pad. Phys. Rev. A 69(5), 052319 (2004)

    Article  ADS  Google Scholar 

  13. Hu, J.Y., Yu, B., Jing, M.Y., et al.: Experimental quantum secure direct communication with single photons. Light Sci. Appl. 5(9), 16144 (2016)

    Article  Google Scholar 

  14. Wei, K.J., Ma, H.Q., Yang, J.H.: Experimental circular quantum secret sharing over telecom fiber network. Opt. Express 21(4), 16663–16669 (2013)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  16. Deng, F.G., Li, X.H., Li, C.Y., Zhou, P., Zhou, H.Y.: Multiparty quantum-state sharing of an arbitrary two-particle state with Einstein–Podolsky–Rosen pairs. Phys. Rev. A 72, 044301 (2005)

    Article  ADS  Google Scholar 

  17. Cao, H., Ma, W.P.: \((t, n)\) Threshold quantum state sharing scheme based on linear equations and unitary operation. IEEE Photonics J. 9(1), 1–7 (2017)

    Article  MathSciNet  Google Scholar 

  18. Gordon, G., Rigolin, G.: Generalized quantum-state sharing. Phys. Rev. A 73, 062316 (2006)

    Article  ADS  Google Scholar 

  19. Qin, H.W., Zhu, X.H., Dai, Y.W.: \((t, n)\) Threshold quantum secret sharing using the phase shift operation. Q. Inf. Process 14, 2997–3004 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  20. 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)

    Article  MATH  Google Scholar 

  21. Maitra, A., De, S.J., Paul, G., Pal, A.K.: Proposal for quantum rational secret sharing. Phys. Rev. A 92, 022305 (2015)

    Article  ADS  Google Scholar 

  22. Sarvepalli, P., Raussendorf, R.: Matroids and quantum-secret-sharing schemes. Phys. Rev. A 81, 052333 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  23. Karimipour, V., Asoudeh, M.: Quantum secret sharing and random hopping: Using single states instead of entanglement. Phys. Rev. A 92, 030301(R) (2015)

    Article  ADS  MathSciNet  Google Scholar 

  24. Gheorghiu, V., Sanders, B.C.: Accessing quantum secrets via local operations and classical communication. Phys. Rev. A 88(2), 022340 (2013)

    Article  ADS  Google Scholar 

  25. Tavakoli, A., Herbauts, I., Zukowski, M., Bourennane, M.: Secret sharing with a single d-level quantum system. Phys. Rev. A 92, 030302(R) (2015)

    Article  ADS  Google Scholar 

  26. Heilmann, R., Gräfe, M., Nolte, S.: A novel integrated quantum circuit for high-order W-state generation and its highly precise characterization. Sci. Bull. 60(1), 96–100 (2015)

    Article  Google Scholar 

  27. Xu, J.S., Li, C.F.: Quantum integrated circuit: classical characterization. Sci. Bull. 60(1), 141–141 (2015)

    Article  Google Scholar 

  28. Du, F.F., Deng, F.G.: Heralded entanglement concentration for photon systems with linear-optical elements. Sci. China Phys. Mech. Astron. 58(4), 40303 (2015)

    Article  Google Scholar 

  29. Li, T., Yin, Z.Q.: Quantum superposition, entanglement, and state teleportation of a microorganism on an electromechanical oscillator. Sci. Bull. 61(2), 163–171 (2016)

    Article  MathSciNet  Google Scholar 

  30. Deng, F.G., Ren, B.C., Li, X.H.: Quantum hyperentanglement and its applications in quantum information processing. Sci. Bull. 62(1), 46–68 (2017)

    Article  Google Scholar 

  31. Wang, Z., Zhang, C., Huang, Y.F., et al.: Experimental verification of genuine multipartite entanglement without shared reference frames. Sci. Bull. 61(9), 714–719 (2016)

    Article  Google Scholar 

  32. Zhang, K.J., Zhang, L., Song, T.T., et al.: A potential application in quantum networks Deterministic quantum operation sharing schemes with Bell states. Sci. China Phys. Mech. Astron. 6(59), 660302 (2016)

    Article  Google Scholar 

  33. Liu, W.O., Peng, J.Y., Wang, C., et al.: Hybrid quantum private communication with continuous-variable and discrete-variable signals. Sci. China Phys. Mech. Astron. 58(2), 20301 (2015)

    Article  Google Scholar 

  34. Zheng, C., Long, G.F.: Quantum secure direct dialogue using Einstein–Podolsky–Rosen pairs. Sci. China Phys. Mech. Astron. 57(7), 1238 (2014)

    Article  ADS  Google Scholar 

  35. Rahaman, R., Parker, M.G.: Quantum scheme for secret sharing based on local distinguishability. Phys. Rev. A 91, 022330 (2015)

    Article  ADS  Google Scholar 

  36. Yang, Y.H., Gao, F., Wu, X., et al.: Quantum secret sharing via local operations and classical communication. Sci. Rep. 5, 16967 (2015)

    Article  ADS  Google Scholar 

  37. Bai, C.M., Li, Z.H., Xu, T.T., et al.: Quantum secret sharing using the d-dimensional GHZ state. Q. Inf. Process. 16, 59 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  38. Wang, J., Li, L., Peng, H.: Quantum-secret-sharing scheme based on local distinguishability of orthogonal multiqudit entangled states. Phys. Rev. A 95(2), 022320 (2017)

    Article  ADS  Google Scholar 

  39. Qin, H., Dai, Y.: Verifiable (t, n) threshold quantum secret sharing using d-dimensional Bell state. Inf. Process. Lett. 116(5), 351–355 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  40. Gisin, N., Ribordy, G., Tittel, W., Zbinden, H.: Quantum cryptography. Rev. Mod. Phys. 74(1), 145 (2002)

    Article  ADS  MATH  Google Scholar 

  41. Gisin, N., Fasel, S., Zbinden, H., Ribordy, G.: Trojan-horse attacks on quantum-keydistribution systems. Phys. Rev. A 73, 022320 (2006)

    Article  ADS  Google Scholar 

  42. Deng, F., Li, X., Zhou, H., Zhang, Z.: Improving the security of multiparty quantum secret sharing against Trojan horse attack. Phys. Rev. A 72(4), 044302 (2005)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  44. Lin, J., Yang, C.W., Hwang, T.: Quantum private comparison of equality protocol without a third party. Q. Inf. Process. 13(2), 239–247 (2014)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

We want to express our gratitude to anonymous referees for their valuable and constructive comments. This work was sponsored by the National Natural Science Foundation of China under Grant Nos. 61373150 and 61602291, and Industrial Research and Development Project of Science and Technology of Shaanxi Province under Grant No. 2013k0611.

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Authors and Affiliations

  1. College of Mathematics and Information Science, Shaanxi Normal University, Xi’an, 710119, China

    Chen-Ming Bai, Zhi-Hui Li & Cheng-Ji Liu

  2. College of Computer Science, Shaanxi Normal University, Xi’an, 710119, China

    Yong-Ming Li

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  1. Chen-Ming Bai
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  2. Zhi-Hui Li
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Correspondence to Zhi-Hui Li.

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Bai, CM., Li, ZH., Liu, CJ. et al. Quantum secret sharing using orthogonal multiqudit entangled states. Quantum Inf Process 16, 304 (2017). https://doi.org/10.1007/s11128-017-1739-z

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