Skip to main content
Log in

High-dimensional deterministic multiparty quantum secret sharing without unitary operations

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

A deterministic multiparty quantum secret sharing scheme is put forward, in which Bell states in high-dimensional Hilbert space are used. Only by preforming High-dimensional Bell measurements, all agents can recover the secret according to the dealer’s announcement when collaborating with each other. It shows that unitary operation for encoding deterministic secret is unnecessary in quantum communication. The security of the transmission of the high-dimensional Bell states can be ensured by randomly using one of the two mutually unbiased bases for eavesdropping checking, and thus by which the proposed quantum secret sharing scheme is secure against usual attacks. In addition, the proposed scheme has three advantages: generality, high resource capacity and high security.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Blakley, G.R.: Safeguarding cryptographic keys. In: Proceedings of the National Computer Conference, New York, pp. 313–317 (1979)

  2. Shamir A.: How to share a secret. Commun. ACM 22(11), 612–613 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  3. 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. Bangalore, India, pp. 175–179 (1984)

  4. Hillery M., Buzek V., Berthiaume A.: Quantum secret sharing. Phys. Rev. A 59(3), 1829–1834 (1999)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  5. Cleve R., Gottesman D., Lo H.K.: How to share a quantum secret. Phys. Rev. Lett. 83(3), 648–651 (1999)

    Article  ADS  Google Scholar 

  6. Deng F.G., Zhou H.Y., Long G.L.: Circular quantum secret sharing. J. Phys. A Math. Gen. 39(45), 14089–14099 (2006)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  7. Gordon G., Rigolin G.: Generalized quantum-state sharing. Phys. Rev. A 73(6), 062316 (2006)

    Article  ADS  Google Scholar 

  8. Takesue H., Inoue K.: Quantum secret sharing based on modulated high-dimensional time-bin entanglement. Phys. Rev. A 74(1), 012315 (2006)

    Article  ADS  Google Scholar 

  9. Zheng S.B.: Splitting quantum information via W states. Phys. Rev. A 74(5), 054303 (2006)

    Article  ADS  Google Scholar 

  10. Gaertner S., Kurtsiefer C., Bourennane M. et al.: Experimental demonstration of four-party quantum secret sharing. Phys. Rev. Lett. 98(2), 020503 (2007)

    Article  ADS  Google Scholar 

  11. Bogdanski J., Rafiei N., Bourennane M.: Experimental quantum secret sharing using telecommunication fiber. Phys. Rev. A 78(6), 062307 (2008)

    Article  ADS  Google Scholar 

  12. Markham D., Sanders B.C.: Graph states for quantum secret sharing. Phys. Rev. A 78(4), 042309 (2008)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  13. Muralidharan S., Panigrahi P.K.: Quantum-information splitting using multipartite cluster states. Phys. Rev. A 78(6), 062333 (2008)

    Article  ADS  Google Scholar 

  14. Yu I.C., Lin F.L., Huang C.Y.: Quantum secret sharing with multilevel mutually (un)biased bases. Phys. Rev. A 78(1), 012344 (2008)

    Article  ADS  Google Scholar 

  15. Choudhury S., Muralidharan S., Panigrahi P.K.: Quantum teleportation and state sharing using a genuinely entangled six-qubit state. J. Phys. A Math. Theor. 42(11), 115303 (2009)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  16. He G.P., Wang Z.D.: Single qubit quantum secret sharing with improved security. Quantum Inf. Comput. 10(1-2), 28–40 (2010)

    MathSciNet  MATH  Google Scholar 

  17. Keet A., Fortescue B., Markham D. et al.: Quantum secret sharing with qudit graph states. Phys. Rev. A 82(6), 062315 (2010)

    Article  ADS  Google Scholar 

  18. Li Q., Chan W.H., Long D.Y.: Semiquantum secret sharing using entangled states. Phys. Rev. A 82(2), 022303 (2010)

    Article  ADS  Google Scholar 

  19. Sarvepalli P., Raussendorf R.: Matroids and quantum-secret-sharing schemes. Phys. Rev. A 81(5), 052333 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  20. Shi R.H., Huang L.S., Yang W. et al.: Asymmetric multi-party quantum state sharing of an arbitrary m-qubit state. Quantum Inf. Process. 10(1), 53–61 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  21. Li Q., Long D.Y., Chan W.H. et al.: Sharing a quantum secret without a trusted party. Quantum Inf. Process. 10(1), 97–106 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  22. Shi R.H., Huang L.S., Yang W. et al.: Multi-party quantum state sharing of an arbitrary two-qubit state with Bell states. Quantum Inf. Process. 10(2), 231–239 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  23. Nie Y.Y., Li Y.H., Liu J.C. et al.: Quantum information splitting of an arbitrary three-qubit state by using two four-qubit cluster states. Quantum Inf. Process. 10(3), 297–305 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  24. Hou K., Liu G.H., Zhang X.Y. et al.: An efficient scheme for five-party quantum state sharing of an arbitrary m-qubit state using multiqubit cluster states. Quantum Inf. Process. 10(4), 463–473 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  25. Nie Y.Y., Li Y.H., Liu J.C. et al.: Quantum state sharing of an arbitrary four-qubit GHZ-type state by using a four-qubit cluster state. Quantum Inf. Process. 10(5), 603–608 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  26. Nie, Y.Y., Li, Y.H., Liu, J.C., et al.: Quantum information splitting of an arbitrary three-qubit state by using a genuinely entangled five-qubit state and a Bell-state. Quantum Inf. Process. doi:10.1007/s11128-011-0264-8

  27. Saha, D., Panigrahi, P.K.: N-qubit quantum teleportation, information splitting and superdense coding through the composite GHZCBell channel. Quantum Inf. Process. doi:10.1007/s11128-011-0270-x

  28. Shi, R.H., Zhong, H.: Multiparty quantum secret sharing with the pure entangled two-photon states. Quantum Inf. Process. doi:10.1007/s11128-011-0239-9

  29. Zhang Z.J., Man Z.X.: Multiparty quantum secret sharing of classical messages based on entanglement swapping. Phys. Rev. A 72(2), 022303 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  30. Shi R.H., Huang L.S., Yang W. et al.: Multiparty quantum secret sharing with Bell states and Bell measurements. Opt. Commun. 283(11), 2476–2480 (2010)

    Article  ADS  Google Scholar 

  31. Lin S., Gao F., Guo F.Z. et al.: Comment on “Multiparty quantum secret sharing of classical messages based on entanglement swapping”. Phys. Rev. A 76(3), 036301 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  32. Wang S.H., Chong S.K., Hwang T.: On “multiparty quantum secret sharing with Bell states and Bell measurements”. Opt. Commun. 283(21), 4405–4407 (2010)

    Article  ADS  Google Scholar 

  33. Wang T.Y., Wen Q.Y., Zhu F.C.: Cryptanalysis of multiparty quantum secret sharing with Bell states and Bell measurements. Opt. Commun. 284(6), 1711–1713 (2011)

    Article  ADS  Google Scholar 

  34. Zhang Z.J., Liu Y.M., Fang M. et al.: Multiparty quantum secret sharing scheme of classical messages by swapping qudit-state entanglement. Int. J. Mod. Phys. C 18(12), 1885–1901 (2007)

    Article  ADS  MATH  Google Scholar 

  35. Bennett C.H., Brassard G., Mermin N.D.: Quantum cryptography without Bell’s theorem. Phys. Rev. Lett. 68(5), 557–559 (1992)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  36. Wootters W.K., Fields B.D.: Optimal state-determination by mutually unbiased measurements. Ann. Phys. 191, 363–381 (1989)

    Article  ADS  MathSciNet  Google Scholar 

  37. Pittenger A.O., Rubin M.H.: Mutually unbiased bases, generalized spin matrices and separability. Linear Algebra Appl. 390, 255–278 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  38. Liu, Z.H., Chen, H.W., Liu, W.J., et al.: Deterministic secure quantum communication without unitary operation based on high-dimensional entanglement swapping. Sci. China F-Info. Sci. doi:10.1007/s11432-011-4371-z

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Zhi-Hao Liu.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Liu, ZH., Chen, HW., Xu, J. et al. High-dimensional deterministic multiparty quantum secret sharing without unitary operations. Quantum Inf Process 11, 1785–1795 (2012). https://doi.org/10.1007/s11128-011-0333-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11128-011-0333-z

Keywords

Navigation