Skip to main content
SpringerLink
Log in

Multi-dimensional quantum state sharing based on quantum Fourier transform

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

A scheme of multi-dimensional quantum state sharing is proposed. The dealer performs the quantum SUM gate and the quantum Fourier transform to encode a multi-dimensional quantum state into an entanglement state. Then the dealer distributes each participant a particle of the entanglement state, to share the quantum state among n participants. In the recovery, \(n-1\) participants measure their particles and supply their measurement results; the last participant performs the unitary operation on his particle according to these measurement results and can reconstruct the initial quantum state. The proposed scheme has two merits: It can share the multi-dimensional quantum state and it does not need the entanglement measurement.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  ADS  MathSciNet  MATH  Google Scholar 

  3. Li, Y.M., Zhang, K.S., Peng, K.C.: Multiparty secret sharing of quantum information based on entanglement swapping. Phys. Lett. A 324, 420–424 (2004)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  4. 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 

  5. Liu, J., Liu, Y.M., Zhang, Z.J.: Generalized multiparty quantum single-qutrit state sharing. Int. J. Theor. Phys. 47, 2353–2362 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  6. Zhang, Z.J., Yang, J., Man, Z.X., Li, Y.: Multiparty secret sharing of quantum information using and identifying Bell state. Eur. Phys. J. D 33, 133–136 (2005)

    Article  ADS  Google Scholar 

  7. Qin, H.W., Dai, Y.W.: Dynamic quantum secret sharing by using \(d\)-dimensional GHZ state. Quantum Inf. Process. 16, 1–13 (2017)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  10. Han, L.F., Liu, Y.M., Liu, J., Zhang, Z.J.: Multiparty quantum secret sharing of secure direct communication using single photons. Opt. Commun. 281, 2690–2694 (2008)

    Article  ADS  Google Scholar 

  11. Sarvepalli, P.K., Klappenecker, A.: Sharing classical secrets with Calderbank–Shor–Steane codes. Phys. Rev. A 80, 022321 (2009)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  12. Song, T.T., Zhang, J., Gao, F., Wen, Q.Y., Zhu, F.C.: Participant attack on quantum secret sharing based on entanglement swapping. Chin. Phys. B 18, 1333–1337 (2009)

    Article  ADS  Google Scholar 

  13. Gao, F., Qin, S.J., Wen, Q.Y., Zhu, F.C.: Cryptanalysis of multiparty controlled quantum secure direct communication using Greenberger–Horne–Zeilinger state. Opt. Commun. 382, 192–195 (2010)

    Article  ADS  Google Scholar 

  14. Guo, T.F., Qin, S.J., Gao, F., Wen, Q.Y., Zhu, F.C.: Participant attack on a kind of MQSS schemes based on entanglement swapping. Eur. Phys. J. D 56, 445–448 (2010)

    Article  ADS  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  16. Yang, Y.G., Jia, X., Wang, H.Y., Zhang, H.: Verifiable quantum \((k, n)\)-threshold secret sharing. Quantum Inf. Process. 11, 1619–1625 (2012)

    Article  ADS  MathSciNet  Google Scholar 

  17. Liu, L.L., Tsai, C.W., Hwang, T.: Quantum secret sharing using symmetric W state. Int. J. Theor. Phys. 51, 2291–2306 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  18. Shi, R.H., Lv, G.L., Wang, Y., Huang, D.Z., Guo, Y.: On quantum secret sharing via Chinese remainder theorem with the non-maximally entanglement state analysis. Int. J. Theor. Phys. 52, 539–548 (2013)

    Article  MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

  20. Hsu, J.L., Chong, S.K., Hwang, T., Tsai, C.W.: Dynamic quantum secret sharing. Quantum Inf. Process. 12, 331–344 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  21. Dehkordi, M.H., Fattahi, E.: Threshold quantum secret sharing between multiparty and multiparty using Greenberger–Horne–Zeilinger state. Quantum Inf. Process. 12, 1299–1306 (2013)

    Article  ADS  MATH  Google Scholar 

  22. Wang, H.B., Huang, Y.G., Fang, X., Gu, B., Fu, D.S.: High-capacity three-party quantum secret sharing with single photons in both the polarization and the spatial-mode degrees of freedom. Int. J. Theor. Phys. 52, 1043–1051 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  23. Gao, G.: Secure multiparty quantum secret sharing with the collective eavesdropping-check character. Quantum Inf. Process. 12, 55–68 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  24. Chen, R.K., Zhang, Y.Y., Shi, J.H., Li, F.G.: A multiparty error-correcting method for quantum secret sharing. Quantum Inf. Process. 13, 21–31 (2014)

    Article  ADS  MATH  Google Scholar 

  25. Liu, F., Qin, S.J., Wen, Q.Y.: A quantum secret-sharing protocol with fairness. Phys. Scr. 89, 075104 (2014)

    Article  ADS  Google Scholar 

  26. Chen, X.B., Dou, Z., Xu, G., He, X.Y., Yang, Y.X.: A kind of university quantum secret sharing protocol. Sci. Rep. 7, 39845 (2017)

    Article  ADS  Google Scholar 

  27. Cao, H., Ma, W.P.: \((t, n)\) threshold quantum state sharing scheme based on linear equations and unitary operation. IEEE Photonics J. 9, 7600207 (2017)

    Google Scholar 

  28. Wang, J.T., Xu, G., Chen, X.B., Sun, X.M., Jia, H.Y.: Local distinguishability of Dicke states in quantum secret sharing. Phys. Lett. A 381, 998–1002 (2017)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  29. Matsumoto, R.: Quantum optimal multiple assignment scheme for realizing general access structure of secret sharing. IEICE Trans. Fundam. Electron. 100, 726–728 (2017)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  31. Yang, W., Huang, L.S., Shi, R.H., He, L.B.: Secret sharing based on quantum Fourier transform. Quantum Inf. Process. 12, 2465–2474 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  32. Xiao, H.L., Gao, J.L.: Multi-party \(d\)-level quantum secret sharing scheme. Int. J. Theor. Phys. 52, 2075–2082 (2013)

    Article  MathSciNet  Google Scholar 

  33. Crepeau, C., Gottesman, D., Smith, A.: Secure multiparty quantum computation. In: Proceedings of the Thirty-fourth Annual ACM Symposium on Theory of Computing, Canada, pp. 643–652 (2002)

  34. Ben-Or, M., Crepeau, C., Gottesman, D., Hassidim, A., Smith, A.: Secure multiparty quantum computation with (only) a strict honest majority. In: Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science, USA, pp. 249–260 (2006)

  35. Weinstein, Y.S., Pravia, M.A., Fortunato, E.M., Lloyd, S., Cory, D.G.: Implementation of the quantum Fourier transform. Phys. Rev. Lett. 86, 1889–1891 (2001)

    Article  ADS  Google Scholar 

  36. Jimenez, O., Munoz, C., Klimov, A.B., Delgado, A.: Sharing of \(d\)-dimensional quantum states. Int. J. Quantum Inf. 10, 1250003 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  37. Qin, H.W., Dai, Y.W.: \(d\)-dimensional quantum state sharing with adversary structure. Quantum Inf. Process. 15, 1689–1701 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Automatization, Nanjing University of Science and Technology, Nanjing, 210094, China

    Huawang Qin & Yuewei Dai

  2. Department of Computer Science, National Chengchi University, Taipei, 11605, Taiwan

    Raylin Tso

Authors
  1. Huawang Qin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Raylin Tso
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yuewei Dai
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Huawang Qin.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Qin, H., Tso, R. & Dai, Y. Multi-dimensional quantum state sharing based on quantum Fourier transform. Quantum Inf Process 17, 48 (2018). https://doi.org/10.1007/s11128-018-1827-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-018-1827-8

Keywords

Search

Navigation