Skip to main content
SpringerLink
Log in

High-Dimensional Circular Quantum Secret Sharing Using Orbital Angular Momentum

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

Abstract

Quantum secret sharing is to distribute secret message securely between multi-parties. Here exploiting orbital angular momentum (OAM) state of single photons as the information carrier, we propose a high-dimensional circular quantum secret sharing protocol which increases the channel capacity largely. In the proposed protocol, the secret message is split into two parts, and each encoded on the OAM state of single photons. The security of the protocol is guaranteed by the laws of non-cloning theorem. And the secret messages could not be recovered except that the two receivers collaborated with each other. Moreover, the proposed protocol could be extended into high-level quantum systems, and the enhanced security could be achieved.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. Shor, P. W., Preskill, J.: Simple proof of security of the bb84 quantum key distribution protocol. Phys. Rev. Lett. 85(2), 441 (2000)

    Article  ADS  Google Scholar 

  2. Renner, R.: Security of quantum key distribution. Int. J. Quantum Inf. 6(01), 1–127 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  3. Gottesman, D., Lo, H.-K., Lütkenhaus, N., Preskill, J.: Security of quantum key distribution with imperfect devices. In: Proceedings of international symposium on information theory, 2004. ISIT 2004, vol. 136. IEEE (2004)

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

    Article  ADS  MathSciNet  Google Scholar 

  5. Xiao, L., Long, G.L., Deng, F.-G., Pan, J.-W.: Efficient multiparty quantum-secret-sharing schemes. Phys. Rev. A 69(5), 052307 (2004)

    Article  ADS  Google Scholar 

  6. Guo, G.-P., Guo, G.-C.: Quantum secret sharing without entanglement. Phys. Lett. A 310(4), 247–251 (2003)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  7. Zhang, Z.-J., Li, Y., Man, Z.: Multiparty quantum secret sharing. Phys. Rev. A 71(4), 044301 (2005)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  8. Mattle, K., Weinfurter, H., Kwiat, P.G., Zeilinger, A.: Dense coding in experimental quantum communication. Phys. Rev. Lett. 76(25), 4656 (1996)

    Article  ADS  Google Scholar 

  9. Terhal, B.M.: Quantum dense coding. In: Encyclopedia of algorithms, pp 1–99. Springer (2008)

  10. Bennett, C.H., Wiesner, S.J.: Communication via one-and two-particle operators on einstein-podolsky-rosen states. Phys. Rev. Lett. 69(20), 2881 (1992)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  11. Liu, X., Long, G., Tong, D., Li, F.: General scheme for superdense coding between multiparties. Phys. Rev. A 65(2), 022304 (2002)

    Article  ADS  Google Scholar 

  12. Long, G.-L., Liu, X.-S.: Theoretically efficient high-capacity quantum-key-distribution scheme. Phys. Rev. A 65(3), 032302 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  13. 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(4), 042317 (2003)

    Article  ADS  Google Scholar 

  14. Wang, C., Deng, F.-G., Li, Y.-S., Liu, X.-S., Long, G.L.: Quantum secure direct communication with high-dimension quantum superdense coding. Phys. Rev. A 71(4), 044305 (2005)

    Article  ADS  Google Scholar 

  15. 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(5), 054302 (2006)

    Article  ADS  Google Scholar 

  16. 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 

  17. Ye, T.: Fault tolerant channel-encrypting quantum dialogue against collective noise. Sci. China Phys. Mech. Astron. 58(4), 1–10 (2015)

    Article  Google Scholar 

  18. Zheng, C., Long, G.: Quantum secure direct dialogue using einstein-podolsky-rosen pairs. Sci. China Phys. Mech. Astron. 57(7), 1238–1243 (2014)

    Article  ADS  Google Scholar 

  19. Hu, J., Yu, B., Jing, M., Xiao, L., Jia, S., Qin, G., Long, G.: Experimental quantum secure direct communication with single photons. Light: Sci. Appl. 5, e16144 (2016)

    Article  Google Scholar 

  20. Wang, M.-M., Wang, W., Chen, J.-G., Farouk, A.: Secret sharing of a known arbitrary quantum state with noisy environment. Quantum Inf. Process 14(11), 4211–4224 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  21. Mishra, S., Shukla, C., Pathak, A., Srikanth, R., Venugopalan, A.: An integrated hierarchical dynamic quantum secret sharing protocol. Int. J. Theor. Phys. 54(9), 3143–3154 (2015)

    Article  MATH  Google Scholar 

  22. Peng, J.: Tripartite operation sharing with a six-particle maximally entangled state. Quantum Inf. Process 14(11), 4255–4262 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  23. Hao, L., Li, J., Long, G.: Eavesdropping in a quantum secret sharing protocol based on grover algorithm and its solution. Sci. China Phys. Mech. Astron. 53(3), 491–495 (2010)

    Article  ADS  Google Scholar 

  24. Beveratos, A., Brouri, R., Gacoin, T., Villing, A., Poizat, J.-P., Grangier, P.: Single photon quantum cryptography. Phys. Rev. Lett. 89(18), 187901 (2002)

    Article  ADS  Google Scholar 

  25. Yan, F.-L.: Quantum secret sharing between multiparty and multiparty without entanglement. Phys. Rev. A 72(1), 012304 (2005)

    Article  ADS  Google Scholar 

  26. Deng, F.-G., Zhou, H.-Y., Long, G.L.: Bidirectional quantum secret sharing and secret splitting with polarized single photons. Phys. Lett. A 337(4), 329–334 (2005)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  27. 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(9), 2690–2694 (2008)

    Article  ADS  Google Scholar 

  28. Zhang, J., Itzler, M.A., Zbinden, H., Pan, J.-W.: Advances in ingaas/inp single-photon detector systems for quantum communication. Light: Sci. Appl. 4(5), e286 (2015)

    Article  Google Scholar 

  29. Hu, X, Cheng, Y, Gu, C, Zhu, X, Liu, H: Superconducting nanowire single-photon detectors: recent progress. Sci. Bull. 60(23), 1980–1983 (2015)

    Article  Google Scholar 

  30. Zhang, L., Wan, C., Gu, M., Xu, R., Zhang, S., Kang, L., Chen, J., Wu, P.: Dual-lens beam compression for optical coupling in superconducting nanowire single-photon detectors. Sci. Bull. 60(16), 1434–1438 (2015)

    Article  Google Scholar 

  31. Karlsson, A., Koashi, M., Imoto, N.: Quantum entanglement for secret sharing and secret splitting. Phys. Rev. A 59(1), 162 (1999)

    Article  ADS  Google Scholar 

  32. Bandyopadhyay, S.: Teleportation and secret sharing with pure entangled states. Phys. Rev. A 62(1), 012308 (2000)

    Article  ADS  Google Scholar 

  33. 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(4), 044301 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  34. Deng, F.-G., Long, G.L., Zhou, H.-Y.: An efficient quantum secret sharing scheme with einstein–podolsky–rosen pairs. Phys. Lett. A 340(1), 43–50 (2005)

    Article  ADS  MATH  Google Scholar 

  35. Li, Y., Zhang, K., Peng, K.: Multiparty secret sharing of quantum information based on entanglement swapping. Phys. Lett. A 324(5), 420–424 (2004)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  36. Ai, Q.: Toward quantum teleporting living objects. Sci. Bull. 61(2), 110–111 (2016)

    Article  Google Scholar 

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

    Article  ADS  MathSciNet  MATH  Google Scholar 

  38. Allen, L., Beijersbergen, M. W., Spreeuw, R., Woerdman, J.: Orbital angular momentum of light and the transformation of laguerre-gaussian laser modes. Phys. Rev. A 45(11), 8185 (1992)

    Article  ADS  Google Scholar 

  39. Leach, J., Padgett, M.J., Barnett, S.M., Franke-Arnold, S., Courtial, J.: Measuring the orbital angular momentum of a single photon. Phys. Rev. Lett. 88(25), 257901 (2002)

    Article  ADS  Google Scholar 

  40. Vaziri, A., Weihs, G., Zeilinger, A.: Experimental two-photon, three-dimensional entanglement for quantum communication. Phys. Rev. Lett. 89(24), 240401 (2002)

    Article  ADS  Google Scholar 

  41. Spedalieri, F.M.: Quantum key distribution without reference frame alignment: exploiting photon orbital angular momentum. Opt. Commun. 260(1), 340–346 (2006)

    Article  ADS  Google Scholar 

  42. Mair, A., Vaziri, A., Weihs, G., Zeilinger, A.: Entanglement of the orbital angular momentum states of photons. Nature 412(6844), 313–316 (2001)

    Article  ADS  Google Scholar 

  43. Nicolas, A., Veissier, L., Giacobino, E., Maxein, D., Laurat, J.: Quantum state tomography of orbital angular momentum photonic qubits via a projection-based technique. New J. Phys. 17(3), 033037 (2015)

    Article  ADS  Google Scholar 

  44. Bechmann-Pasquinucci, H., Peres, A.: Quantum cryptography with 3-state systems. Phys. Rev. Lett. 85(15), 3313 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  45. Gröblacher, S., Jennewein, T., Vaziri, A., Weihs, G., Zeilinger, A.: Experimental quantum cryptography with qutrits. New J. Phys. 8(5), 75 (2006)

    Article  ADS  Google Scholar 

  46. 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 

  47. Cerf, N.J., Bourennane, M., Karlsson, A., Gisin, N.: Security of quantum key distribution using d-level systems. Phys. Rev. Lett. 88(12), 127902 (2002)

    Article  ADS  Google Scholar 

  48. Mafu, M., Dudley, A., Goyal, S., Giovannini, D., McLaren, M., Padgett, M.J., Konrad, T., Petruccione, F., Lütkenhaus, N., Forbes, A.: Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases. Phys. Rev. A 88(3), 032305 (2013)

    Article  ADS  Google Scholar 

Download references

Acknowledgments

The authors gratefully acknowledge the support from the National Natural Science Foundation of China through Grants Nos. 61471050, 11404031, and 11374042, and the Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications).

Author information

Authors and Affiliations

  1. State Key Laboratory of Information photonics and Optical Communications and School of Science, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Dawei Tang, Tie-jun Wang, Sichen Mi, Xiao-Meng Geng & Chuan Wang

Authors
  1. Dawei Tang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tie-jun Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sichen Mi
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Xiao-Meng Geng
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Chuan Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chuan Wang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tang, D., Wang, Tj., Mi, S. et al. High-Dimensional Circular Quantum Secret Sharing Using Orbital Angular Momentum. Int J Theor Phys 55, 4963–4971 (2016). https://doi.org/10.1007/s10773-016-3120-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10773-016-3120-x

Keywords

Search

Navigation