Advertisement

Quantum Information Processing

, Volume 12, Issue 2, pp 1089–1107 | Cite as

Bell state entanglement swappings over collective noises and their applications on quantum cryptography

  • Jason Lin
  • Tzonelih Hwang
Article

Abstract

This work presents two robust entanglement swappings against two types of collective noises, respectively. The entanglement swapping can be achieved by performing two Bell state measurements on two logical qubits that come from two original logical Bell states, respectively. Two fault tolerant quantum secret sharing (QSS) protocols are further proposed to demonstrate the usefulness of the newly proposed entanglement swappings. The proposed QSS schemes are not only free from Trojan horse attacks but also quite efficient. Moreover, by adopting two Bell state measurements instead of four-qubit joint measurements, the proposed protocols are practical in combating collective noises. The proposed fault tolerant entanglement swapping can also be used to replace the traditional Bell-state entanglement swapping used in various quantum cryptographic protocols to provide robustness in combating collective noises.

Keywords

Entanglement swapping Collective noise Quantum secret sharing 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bose S., Vedral V., Knight P.L.: Multiparticle generalization of entanglement swapping. Phys. Rev. A 57(2), 822–829 (1998)ADSCrossRefGoogle Scholar
  2. 2.
    Pan J.W., Bouwmeester D., Weinfurter H., Zeilinger A.: Experimental entanglement swapping: entangling photons that never interacted. Phys. Rev. Lett. 80(18), 3891–3894 (1998)MathSciNetADSMATHCrossRefGoogle Scholar
  3. 3.
    Zukowski M., Zeilinger A., Horne M.A., Ekert A.K.: Event-ready-detectors Bell experiment via entanglement swapping. Phys. Rev. Lett. 71(26), 4287–4290 (1993)ADSCrossRefGoogle Scholar
  4. 4.
    Lu H., Guo G.C.: Teleportation of a two-particle entangled state via entanglement swapping. Phys. Lett. A 276(5-6), 209–212 (2000)MathSciNetADSMATHCrossRefGoogle Scholar
  5. 5.
    Gao G.: Quantum key distribution by comparing Bell states. Opt. Commun. 281(4), 876–879 (2008)ADSCrossRefGoogle Scholar
  6. 6.
    Yuan H., Song J., Han L.F., Hou K., Shi S.H.: Improving the total efficiency of quantum key distribution by comparing Bell states. Opt. Commun. 281(18), 4803–4806 (2008)ADSCrossRefGoogle Scholar
  7. 7.
    Shi G.F., Xi X.Q., Tian X.L., Yue R.H.: Bidirectional quantum secure communication based on a shared private Bell state. Opt. Commun. 282(12), 2460–2463 (2009)ADSCrossRefGoogle Scholar
  8. 8.
    Li Y.M., Zhang K.S., Peng K.C.: Multiparty secret sharing of quantum information based on entanglement swapping. Phys. Lett. A 324(5-6), 420–424 (2004)MathSciNetADSMATHCrossRefGoogle Scholar
  9. 9.
    Zhang Z.J., Man Z.X.: Multiparty quantum secret sharing of classical messages based on entanglement swapping. Phys. Rev. A 72(2), 022303 (2005)MathSciNetADSCrossRefGoogle Scholar
  10. 10.
    Zhang Z.J., Yang J., Man Z.X., Li Y.: Multiparty secret sharing of quantum information using and identifying Bell states. Eur Phys J D 33(1), 133–136 (2005)ADSCrossRefGoogle Scholar
  11. 11.
    Sun Y., Wen Q.Y., Gao F., Chen X.B., Zhu F.C.: Multiparty quantum secret sharing based on Bell measurement. Opt. Commun. 282(17), 3647–3651 (2009)ADSCrossRefGoogle Scholar
  12. 12.
    Shi R.H., Huang L.S., Yang W., Zhong H.: Multiparty quantum secret sharing with Bell states and Bell measurements. Opt. Commun. 283(11), 2476–2480 (2010)ADSCrossRefGoogle Scholar
  13. 13.
    Li X.H., Deng F.G., Zhou H.Y.: Efficient quantum key distribution over a collective noise channel. Phys. Rev. A 78(2), 022321 (2008)ADSCrossRefGoogle Scholar
  14. 14.
    Zanardi P., Rasetti M.: Noiseless quantum codes. Phys. Rev. Lett. 79(17), 3306 (1997)ADSCrossRefGoogle Scholar
  15. 15.
    Li X.H., Zhao B.K., Sheng Y.B., Deng F.G., Zhou H.Y.: Fault tolerant quantum key distribution based on quantum dense coding with collective noise. Int. J. Quantom Inf. 7(8), 1479–1489 (2009)MATHCrossRefGoogle Scholar
  16. 16.
    Yang C.-W., Tsai C.-W., Hwang T.: Fault tolerant two-step quantum secure direct communication protocol against collective noises. Sci. China Phys. 54(3), 496–501 (2011)Google Scholar
  17. 17.
    Yang C.-W., Tsai C.-W., Hwang T.: Thwarting intercept-and-resend attack on Zhang’s quantum secret sharing using collective rotation noises. Quantum Inf. Process. 11(1), 113–122 (2012)MathSciNetMATHCrossRefGoogle Scholar
  18. 18.
    Hillery M., Buzek V., Berthiaume A.: Quantum secret sharing. Phys. Rev. A 59(3), 1829–1834 (1999)MathSciNetADSCrossRefGoogle Scholar
  19. 19.
    Gottesman, D.: Theory of quantum secret sharing. Phys. Rev. A 61(4), 042311 (2000)Google Scholar
  20. 20.
    Guo G.P., Guo G.C.: Quantum secret sharing without entanglement. Phys. Lett. A 310(4), 247–251 (2003)MathSciNetADSMATHCrossRefGoogle Scholar
  21. 21.
    Xiao L., Long G.L., Deng F.G., Pan J.W.: Efficient multiparty quantum-secret-sharing schemes. Phys. Rev. A 69(5), 052307 (2004)ADSCrossRefGoogle Scholar
  22. 22.
    Hsu L.Y., Li C.M.: Quantum secret sharing using product states. Phys. Rev. A 71(2), 022321 (2005)ADSCrossRefGoogle Scholar
  23. 23.
    Deng F.G., Long G.L., Zhou H.Y.: An efficient quantum secret sharing scheme with Einstein-Podolsky-Rosen pairs. Phys. Lett. A 340(1-4), 43–50 (2005)ADSMATHCrossRefGoogle Scholar
  24. 24.
    Zhang Z.J., Li Y., Man Z.X.: Multiparty quantum secret sharing. Phys. Rev. A 71(4), 044301 (2005)MathSciNetADSCrossRefGoogle Scholar
  25. 25.
    Zhang Z.J.: Multiparty quantum secret sharing of secure direct communication. Phys. Lett. A 342(1-2), 60–66 (2005)ADSMATHCrossRefGoogle Scholar
  26. 26.
    Deng F.G., Zhou H.Y., Long G.L.: Circular quantum secret sharing. J. Phys. Math. Gen. 39(45), 14089–14099 (2006)MathSciNetADSMATHCrossRefGoogle Scholar
  27. 27.
    Zhou P., Li X.H., Liang Y.J., Deng F.G., Zhou H.Y.: Multiparty quantum secret sharing with pure entangled states and decoy photons. Phys. A 381, 164–169 (2007)MathSciNetCrossRefGoogle Scholar
  28. 28.
    Deng F.G., Li X.H., Zhou H.Y.: Efficient high-capacity quantum secret sharing with two-photon entanglement. Phys. Lett. A 372(12), 1957–1962 (2008)MathSciNetADSMATHCrossRefGoogle Scholar
  29. 29.
    Zhang Z.J., Han L.F., Liu Y.M., Liu J.: Multiparty quantum secret sharing of secure direct communication using single photons. Opt. Commun. 281(9), 2690–2694 (2008)ADSCrossRefGoogle Scholar
  30. 30.
    Wang T.Y., Wen Q.Y., Chen X.B., Guo F.Z., Zhu F.C.: An efficient and secure multiparty quantum secret sharing scheme based on single photons. Opt. Commun. 281(24), 6130–6134 (2008)ADSCrossRefGoogle Scholar
  31. 31.
    Li Q., Chan W.H., Long D.Y.: Semiquantum secret sharing using entangled states. Phys. Rev. A 82(2), 022303 (2010)ADSCrossRefGoogle Scholar
  32. 32.
    Zhang Z.J.: Robust multiparty quantum secret key sharing over two collective-noise channels. Phys. A 361(1), 233–238 (2006)ADSCrossRefGoogle Scholar
  33. 33.
    Wang Z.Y., Yuan H., Gao G., Shi S.H.: Robust multiparty quantum secret key sharing over two collective-noise channels via three-photon mixed states. Commun. Theor. Phys 46(4), 607–609 (2006)ADSCrossRefGoogle Scholar
  34. 34.
    Sun Y., Wen Q.Y., Zhu F.C.: Improving the multiparty quantum secret sharing over two collective-noise channels against insider attack. Opt. Commun. 283(1), 181–183 (2010)ADSCrossRefGoogle Scholar
  35. 35.
    Gu B., Mu L.L., Ding L.G., Zhang C.Y., Li C.Q.: Fault tolerant three-party quantum secret sharing against collective noise. Opt. Commun. 283(15), 3099–3103 (2010)ADSCrossRefGoogle Scholar
  36. 36.
    Knill E., Laflamme R., Viola L.: Theory of quantum error correction for general noise. Phys. Rev. Lett. 84(11), 2525 (2000)MathSciNetADSMATHCrossRefGoogle Scholar
  37. 37.
    Kempe J., Bacon D., Lidar D., Whaley K.: Theory of decoherence-free fault-tolerant universal quantum computation. Phys. Rev. A 63(4), 042307 (2001)ADSCrossRefGoogle Scholar
  38. 38.
    Gisin N., Ribordy G.G., Tittel W., Zbinden H.: Quantum cryptography. Rev. Mod. Phys. 74(1), 145–195 (2002)ADSCrossRefGoogle Scholar
  39. 39.
    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(4), 044302 (2005)ADSCrossRefGoogle Scholar
  40. 40.
    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)ADSCrossRefGoogle Scholar
  41. 41.
    Cai Q.Y.: Eavesdropping on the two-way quantum communication protocols with invisible photons. Phys. Lett. A 351(1-2), 23–25 (2006)ADSMATHCrossRefGoogle Scholar
  42. 42.
    Yang, C.-W., Hwang, T., Luo, Y.-P.: Enhancement on “quantum blind signature based on two-state vector formalism”. Quantum Inf. Process. (2012). doi: 10.1007/s11128-012-0362-2
  43. 43.
    Hsieh C.R., Tasi C.W., Hwang T.: Quantum secret sharing using GHZ-like state. Commun. Theor. Phys 54(6), 1019–1022 (2010)MATHCrossRefGoogle Scholar
  44. 44.
    Shannon C.E.: Communication theory of secrecy system. Bell Syst. Tech. J. 28, 656–715 (1949)MathSciNetMATHGoogle Scholar
  45. 45.
    Bennett C.H., Brassard G., Crepeau C., Maurer U.M.: Generalized privacy amplification. IEEE Trans. Inf. Theory 41(6), 1915–1923 (1995)MathSciNetMATHCrossRefGoogle Scholar
  46. 46.
    Bennett C.H., Brassard G., Robert J.M.: Privacy amplification by public discussion. Siam J. Comput. 17(2), 210–229 (1988)MathSciNetCrossRefGoogle Scholar
  47. 47.
    Chen J.H., Lee K.C., Hwang T.: The enhancement of Zhou et al.’s quantum secret sharing protocol. Int. J. Mod. Phys. C 20(10), 1531–1535 (2009)ADSMATHCrossRefGoogle Scholar
  48. 48.
    Shih H.C., Lee K.C., Hwang T.: New efficient three-party quantum key distribution protocols. IEEE J. Sel. Top. Quantom 15(6), 1602–1606 (2009)CrossRefGoogle Scholar
  49. 49.
    Lin J., Hwang T.: An enhancement on Shi et al.’s multiparty quantum secret sharing protocol. Opt. Commun. 284(5), 1468–1471 (2011)MathSciNetADSCrossRefGoogle Scholar
  50. 50.
    Hwang T., Hwang C.-C., Li C.-M.: Multiparty quantum secret sharing based on GHZ states. Phys. Scr. 83(4), 045004 (2011)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of Computer Science and Information EngineeringNational Cheng Kung UniversityTainan CityTaiwan, ROC

Personalised recommendations