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

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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.

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References

  1. Bose S., Vedral V., Knight P.L.: Multiparticle generalization of entanglement swapping. Phys. Rev. A 57(2), 822–829 (1998)

    Article  ADS  Google Scholar 

  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)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  5. Gao G.: Quantum key distribution by comparing Bell states. Opt. Commun. 281(4), 876–879 (2008)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  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)

    Article  MathSciNet  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  14. Zanardi P., Rasetti M.: Noiseless quantum codes. Phys. Rev. Lett. 79(17), 3306 (1997)

    Article  ADS  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  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. 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)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  19. Gottesman, D.: Theory of quantum secret sharing. Phys. Rev. A 61(4), 042311 (2000)

    Google Scholar 

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

    Article  MathSciNet  ADS  MATH  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  22. Hsu L.Y., Li C.M.: Quantum secret sharing using product states. Phys. Rev. A 71(2), 022321 (2005)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  MATH  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  25. Zhang Z.J.: Multiparty quantum secret sharing of secure direct communication. Phys. Lett. A 342(1-2), 60–66 (2005)

    Article  ADS  MATH  Google Scholar 

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

    Article  MathSciNet  ADS  MATH  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  31. 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 

  32. Zhang Z.J.: Robust multiparty quantum secret key sharing over two collective-noise channels. Phys. A 361(1), 233–238 (2006)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  36. Knill E., Laflamme R., Viola L.: Theory of quantum error correction for general noise. Phys. Rev. Lett. 84(11), 2525 (2000)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  38. Gisin N., Ribordy G.G., Tittel W., Zbinden H.: Quantum cryptography. Rev. Mod. Phys. 74(1), 145–195 (2002)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  41. Cai Q.Y.: Eavesdropping on the two-way quantum communication protocols with invisible photons. Phys. Lett. A 351(1-2), 23–25 (2006)

    Article  ADS  MATH  Google Scholar 

  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. Hsieh C.R., Tasi C.W., Hwang T.: Quantum secret sharing using GHZ-like state. Commun. Theor. Phys 54(6), 1019–1022 (2010)

    Article  MATH  Google Scholar 

  44. Shannon C.E.: Communication theory of secrecy system. Bell Syst. Tech. J. 28, 656–715 (1949)

    MathSciNet  MATH  Google Scholar 

  45. Bennett C.H., Brassard G., Crepeau C., Maurer U.M.: Generalized privacy amplification. IEEE Trans. Inf. Theory 41(6), 1915–1923 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  46. Bennett C.H., Brassard G., Robert J.M.: Privacy amplification by public discussion. Siam J. Comput. 17(2), 210–229 (1988)

    Article  MathSciNet  Google Scholar 

  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)

    Article  ADS  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  49. Lin J., Hwang T.: An enhancement on Shi et al.’s multiparty quantum secret sharing protocol. Opt. Commun. 284(5), 1468–1471 (2011)

    Article  MathSciNet  ADS  Google Scholar 

  50. Hwang T., Hwang C.-C., Li C.-M.: Multiparty quantum secret sharing based on GHZ states. Phys. Scr. 83(4), 045004 (2011)

    Article  ADS  Google Scholar 

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Correspondence to Tzonelih Hwang.

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Lin, J., Hwang, T. Bell state entanglement swappings over collective noises and their applications on quantum cryptography. Quantum Inf Process 12, 1089–1107 (2013). https://doi.org/10.1007/s11128-012-0456-x

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  • DOI: https://doi.org/10.1007/s11128-012-0456-x

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