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International Journal of Theoretical Physics

, Volume 57, Issue 11, pp 3410–3418 | Cite as

Semi-quantum Key Distribution Robust Against Combined Collective Noise

  • Chih-Lun Tsai
  • Tzonelih Hwang
Article

Abstract

This paper first proposes a new coding function for the six-qubit decoherence-free states that can resist both types of collective noise (i.e., dephasing and rotation noise) simultaneously. Subsequently, based on the coding function, a semi-quantum key distribution (SQKD) protocol is designed such that a sender with strong quantum capabilities can send a key to a classical receiver who can merely perform classical operations. This is the first SQKD protocol that can resist the combined collective noise. Analyses show that this protocol is secure and effective.

Keywords

Quantum transmission Qubits Decoherence Collective noise Semi-quantum key distribution 

Notes

Acknowledgments

We would like to thank the Ministry of Science and Technology of the Republic of China for financially supporting this research under Contract No. MOST 104-2221-E-006-102-.

References

  1. 1.
    Kampe, J., Bacon, D., Lidar, D.A., Whaley, K.B.: Theory of decoherence-free fault-tolerant universal quantum computation. Phys. Rev. A 63, 042307 (2000)ADSCrossRefGoogle Scholar
  2. 2.
    Cabello, A.: Six-qubit permutation-based decoherence-free orthogonal basis. Phys. Rev. A 75, 020301 (2007)ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    Qin, S.J., Gao, F., Wen, Q.Y., et al.: Robust quantum secure direct communication over collective rotating channel. Commun. Theor. Phys. 53, 645–647 (2010)ADSCrossRefGoogle Scholar
  4. 4.
    Deng, F.G., Li, X.H., Zhou, H.Y., et al.: Improving the security of multiparty quantum secret sharing against Trojan horse attack. Phys. Rev. A. 72, 044302 (2005)ADSCrossRefGoogle Scholar
  5. 5.
    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, 054302 (2006)ADSCrossRefGoogle Scholar
  6. 6.
    Lidar, D.A., Bacon, D., Kempe, J., et al.: Protecting quantum information encoded in decoherence-free states against exchange errors. Phys. Rev. A. 61, 052307 (2000)ADSCrossRefGoogle Scholar
  7. 7.
    Walton, Z.D., Abouraddy, A.F., Sergienko, A.V., et al.: Decoherence-free subspaces in quantum key distribution. Phys. Rev. Lett. 91, 087901 (2003)ADSCrossRefGoogle Scholar
  8. 8.
    Boileau, J.C., Gottesman, D., Laflamme, R., et al.: Robust polarization-based quantum key distribution over a collective-noise channel. Phys. Rev. Lett. 92, 017901 (2004)ADSCrossRefGoogle Scholar
  9. 9.
    Bourennane, M., Eibl, M., Gaertner, S., et al.: Decoherence-free quantum information processing with four-photon entangled states. Phys. Rev. Lett. 92, 107901 (2004)ADSCrossRefGoogle Scholar
  10. 10.
    Yamamoto, T., Shimamura, J., Ozdemir, S.K., et al.: Faithful qubit distribution assisted by one additional qubit against collective noise. Phys. Rev. Lett. 95, 040503 (2005)ADSCrossRefGoogle Scholar
  11. 11.
    Wang, X.B.: Fault tolerant quantum key distribution protocol with collective random unitary noise. Phys. Rev. A. 72, 050304 (2005)ADSCrossRefGoogle Scholar
  12. 12.
    Zhang, Z.J.: Robust multiparty quantum secret key sharing over two collective-noise channels. Physica A 361, 233–238 (2006)ADSCrossRefGoogle Scholar
  13. 13.
    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 (1984)Google Scholar
  14. 14.
    Zhang, Z.J., Man, Z.X., Shi, S.H.: An efficient multiparty quantum key distribution scheme. Int. J. Quantum Inf. 3(3), 555–560 (2005)CrossRefGoogle Scholar
  15. 15.
    Zou, X., Qiu, D., Li, L., Wu, L., Li, L.: Semiquantum-key distribution using less than four quantum states. Phys. Rev. A 79(5), 052312 (2009)ADSCrossRefGoogle Scholar
  16. 16.
    Boyer, M., Gelles, R., Kenigsberg, D., Mor, T.: Semiquantum key distribution. Phys. Rev. A. 79(3), 032341 (2009)ADSMathSciNetCrossRefGoogle Scholar
  17. 17.
    Wang, J., Zhang, S., Zhang, Q., Tang, C.J.: Semiquantum key distribution using entangled states. Chinese Phys. Lett. 28(10), 100301 (2011)ADSCrossRefGoogle Scholar
  18. 18.
    Bennett, C.H., Brassard, G.: Generalized privacy amplification. IEEE Trans. Inf. Theory 41, 1915–1953 (1995)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Bennett, C.H., Brassard, G., Robert, J.M.: Privacy amplification by public discussion. SIAM J. Comput. 17, 210–229 (1988)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Zanardi, P., Rasetti, M.: Noiseless quantum codes. Phys. Rev.Lett. 79, 3306 (1997)ADSCrossRefGoogle Scholar
  21. 21.
    Jennewein, T., Simon, C., Weihs, G., Weinfurter, H., Zeilinger, A.: Quantum cryptography with entangled photons. Phys. Rev. Lett. 84(20), 4729–4732 (2000). ADSCrossRefGoogle ScholarADSCrossRefGoogle Scholar
  22. 22.
    Beveratos, A., Brouri, R., Gacoin, T., Villing, A., Poizat, J.P., Grangier, P.: Single photon quantum cryptography. Phys. Rev. Lett. 89(18), 187901 (2002). ADSCrossRefGoogle ScholarADSCrossRefGoogle Scholar
  23. 23.
    Hughes, R.J., Nordholt, J.E., Derkacs, D., Peterson, C.G.: Practical free-space quantum key distribution over 10 km in daylight and at night. New J. Phys. 4, 43 (2002). ADSCrossRefGoogle ScholarADSCrossRefGoogle Scholar
  24. 24.
    Stucki, D., Gisin, N., Guinnard, O., Ribordy, G., Zbinden, H.: Quantum key distribution over 67 km with a plug&play system. New J. Phys. 4, 41 (2002). ADSCrossRefGoogle ScholarADSCrossRefGoogle Scholar
  25. 25.
    Gobby, C., Yuan, Z.L., Shields, A.J.: Quantum key distribution over 122 km of standard telecom fiber. Appl. Phys. Lett. 84(19), 3762–3764 (2004). ADSCrossRefGoogle ScholarADSCrossRefGoogle Scholar
  26. 26.
    Yu-Guang, Y., Yuan, W., Yi-Weiand, T., Qiao-Yan, W.: Universal three-party quantum secret sharing against collective noise. Commun. Theor. Phys. 55, 589–593 (2011)ADSCrossRefGoogle Scholar
  27. 27.
    Li, C.-M., Yu, K.-F., Kao, S.-H., Hwang, T.: Authenticated semi-quantum key distributions without classical channe. Quantum. Inf. Process 15, 2881–2893 (2016)ADSMathSciNetCrossRefGoogle Scholar
  28. 28.
    Gao, F., Wen, Q.Y., Zhu, F.C.: Comment on: Quantum exam. Phys. Lett. A 360(6), 748–750 (2007)ADSCrossRefGoogle Scholar
  29. 29.
    Wang, J., Zhang, Q., Tang, C.: Quantum secure direct communication without using perfect quantum channel. Int. J. Mod. Phys. C 17(5), 685 (2006)ADSMathSciNetCrossRefGoogle Scholar
  30. 30.
    Li, Q., Chan, W.H., Zhang, S.: Semiquantum key distribution with secure delegated quantum computation. Sci. Rep. 6, 19898 (2016)Google Scholar
  31. 31.
    Sun, Z.W., Du, R.-G., Long, D.-Y.: Quantum key distribution with limited classical bob. International Journal of Quantum Information 11(01), 1350005 (2013)ADSMathSciNetCrossRefGoogle Scholar
  32. 32.
    Yu, K.-F, Yang, C.-W., Liao, C.-H., Hwang, T.: Authenticated Semi-quantum Key Distribution Protocol Using Bell States. Quantum Inf. Process 13(6), 1457–1465 (2014)ADSMathSciNetCrossRefGoogle Scholar
  33. 33.
    Meslouhi, A., Hassouni, Y.: Cryptanalysis on authenticated semi-quantum key distribution protocol using Bell states. Quantum Inf. Process 16(1), 18 (2016)ADSMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Computer Science and Information EngineeringNational Cheng Kung UniversityTainan CityRepublic of China

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