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High-Efficiency Three-Party Quantum Key Agreement Protocol with Quantum Dense Coding and Bell States

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Abstract

We propose a high-efficiency three-party quantum key agreement protocol, by utilizing two-photon polarization-entangled Bell states and a few single-photon polarization states as the information carriers, and we use the quantum dense coding method to improve its efficiency. In this protocol, each participant performs one of four unitary operations to encode their sub-secret key on the passing photons which contain two parts, the first quantum qubits of Bell states and a small number of single-photon states. At the end of this protocol, based on very little information announced by other, all participants involved can deduce the same final shared key simultaneously. We analyze the security and the efficiency of this protocol, showing that it has a high efficiency and can resist both outside attacks and inside attacks. As a consequence, our protocol is a secure and efficient three-party quantum key agreement protocol.

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References

  1. 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, pp. 175–179. IEEE, New York (1984)

  2. Ekert, A.K.: Quantum cryptography based on Bell’s theorem. Phys. Rev. Lett. 67, 661–663 (1991)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  3. Bennett, C.H., Brassard, G., Mermin, N.D.: Quantum cryptography without Bell’s theorem. Phys. Rev. Lett. 68, 557 (1992)

    Article  ADS  MathSciNet  MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

  5. 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, 042317 (2003)

    Article  ADS  Google Scholar 

  6. Zhang, W., Ding, D.S., Sheng, Y.B., Zhou, L., Shi, B.S., Guo, G.C.: Quantum secure direct communication with quantum memory. Phys. Rev. Lett. 118, 220501 (2017)

    Article  ADS  Google Scholar 

  7. Zhu, F., Zhang, W., Sheng, Y.B., Huang, Y.D.: Experimental long-distance quantum secure direct communication. Sci. Bull. 62, 1519–1524 (2017)

    Article  Google Scholar 

  8. Deng, F.G., Long, G.L.: Secure direct communication with a quantum one-time pad. Phys. Rev. A 69, 052319 (2004)

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

  10. Wu, F.Z., Yang, G.J., Wang, H.B., Xiong, J., Alzahrani, F., Hobiny, A., Deng, F.G.: High-capacity quantum secure direct communication with two-photon six-qubit hyperentangled states. Sci. China-Phys. Mech. Astron. 60, 120313 (2017)

    Article  ADS  Google Scholar 

  11. Chen, S.S., Zhou, L., Zhong, W., Sheng, Y.B.: Three-step three-party quantum secure direct communication. Sci. China-Phys. Mech. Astron. 61, 090312 (2018)

    Article  Google Scholar 

  12. Niu, P.H., Zhou, Z.R., Lin, Z.S., Sheng, Y.B., Yin, L.G., Long, G.L.: Measurement-device-independent quantum communication without encryption. Sci. Bull. 63, 1345 (2018)

    Article  Google Scholar 

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

    Article  ADS  MathSciNet  MATH  Google Scholar 

  14. Liu, B., Xiao, D., Jia, H.Y., Liu, R.Z.: Collusive attacks to “circle-type” multi-party quantum key agreement protocols. Quantum Inf. Process. 15, 2113–2124 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  15. Sun, Z.W., Zhang, C., Wang, B.H., Li, Q., Long, D.Y.: Improvements on “Multiparty quantum key agreement with single particles”. Quantum Inf. Process. 12, 3411–3420 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  16. Huang, W., Wen, Q.Y., Liu, B., Gao, F., Sun, Y.: Quantum key agreement with EPR pairs and single-particle measurements. Quantum Inf. Process. 13, 649–663 (2014)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  17. Zhou, N., Zeng, G., Xiong, J.: Quantum key agreement protocol. Electron. Lett. 40, 1149–1150 (2004)

    Article  Google Scholar 

  18. Chong, S.K., Hwang, T.: Quantum key agreement protocol based on BB84. Opt. Commun. 283, 1192–1195 (2010)

    Article  ADS  Google Scholar 

  19. Shi, R.H., Zhong, H.: Multi-party quantum key agreement with bell states and bell measurements. Quantum Inf. Process. 12, 921–932 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  20. Liu, B., Gao, F., Huang, W., Wen, Q.Y.: Multiparty quantum key agreement with single particles. Quantum Inf. Process. 12, 1797–1805 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  21. Shukla, C., Alam, N., Pathak, A.: Protocols of quantum key agreement solely using Bell states and Bell measurement. Quantum Inf. Process. 13, 2391–2405 (2014)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  22. Sun, Z.W., Yu, J.P., Wang, P.: Efficient multi-party quantum key agreement by cluster states. Quantum Inf. Process. 15, 373–384 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  23. Sun, Z.W., Zhang, C., Wang, P., Yu, J.P., Zhang, Y., Long, D.Y.: Multi-party quantum key agreement by an entangled six-qubit state. Int. J. Theor. Phys. 55, 1920–1929 (2016)

    Article  MATH  Google Scholar 

  24. Yin, X.R., Ma, W.P., Liu, W.Y.: Three-party quantum key agreement with two-photon entanglement. Int. J. Theor. Phys. 52, 3915–3921 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  25. Xu, G.B., Wen, Q.Y., Gao, F., Qin, S.J.: Novel multiparty quantum key agreement protocol with GHZ states. Quantum Inf. Process. 13, 2587–2594 (2014)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  26. Huang, W., Su, Q., Xu, B.J.: Improved multiparty quantum key agreement in travelling mode. Sci. China-Phys. Mech. Astron. 59, 120311 (2016)

    Article  Google Scholar 

  27. Cai, B.B., Guo, G.D., Lin, S.: Multi-party quantum key agreement without entanglement. Int. J. Theor. Phys. 56, 1039 (2017)

    Article  MATH  Google Scholar 

  28. Cao, H., Ma, W.P.: Multiparty quantum key agreement based on quantum search algorithm. Sci. Rep. 7, 45046 (2017)

    Article  ADS  Google Scholar 

  29. Huang, W., Su, Q., He, Y.H., Fan, F., Xu, B.J.: Efficient multiparty quantum key agreement with collective detection. Sci. Rep. 7, 15264 (2017)

    Article  ADS  Google Scholar 

  30. Chong, S.K., Tsai, C.W., Hwang, T.: Improvement on “Quantum key agreement protocol with maximally entangled state”. Int. J. Theor. Phys. 50, 1793–1802 (2011)

    Article  MATH  Google Scholar 

  31. Huang, W., Wen, Q.Y., Liu, B., Su, Q., Gao, F.: Cryptanalysis of a multi-party quantum key agreement protocol with single particles. Quantum Inf. Process. 13, 1651–1657 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  32. Huang, W., Su, Q., Wu, X., Li, Y.B., Sun, Y.: Quantum key agreement against collective decoherence. Int. J. Theor. Phys. 53, 2891–2901 (2014)

    Article  MATH  Google Scholar 

  33. Shen, D.S., Ma, W.P., Wang, L.L.: Two-party quantum key agreement with four-qubit cluster states. Quantum Inf. Process. 13, 2313–2324 (2014)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  34. He, Y.F., Ma, W.P.: Quantum key agreement protocols with four-qubit cluster states. Quantum Inf. Process. 14, 3483–3498 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  35. Zhu, Z.C., Hu, A.Q., Fu, A.M.: Participant attack on three-party quantum key agreement with two-photon entanglement. Int. J. Theor. Phys. 55, 55–61 (2016)

    Article  MATH  Google Scholar 

  36. He, Y.F., Ma, W.P.: Two-party quantum key agreement based on four-particle GHZ states. Int. J. Theor. Phys. 14, 1650007 (2016)

    MathSciNet  MATH  Google Scholar 

  37. Diffie, W., Hellman, M.: New directions in cryptography. IEEE Trans. Inf. Theory 22(6), 644 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  38. Bennett, C.H., Wiesner, S.J.: Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states. Phys. Rev. Lett. 69, 2881 (1992)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  39. Deng, F.G., Li, X.H., Zhou, H.Y., Zhang, Z.: Improving the security of multiparty quantum secret sharing against Trojan horse attack. Phys. Rev. A 72, 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, 054302 (2006)

    Article  ADS  Google Scholar 

  41. Jennewein, T., Simon, C., Weihs, G., Weinfurter, H., Zeilinger, A.: Quantum cryptography with entangled photons. Phys. Rev. Lett. 84, 4729–4732 (2000)

    Article  ADS  Google Scholar 

  42. Stucki, D., Gisin, N., Guinnard, O., Ribordy, G., Zbinden, H.: Quantum key distribution over 67 km with a plug and play system. New J. Phys. 4, 41 (2002)

    Article  ADS  Google Scholar 

  43. 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)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  45. Gobby, C., Yuan, Z.L., Shields, A.J.: Quantum key distribution over 122 km of standard telecom fiber. Appl. Phys. Lett. 84, 3762–3764 (2004)

    Article  ADS  Google Scholar 

  46. Cabello, A.: Quantum key distribution in the Holevo limit. Phys. Rev. Lett. 85, 5635 (2000)

    Article  ADS  Google Scholar 

  47. Yu, R.F., Lin, Y.J., Zhou, P.: Joint remote preparation of arbitrary two- and three-photon state with linear-optical elements. Quantum Inf. Process. 15, 4785 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  48. Lin, J.Y., He, J.G., Gao, Y.C., Li, X.M., Zhou, P.: Controlled remote implementation of an arbitrary single-qubit operation with partially entangled quantum channel. Int. J. Theor. Phys. 56, 1085 (2017)

    Article  MATH  Google Scholar 

  49. Zhou, P., Jiao, X.F., Lv, S.X.: Parallel remote state preparation of arbitrary single-qubit states via linear- optical elements by using hyperentangled Bell states as the quantum channel. Quantum Inf. Process. 17, 298 (2018)

    Article  ADS  MATH  Google Scholar 

  50. Lv, S.X., Zhao, Z.W., Zhou, P.: Joint remote control of an arbitrary single-qubit state by using a multiparticle entangled state as the quantum channel. Quantum Inf. Process. 17, 8 (2018)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  51. Lv, S.X., Zhao, Z.W., Zhou, P.: Multiparty-controlled joint remote preparation of an arbitrary m-qudit state with d-dimensional Greenberger- Horne- Zeilinger states. Int. J. Theor. Phys. 57, 148 (2018)

    Article  MATH  Google Scholar 

  52. Shor, P.W.: In: Proceedings of the 35th Symposium on the Foundations of Computer Science, vol. 124. IEEE, New York (1994)

  53. Sheng, Y.B., Zhou, L.: Blind quantum computation with a noise channel. Phys. Rev. A 98, 052343 (2018)

    Article  ADS  Google Scholar 

  54. Song, X.K., Ai, Q., Qiu, J., Deng, F.G.: Physically feasible three-level transitionless quantum driving with multiple Schrodinger dynamics. Phys. Rev. A 93, 052324 (2016)

    Article  ADS  Google Scholar 

  55. Sheng, Y.B., Zhou, L.: Distributed secure quantum machine learning. Sci. Bull. 62, 1025 (2017)

    Article  Google Scholar 

  56. Buluta, I., Nori, F.: Quantum simulators. Science 326, 108–111 (2009)

    Article  ADS  Google Scholar 

  57. Wang, B.X., Tao, M.J., Ai, Q.: Efficient quantum simulation of photosynthetic light harvesting. npj. Quantum Inf. 4, 52 (2018)

    Article  Google Scholar 

  58. Kim, Y.H., Kulik, S.P., Shih, Y.: Quantum teleportation of a polarization state with a complete bell state measurement. Phys. Rev. Lett. 86, 1370–1373 (2001)

    Article  ADS  Google Scholar 

  59. Walton, Z.D., Abouraddy, A.F., Sergienko, A.V., Saleh, B.E.A., Teich, M.C.: Decoherence-free subspaces in quantum key distribution. Phys. Rev. Lett. 91, 087901 (2003)

    Article  ADS  Google Scholar 

  60. Li, X.H., Deng, F.G., Zhou, H.Y.: Efficient quantum key distribution over a collective noise channel. Phys. Rev. A 78, 022321 (2008)

    Article  ADS  Google Scholar 

  61. Deng, F.G., Li, X.H., Li, T.: Quantum error rejection and fault tolerant quantum communication. Acta Phys. Sin. 67, 130301 (2018)

    Google Scholar 

  62. Song, X.K., Zhang, H., Ai, Q., Qiu, J., Deng, F.G.: Shortcuts to adiabatic holonomic quantum computation in decoherence-free subspace with transitionless quantum driving algorithm. New J. Phys. 18, 023001 (2016)

    Article  ADS  Google Scholar 

  63. Kalamidas, D.: Single-photon quantum error rejection and correction with linear optics. Phys. Lett. A 343, 331–335 (2005)

    Article  ADS  MATH  Google Scholar 

  64. Li, X.H., Deng, F.G., Zhou, H.Y.: Faithful qubit transmission against collective noise without ancillary qubits. Appl. Phys. Lett. 91, 144101 (2007)

    Article  ADS  Google Scholar 

  65. Li, T., Wang, G.Y., Deng, F.G., Long, G.L.: Deterministic error correction for nonlocal spatial-polarization hyperentanglement. Sci. Rep. 6, 20677 (2016)

    Article  ADS  Google Scholar 

  66. Jiang, Y.X., Guo, P.L., Gao, C.Y., Wang, H.B., Alzahrani, F., Hobiny, A., Deng, F.G.: Self-error-rejecting photonic qubit transmission in polarization-spatial modes with linear optical elements. Sci. China-Phys. Mech. Astron. 60, 120312 (2017)

    Article  ADS  Google Scholar 

  67. Yamamoto, T., Shimamura, J., Ödemir, S.K., Koashi, M., Imoto, N.: Faithful qubit distribution assisted by one additional qubit against collective noise. Phys. Rev. Lett. 95, 040503 (2005)

    Article  ADS  Google Scholar 

  68. Bennett, C.H., Brassard, G., Popescu, S., Schumacher, B., Smolin, J.A., Wootters, W.K.: Purification of noisy entanglement and faithful teleportation via noisy channels. Phys. Rev. Lett. 76, 722 (1996)

    Article  ADS  Google Scholar 

  69. Pan, J.W., Simon, C., Brukner, C., Zeilinger, A.: Entanglement purification for quantum communication. Nature 410, 1067–1070 (2001)

    Article  ADS  Google Scholar 

  70. Sheng, Y.B., Deng, F.G., Zhou, H.Y.: Efficient polarization-entanglement purification based on parametric down-conversion sources with cross-Kerr nonlinearity. Phys. Rev. A 77, 042308 (2008)

    Article  ADS  Google Scholar 

  71. Sheng, Y.B., Deng, F.G.: Deterministic entanglement purification and complete nonlocal Bell-state analysis with hyperentanglement. Phys. Rev. A 81, 032307 (2010)

    Article  ADS  Google Scholar 

  72. Sheng, Y.B., Deng, F.G.: One-step deterministic polarization entanglement purification using spatial entanglement. Phys. Rev. A 82, 044305 (2010)

    Article  ADS  Google Scholar 

  73. Li, X.H.: Deterministic polarization-entanglement purification using spatial entanglement. Phys. Rev. A 82, 044304 (2010)

    Article  ADS  Google Scholar 

  74. Deng, F.G.: One-step error correction for multipartite polarization entanglement. Phys. Rev. A 83, 062316 (2011)

    Article  ADS  Google Scholar 

  75. Sheng, Y.B., Zhou, L., Long, G.L.: Hybrid entanglement purification for quantum repeaters. Phys. Rev. A 88, 022302 (2013)

    Article  ADS  Google Scholar 

  76. Sheng, Y.B., Zhou, L.: Deterministic polarization entanglement purification using time-bin entanglement. Laser Phys. Lett. 11, 085203 (2014)

    Article  ADS  Google Scholar 

  77. Ren, B.C., Du, F.F., Deng, F.G.: Two-step hyperentanglement purification with the quantum-state-joining method. Phys. Rev. A 90, 052309 (2014)

    Article  ADS  Google Scholar 

  78. Wang, G.Y., Liu, Q., Deng, F.G.: Hyperentanglement purification for two-photon six-qubit quantum systems. Phys. Rev. A 94, 032319 (2016)

    Article  ADS  Google Scholar 

  79. Zhou, L., Sheng, Y.B.: Purification of logic-qubit entanglement. Sci. Rep. 6, 28813 (2016)

    Article  ADS  Google Scholar 

  80. Zhou, L., Sheng, Y.B.: Polarization entanglement purification for concatenated Greenberger-Horne-Zeilinger state. Ann. Phys. 10, 385 (2017)

    MathSciNet  MATH  Google Scholar 

  81. Deng, F.G., Ren, B.C., Li, X.H.: Quantum hyperentanglement and its applications in quantum information processing. Sci. Bull. 62, 46 (2017)

    Article  Google Scholar 

  82. Liu, Z.C., Hong, J.S., Guo, J.J., Li, T., Ai, Q., Alsaedi, A., Hayat, T., Deng, F.G.: Entanglement purification of nonlocal quantum-dot-confined electrons assisted by double-sided optical microcavities. Ann. Phys. (Berlin) 530, 1800029 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  83. Wang, G.Y., Li, T., Ai, Q., Alsaedi, A., Hayat, T., Deng, F.G.: Faithful entanglement purification for high-capacity quantum communication with two-photon four-qubit systems. Phys. Rev. Appl. 10, 054058 (2018)

    Article  ADS  Google Scholar 

  84. Bennett, C.H., Bernstein, H.J., Popescu, S., Schumacher, B.: Concentrating partial entanglement by local operations. Phys. Rev. A 53, 2046 (1996)

    Article  ADS  Google Scholar 

  85. Sheng, Y.B., Deng, F.G., Zhou, H.Y.: Nonlocal entanglement concentration scheme for partially entangled multipartite systems with nonlinear optics. Phys. Rev. A 77, 062325 (2008)

    Article  ADS  Google Scholar 

  86. Sheng, Y.B., Zhou, L., Zhao, S.M., Zheng, B.Y.: Efficient single-photon-assisted entanglement concentration for partially entangled photon pairs. Phys. Rev. A 85, 012307 (2012)

    Article  ADS  Google Scholar 

  87. Deng, F.G.: Optimal nonlocal multipartite entanglement concentration based on projection measurements. Phys. Rev. A 85, 022311 (2012)

    Article  ADS  Google Scholar 

  88. Sheng, Y.B., Zhou, L., Zhao, S.M.: Efficient two-step entanglement concentration for arbitrary W states. Phys. Rev. A 85, 042302 (2012)

    Article  ADS  Google Scholar 

  89. Ren, B.C., Du, F.F., Deng, F.G.: Hyperentanglement concentration for two-photon four-qubit systems with linear optics. Phys. Rev. A 88, 012302 (2013)

    Article  ADS  Google Scholar 

  90. Ren, B.C., Long, G.L.: General hyperentanglement concentration for photon systems assisted by quantum dot spins inside optical microcavities. Opt. Express 22, 6547–6561 (2014)

    Article  ADS  Google Scholar 

  91. Li, X.H., Ghose, S.: Hyperentanglement concentration for time-bin and polarization hyperentangled photons. Phys. Rev. A 91, 062302 (2015)

    Article  ADS  Google Scholar 

  92. Liu, J., Zhou, L., Zhong, W., Sheng, Y.B.: Logic Bell state concentration with parity check measurement. Front. Phys. 14, 21601 (2019)

    Article  Google Scholar 

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Acknowledgments

This work is supported by the National Natural Science Foundation of China under Grant No. 11674033, No. 11474026, and No. 11505007.

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He, WT., Wang, J., Zhang, TT. et al. High-Efficiency Three-Party Quantum Key Agreement Protocol with Quantum Dense Coding and Bell States. Int J Theor Phys 58, 2834–2846 (2019). https://doi.org/10.1007/s10773-019-04167-8

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