Abstract
The first rational quantum secure direct communication scheme is proposed, in which we use the game theory with incomplete information to model the rational behavior of the participant, and give the strategy space and utility function. The rational participant can get his maximal utility when he performs the protocol faithfully, and then the Nash equilibrium of the protocol can be achieved. Compared to the traditional schemes, our scheme will be more practical in the presence of rational participant.
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Bennett, C.H., Brassard, G.: Quantum cryptography: public-key distribution and coin tossing. In: IEEE International Conference on Computers, Systems, and Signal Processing, Bangalore, India, pp. 175–179 (1984)
Long, G.L., Liu, X.S.: Theoretically efficient high-capacity quantum-key-distribution scheme. Phys. Rev. A 65, 032302 (2002)
Deng, F.G., Long, G.L.: Secure direct communication with a quantum one-time pad. Phys. Rev. A 69, 052319 (2004)
Hu, J.Y., Yu, B., Jing, M.Y., et al.: Experimental quantum secure direct communication with single photons. Light Sci. Appl. 5, e16144 (2016)
Zhang, W., Ding, D.S., Sheng, Y.B., et al.: Quantum secure direct communication with quantum memory. Phys. Rev. Lett. 118, 220501 (2017)
Zhu, F., Zhang, W., Sheng, Y., et al.: Experimental long-distance quantum secure direct communication. Sci. Bull. 62, 1519–1524 (2017)
Bostrom, K., Felbinger, T.: Deterministic secure direct communication using entanglement. Phys. Rev. Lett. 89, 187902 (2002)
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)
Wang, C., Deng, F.G., Li, Y.S., et al.: Quantum secure direct communication with high-dimension quantum superdense coding. Phys. Rev. A 71, 044305 (2005)
Xia, Y., Fu, C.B., Li, F.Y., et al.: Controlled secure direct communication by using GHZ entangled state. J. Korean Phys. Soc. 47, 753–756 (2005)
Zhu, A.D., Xia, Y., Fan, Q.B., Zhang, S.: Secure direct communication based on secret transmitting order of particles. Phys. Rev. A 73, 022338 (2006)
Deng, F.G., Li, X.H., Li, C.Y., et al.: Quantum secure direct communication network with Einstein–Podolsky–Rosen pairs. Phys. Lett. A 359, 359–365 (2006)
Xia, Y., Song, J., Song, H.S.: Multiparty remote state preparation. J. Phys. B At. Mol. Opt. Phys. 40, 3719–3724 (2007)
Xiu, X.M., Dong, H.K., Li, D., Gao, Y.J., Chi, F.: Deterministic secure quantum communication using four-particle genuine entangled state and entangled swapping. Opt. Commun. 282, 2457–2459 (2009)
Wang, C., Hao, L., Song, S.Y., et al.: Quantum direct communication based on quantum search algorithm. Int. J. Quantum Inf. 8, 443–450 (2010)
Hao, L., Li, J.L., Long, G.L.: Eavesdropping in a quantum secret sharing protocol based on Grover algorithm and its solution. Sci. China Phys. Mech. Astron. 53, 491–495 (2010)
Gu, B., Huang, Y.G., Fang, X., Zhang, C.Y.: A two-step quantum secure direct communication protocol with hyperentanglement. Chin. Phys. B 20, 100309 (2011)
Shi, J., Gong, Y.X., Xu, P., Zhu, S.N., Zhan, Y.B.: Quantum secure direct communication by using three-dimensional hyperentanglement. Commun. Theor. Phys. 56, 831–836 (2011)
Liu, D., Chen, J.L., Jiang, W.: High-capacity quantum secure direct communication with single photons in both polarization and spatial-mode degrees of freedom. Int. J. Theor. Phys. 51, 2923–2929 (2012)
Li, Y.H., Li, X.L., Sang, M.H., Nie, Y.Y., Wang, Z.S.: Bidirectional controlled quantum teleportation and secure direct communication using five-qubit entangled state. Quantum Inf. Process. 12, 3835–3844 (2013)
Yu, C.H., Guo, G.D., Lin, S.: Quantum secure direct communication with authentication using two nonorthogonal states. Int. J. Theor. Phys. 52, 1937–1945 (2013)
Kao, S.H., Hwang, T.: Multiparty controlled quantum secure direct communication based on quantum search algorithm. Quantum Inf. Process. 12, 3791–3805 (2013)
Yadav, P., Srikanth, R., Pathak, A.: Two-step orthogonal-state-based protocol of quantum secure direct communication with the help of order-rearrangement technique. Quantum Inf. Process. 13, 2731–2743 (2014)
Zheng, C., Long, G.F.: Quantum secure direct dialogue using Einstein–Podolsky–Rosen pairs. Sci. China Phys. Mech. Astron. 57, 1238–1243 (2014)
Li, W.L., Chen, J.B., Wang, X.L., Li, C.: Quantum secure direct communication achieved by using multi-entanglement. Int. J. Theor. Phys. 54, 100–105 (2015)
Li, Y.B., Song, T.T., Huang, W., Zhan, W.W.: Fault-tolerant quantum secure direct communication protocol based on decoherence-free states. Int. J. Theor. Phys. 54, 589–597 (2015)
Tan, X.Q., Zhang, X.Q.: Controlled quantum secure direct communication by entanglement distillation or generalized measurement. Quantum Inf. Process. 15, 2137–2154 (2016)
Wang, H., Zhang, Y.Q., Liu, X.F., et al.: Efficient quantum dialogue using entangled states and entanglement swapping without information leakage. Quantum Inf. Process. 15, 2593–2603 (2016)
Luo, Y.P., Hwang, T.: Authenticated semi-quantum direct communication protocols using Bell states. Quantum Inf. Process. 15, 947–958 (2016)
Guerra, A.G.A.H., Rios, F.F.S., Ramos, R.V.: Quantum secure direct communication of digital and analog signals using continuum coherent states. Quantum Inf. Process. 15, 4747–4758 (2016)
Yang, L., Ma, H.Y., Zheng, C., et al.: Quantum communication scheme based on quantum teleportation. Acta Physica Sin. 66, 230303 (2017). (in Chinese)
Deng, F.G., Ren, B.C., Li, X.H.: Quantum hyperentanglement and its applications in quantum information processing. Sci. Bull. 62, 46–68 (2017)
Wu, F.Z., Yang, G.J., Wang, H.B., et al.: High-capacity quantum secure direct communication with two-photon six-qubit hyperentangled states. Sci. China Phys. Mech. Astron. 60, 120313 (2017)
Sheng, Y.B., Zhou, L.: Distributed secure quantum machine learning. Sci. Bull. 62, 1025–1029 (2017)
Zhou, N.R., Li, J.F., Yu, Z.B., et al.: New quantum dialogue protocol based on continuous-variable two-mode squeezed vacuum states. Quantum Inf. Process. 16, 4 (2017)
Wang, S.K., Zha, X.W., Wu, H.: Controlled secure direct communication with seven-qubit entangled states. Int. J. Theor. Phys. 57, 48–58 (2018)
Halpern, J., Teague, V.: Rational secret sharing and multiparty computation. In: Proceedings of the 36th Annual ACM Symposium on Theory of Computing, pp. 623–632. ACM Press, New York (2004)
Kol, G., Naor, M.: Cryptography and game theory: design protocols for exchanging information. In: Proceedings of the 5th Theory of Cryptography Conference, pp. 320–339. Springer, Berlin (2008)
Fuchsbauer, G., Katz, J., Naccache, D.: Efficient secret sharing in the standard communication model. In: Proceedings of the 7th Theory of Cryptography Conference, pp. 419–436. Springer, Berlin (2010)
Zhang, Z.F., Liu, M.L.: Rational secret sharing as extensive game. Sci. China Inf. Sci. 56, 1–13 (2013)
Maitra, A., De, S.J., Paul, G., Pal, A.K.: Proposal for quantum rational secret sharing. Phys. Rev. A 92, 022305 (2015)
Linstone, H.A., Turoff, M.: The Delphi Method: Techniques and Applications, 3rd edn, pp. 5–10, 202–235. Addison-Wesley, Boston (1979)
Okoli, C., Pawlowski, S.D.: The Delphi method as a research tool: an example, design considerations and applications. Inf. Manag. 42, 15–29 (2004)
Sheng, Y.B., Zhou, L.: Deterministic polarization entanglement purification using time-bin entanglement. Laser Phys. Lett. 11, 085203 (2014)
Sheng, Y.B., Zhou, L.: Deterministic entanglement distillation for secure double-server blind quantum computation. Sci. Rep. 5, 7815 (2015)
Liu, H.J., Xia, Y., Song, J.: Efficient hyperentanglement concentration for N-particle Greenberger–Horne–Zeilinger state assisted by weak cross-Kerr nonlinearity. Quantum Inf. Process. 15, 2033–2052 (2016)
Liu, H.J., Fan, L.L., Xia, Y., et al.: Efficient entanglement concentration for partially entangled cluster states with weak cross-Kerr nonlinearity. Quantum Inf. Process. 14, 2909–2928 (2015)
Zhou, L., Sheng, Y.B.: Recyclable amplification protocol for the single-photon entangled state. Laser Phys. Lett. 12, 045203 (2015)
Ou-Yang, Y., Feng, Z.F., Zhou, L., Sheng, Y.B.: Protecting single-photon entanglement with imperfect single-photon source. Quantum Inf. Process. 14, 635–651 (2015)
Mouzali, A., Merazka, F., Markham, D.: Quantum secret sharing with error correction. Commun. Theor. Phys. 58, 661–671 (2012)
Chen, R.K., Zhang, Y.Y., Shi, J.H., Li, F.G.: A multiparty error-correcting method for quantum secret sharing. Quantum Inf. Process. 13, 21–31 (2014)
Jennewein, T., Simon, C., Weihs, G., et al.: Quantum cryptography with entangled photons. Phys. Rev. Lett. 84, 4729–4732 (2000)
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. 43, 1–14 (2002)
Stucki, D., Gisin, N., Guinnard, O., et al.: Quantum key distribution over 67 km with a plug&play system. New J. Phys. 41, 1–8 (2002)
Beveratos, A., Brouri, R., Gacoin, T., et al.: Single photon quantum cryptography. Phys. Rev. Lett. 89, 187901 (2002)
Gobby, C., Yuan, Z.L., Shields, A.J.: Quantum key distribution over 122 km standard telecom fiber. Appl. Phys. Lett. 84, 3762–3764 (2004)
Deng, F.G., Long, G.L.: Controlled order rearrangement encryption for quantum key distribution. Phys. Rev. A 68, 042315 (2003)
Li, X.H., Deng, F.G., Zhou, H.Y.: Efficient quantum key distribution over a collective noise channel. Phys. Rev. A 78, 022321 (2008)
Jakobi, M., Simon, C., Gisin, N., et al.: Practical private database queries based on a quantum-key-distribution protocol. Phys. Rev. A 83, 022301 (2011)
Gao, F., Liu, B., Huang, W., Wen, Q.Y.: Postprocessing of the oblivious key in quantum private query. IEEE J. Sel. Top. Quantum Electron. 21, 6600111 (2015)
Wei, C.Y., Wang, T.Y., Gao, F.: Practical quantum private query with better performance in resisting joint-measurement attack. Phys. Rev. A 93, 042318 (2016)
Wei, C.Y., Cai, X.Q., Liu, B., et al.: A generic construction of quantum-oblivious-key-transfer-based private query with ideal database security and zero failure. IEEE Trans. Comput. 67, 2–8 (2018)
Acknowledgements
This study is supported by Natural Science Foundation of China (Grant No. 61602247) and Natural Science Foundation of Jiangsu Province (Grant No. BK20160840).
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Qin, H., Tang, W.K.S. & Tso, R. Establishing rational networking using the DL04 quantum secure direct communication protocol. Quantum Inf Process 17, 152 (2018). https://doi.org/10.1007/s11128-018-1925-7
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DOI: https://doi.org/10.1007/s11128-018-1925-7