Abstract
Sequential quantum secret sharing (QSS) schemes do not use entangled states for secret sharing, rather they rely on sequential operations of the players on a single state which is circulated between the players. In order to check the viability of these schemes under imperfect operations and noise in the channels, we consider one such scheme in detail and show that under moderate conditions it is still possible to extract viable secure shared keys in this scheme. Although we specifically consider only one type of sequential scheme and three different noise models, our method is fairly general to be applied to other QSS schemes and noise models as well.
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Bennett, C.H., Brassard, G.: Quantum cryptography: public keydistribution and coin tossing. In: Proceedings of IEEEInternational Conference on Computers, Systems and SignalProcessing, vol. 175, pp. 8. New York (1984)
Ekert, A.: Quantum cryptography based on Bell’s theorem. Phys. Rev. Lett. 67, 661–663 (1991)
Hillery, M., Buzek, V., Berthiaume, A.: Quantum secret sharing. Phys. Rev. A 59, 1829 (1999)
De Sen, A., Sen, U., Zukowski, M.: Multiqubit W states lead to stronger nonclassicality than Greenberger–Horne–Zeilinger states. Phys. Rev. A 68, 032309 (2003)
Xiao, L., Long, G.L., Deng, F.-G., Pan, J.-W.: Efficient multiparty quantum-secret-sharing schemes. Phys. Rev. A 59, 1829 (1999)
Karlsson, A., Koashi, M., Imoto, N.: Quantum entanglement for secret sharing and secret splitting. Phys. Rev. A 59, 162 (1999)
Xiao, L., Lu Long, G., Deng, F.-G., Pan, J.-W.: Efficient multiparty quantum-secret-sharing schemes. Phys. Rev. A 69, 052307 (2004)
Zhang, Z-j, Man, Z-x: Multiparty quantum secret sharing of classical messages based on entanglement swapping. Phys. Rev. A 72, 022303 (2005)
Deng, F.-G., Long, G.L., Zhou, H.-Y.: Probabilistic teleportation of an arbitrary GHZ-class state with a pure entangled two-particle quantum channel and its application in quantum state sharing. Phys. Lett. A 340, 43 (2005)
Bagherinezhad, S., Karimipour, V.: Quantum secret sharing based on reusable Greenberger–Horne–Zeilinger states as secure carriers. Phys. Rev. A 67, 044302 (2003)
Chen, Y.-A., et al.: Experimental quantum secret sharing and third-man quantum cryptography. Phys. Rev. Lett. 95, 200502 (2005)
Gaertner, S., Kurtsiefer, C., Bourennane, M., Weinfurter, H.: Experimental demonstration of four-party quantum secret sharing. Phys. Rev. Lett. 98, 020503 (2007)
Tyc, T., Sanders, B.C.: How to share a continuous-variable quantum secret by optical interferometry. Phys. Rev. A 65, 042310 (2002)
Lance, A.M., Symul, T., Bowen, W.P., Tyc, T., Sanders, B.C., Lam, P.K.: Continuous variable (2,3) threshold quantum secret sharing schemes. New J. Phys. 5, 4 (2003)
Lance, A.M., Symul, T., Bowen, W.P., Sanders, B.C., Lam, P.K.: Tripartite quantum state sharing. Phys. Rev. Lett. 92, 177903 (2004)
Grosshans, F., Van Assche, G., Wenger, J., Brouri, R., Cerf, N.J., Grangiera, P.: Quantum key distribution using gaussian-modulated coherent states. Nature 421, 238–241 (2003)
Grosshans, F., Grangier, P.: Continuous variable quantum cryptography using coherent states. Phys. Rev. Lett. 88, 057902 (2002)
Schmid, C., Trojek, P., Bourennane, M., Kurtsiefer, C., Zukowski, M., Weinfurter, H.: Single qubit quantum secret sharing. Phys. Rev. Lett. 95, 230505 (2005)
Yan, F.-L., Gao, T.: Quantum secret sharing between multiparty and multiparty without entanglement. Phys. Rev. A 72, 012304 (2005)
He, G.-P.: Secret sharing without monitoring signal disturbance. Phys. Rev. Lett. 98, 028901 (2007)
Karimipour, V., Asoudeh, M.: Quantum secret sharing and random hopping; using single states instead of entanglement. Phys. Rev. A 92, 030301 (2015). (Rapid Communications)
Tavakoli, A., Herbauts, I., Zukowski, M., Bourennane, M.: Sequential quantum secret sharing in noisy environments (preprint). arXiv:1501.05582
Chen, K., Lo, H.-K.: Multi-partite quantum cryptographic protocols with noisy GHZ states. Quantum Inf. Comput. 7, 689 (2007)
Kogias, I., Xiang, Y., He, Q., Adesso, G.: Unconditional security of entanglement-based continuous-variable quantum secret sharing. Phys. Rev. A 95, 012315 (2017)
Ray, M., Chatterjee, S., Chakrabarty, I.: Sequential quantum secret sharing in a noisy environment aided with weak measurements. Phys. J. D 70, 114 (2016)
Adhikari, S., Chakrabarty, I., Agrawal, P.: Probabilistic secret sharing through noisy quantum channels. Quantum Inf. Comput. 12, 0253 (2012)
Bohmann, M., Sperling, J., Vogel, W.: Entanglement and phase properties of noisy NOON states. Phys. Rev. A 91, 042332 (2015)
Bohmann, M., Sperling, J., Vogel, W.: Entanglement verification ofnoisy NOON states. Phys. Rev. A 96, 012321 (2017)
Zhang, Z-j, Li, Y., Man, Z-x: Multiparty quantum secret sharing. Phys. Rev. A 71, 044301 (2005)
Zhu, X., Fan, Z.: Secure direct communication based on secret transmitting order of particles. Phys. Rev. A 73, 022338 (2006)
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, 044302 (2005)
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)
Schmid, C., et al.: Reply to comment on experimental single qubit quantum secret sharing. Phys. Rev. Lett. 98, 028902 (2007)
He, G.P., Wang, Z.D.: Single qubit quantum secret sharing with improved security. Quantum Inf. Comput. 10, 28 (2010)
Lance, A.M., Symul, T., Bowen, W.P., Tyc, T., Sanders, B.C., Lam, P.K.: Continuous variable (2, 3) threshold quantum secret sharing schemes. New J. Phys. 5, 4 (2003)
Markham, D., Sanders, B.C.: Graph states for quantum secret sharing. Phys. Rev. A 78, 042309 (2008)
Lau, H.-K., Weedbrook, C.: Quantum secret sharing with continuous-variable cluster states. Phys. Rev. A 88, 042313 (2013)
Wu, Y., Cai, R., He, G., Zhang, J.: Quantum secret sharing with continuous variable graph state. Quantum Inf. Proc. 13, 1085 (2014)
Acknowledgements
This work was financially supported by the Grant no. 96011347 from Iran National Science Foundation (INSF). M. A. would like to thank Abdus Salam International Center for Theoretical Physics (ICTP), where part of this research was carried out. She also thanked V. Karimipour for many discussions and Fabio Benatti for his valuable comments.
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Khakbiz, P., Asoudeh, M. Sequential quantum secret sharing in noisy environments. Quantum Inf Process 18, 11 (2019). https://doi.org/10.1007/s11128-018-2123-3
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DOI: https://doi.org/10.1007/s11128-018-2123-3