Abstract
As an unavoidable factor of real-world implementation of quantum cryptograph, quantum noise severally affects the security and reliability of the quantum system. In this paper, we study how QSS, an important branch of quantum cryptograph, is affected by noise or decoherence. QSS protocols for sharing classical information and quantum states are studied in four types of noise that usually encountered in real-world, i.e., the bit-flip, phase-flip (phase-damping), depolarizing and amplitude-damping noise, respectively. Two methods are introduced to evaluate the effect of noise. For the QSS protocol sharing classical information, the efficiency for generating secret key is used. Our results show that the efficiencies are quiet different from each other in four types of noise. While for the protocol sharing quantum states, the output states and the state-independent average fidelity are studied, respectively. It indicates that the players will get two different output states in the amplitude-damping noise, but get one output state in the other three types of noise. Besides, the state-independent average fidelity behaves differently from each other. Our study will be helpful for analyzing and improving quantum secure communications protocols in real-world.
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Bennett, C.H., Brassard, G.: Quantum cryptography: public key distribution and coin tossing. In: Proceedings of IEEE International Conference on Computers Systems and Signal Processing, New York, pp. 175–179. IEEE (1984)
Hillery, M., Bužek, V., Berthiaume, A.: Quantum secret sharing. Phys. Rev. A 59(3), 1829 (1999)
Terhal, B.M., DiVincenzo, D.P., Leung, D.W.: Hiding bits in bell states. Phys. Rev. Lett. 86(25), 5807 (2001)
Wang, M.M., Chen, X.B., Yang, Y.X.: A blind quantum signature protocol using the GHZ states. Sci. China Phys. Mech. Astron. 56(9), 1636 (2013)
Shamir, A.: How to share a secret. Commun. ACM 22(11), 612 (1979)
Xia, Z., Wang, X., Sun, X., Wang, B.: Steganalysis of least significant bit matching using multi-order differences. Secur. Commun. Netw. 7(8), 1283 (2014)
Xia, Z., Wang, X., Sun, X., Liu, Q., Xiong, N.: Steganalysis of LSB matching using differences between nonadjacent pixels. Multimed. Tools Appl. 75(4), 1947 (2016)
Ma, T., Zhou, J., Tang, M., Tian, Y., Al-Dhelaan, A., Al-Rodhaan, M., Lee, S.: Social network and tag sources based augmenting collaborative recommender system. IEICE Trans. Inf. Syst. E98–D(4), 902 (2015)
Grover, L.K.: Quantum mechanics helps in searching for a needle in a haystack. Phys. Rev. Lett. 79(2), 325 (1997)
Xia, Z., Wang, X., Sun, X., Wang, Q.: A secure and dynamic multi-keyword ranked search scheme over encrypted cloud data. IEEE Trans. Parallel Distrib. Syst. 27(2), 340 (2016)
Fu, Z., Sun, X., Liu, Q., Zhou, L., Shu, J.: Achieving efficient cloud search services: multi-keyword ranked search over encrypted cloud data supporting parallel computing. IEICE Trans. Commun. E98.B(1), 190 (2015)
Fu, Z., Ren, K., Shu, J., Sun, X., Huang, F.: Enabling personalized search over encrypted outsourced data with efficiency improvement. IEEE Trans. Parallel Distrib. Syst. 27(9), 2546 (2016)
Blakley, G.R.: Safeguarding cryptographic key. In: Proceedings of the 1979 AFIPS National Computer Conference, Monval, NJ, USA, pp. 313–317. AFIPS Press (1979)
Xiao, L., Long, G.L., Deng, F.G., Pan, J.W.: Efficient multiparty quantum-secret-sharing schemes. Phys. Rev. A 69(5), 052307 (2004)
Yu, I.C., Lin, F.L., Huang, C.Y.: Quantum secret sharing with multilevel mutually (un) biased bases. Phys. Rev. A 78, 12344 (2008)
Guo, G.P., Guo, G.C.: Quantum secret sharing without entanglement. Phys. Lett. A 310(4), 247 (2003)
Zhang, Z.J., Li, Y., Man, Z.X.: Multiparty quantum secret sharing. Phys. Rev. A 71(4), 044301 (2005)
Cleve, R., Gottesman, D., Lo, H.K.: How to share a quantum secret. Phys. Rev. Lett. 83(3), 648 (1999)
Gottesman, D.: Theory of quantum secret sharing. Phys. Rev. A 61(4), 042311 (2000)
Lance, A.M., Symul, T., Bowen, W.P., Sanders, B.C., Lam, P.K.: Tripartite quantum state sharing. Phys. Rev. Lett. 92(17), 177903 (2004)
Badzia̧g, P., Horodecki, M., Horodecki, P., Horodecki, R.: Local environment can enhance fidelity of quantum teleportation. Phys. Rev. A 62(1), 012311 (2000)
Taketani, B.G., de Melo, F., de Matos Filho, R.L.: Optimal teleportation with a noisy source. Phys. Rev. A 85(2), 020301 (2012)
Knoll, L.T., Schmiegelow, C.T., Larotonda, M.A.: Noisy quantum teleportation: an experimental study on the influence of local environments. Phys. Rev. A 90(4), 042332 (2014)
Rigolin, G., Fortes, R.: Fighting noise with noise in realistic quantum teleportation. Phys. Rev. A 92(1), 012338 (2015)
Xiang, G.Y., Li, J., Yu, B., Guo, G.C.: Remote preparation of mixed states via noisy entanglement. Phys. Rev. A 72(1), 012315 (2005)
Chen, A.X., Deng, L., Li, J.H., Zhan, Z.M.: Remote preparation of an entangled state in nonideal conditions. Commun. Theor. Phys. 46(2), 221 (2006)
Guan, X.W., Chen, X.B., Wang, L.C., Yang, Y.X.: Joint remote preparation of an arbitrary two-qubit state in noisy environments. Int. J. Theor. Phys. 53(7), 2236 (2014)
Liang, H.Q., Liu, J.M., Feng, S.S., Chen, J.G., Xu, X.Y.: Effects of noises on joint remote state preparation via a GHZ-class channel. Quantum Inf. Process. 14(10), 3857 (2015)
Wang, M.M., Qu, Z.G.: Effect of quantum noise on deterministic joint remote state preparation of a qubit state via a GHZ channel. Quantum Inf. Process. 15(11), 4805 (2016)
Thapliyal, K., Pathak, A., Banerjee, S.: Quantum cryptography over non-Markovian channels (2016). arXiv:1608.06071
Sharma, V., Thapliyal, K., Pathak, A., Banerjee, S.: A comparative study of protocols for secure quantum communication under noisy environment: single-qubit-based protocols versus entangled-state-based protocols. Quantum Inf. Process. 15(11), 4681 (2016)
Wang, M.M., Wang, W., Chen, J.G., Farouk, A.: Secret sharing of a known arbitrary quantum state with noisy environment. Quantum Inf. Process. 14(1), 4211 (2015)
Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)
Karlsson, A., Koashi, M., Imoto, N.: Quantum entanglement for secret sharing and secret splitting. Phys. Rev. A 59(1), 162 (1999)
Qin, S.J., Gao, F., Wen, Q.Y., Zhu, F.C.: Cryptanalysis of the Hillery-Buzcaronek-Berthiaume quantum secret-sharing protocol. Phys. Rev. A 76(6), 062324 (2007)
Gisin, N., Ribordy, G., Tittel, W., Zbinden, H.: Quantum cryptography. Rev. Mod. Phys. 74, 145 (2002)
Acknowledgments
This project was supported by NSFC (Grant Nos. 61601358, 61373131), PAPD and CICAEET.
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Wang, MM., Qu, ZG., Elhoseny, M. (2017). Quantum Secret Sharing in Noisy Environment. In: Sun, X., Chao, HC., You, X., Bertino, E. (eds) Cloud Computing and Security. ICCCS 2017. Lecture Notes in Computer Science(), vol 10603. Springer, Cham. https://doi.org/10.1007/978-3-319-68542-7_9
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DOI: https://doi.org/10.1007/978-3-319-68542-7_9
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