Abstract
Here we analyze the security of quantum dense coding protocol in which the keys are encoded on d-dimensional Hilbert space. The incoherent attack is considered during the qubits transmission through practical quantum channels. To show the performance of the protocol, the mutual information is numerically calculated under the potential eavesdropping behavior by applying a cloning-based individual attack, along with an upper bound on the error rate that ensures unconditional security against incoherent attacks.
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References
Jennewein, T., Simon, C., Weihs, G., Weinfurter, H., Zeilinger, A.: Quantum cryptography with entangled photons. Phys.Rev.Lett 84, 4729 (2000)
Bouwmeester, D., Pan, J. -W., Mattle, K., Eibl, M., Weinfurter, H., Zeilinger, A.: Experimental quantum teleportation. Nature 390, 575 (1997)
Hillery, M., Bužek, V., Berthiaume, A.: Quantum secret sharing. Phys. Rev. A 59(3), 1829 (1999)
Long, G.L., Liu, X.S.: Theoretically efficient high-capacity quantum-key-distribution scheme. Phys Rev A 65(3), 032302 (2002)
Chen, S.S., Zhou, L., Zhong, W., Sheng, Y. B.: Three-step three-party quantum secure direct communication. Science China Physics, Mechanics & Astronomy 61(9), 90312 (2018)
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. Science China Physics, Mechanics & Astronomy 60(12), 120313 (2017)
Sheng, Y.B., Zhou, L.: Distributed secure quantum machine learning. Science Bulletin 62(14), 1025–1029 (2017)
Bennett, C.H., Wiesner, S.J.: Communication via one-and two-particle operators on einstein-podolsky-rosen states. Phys. Rev. Lett. 69(20), 2881 (1992)
Gorbachev, V.N., Trubilko, A.I., Rodichkina, A.A., Zhiliba, A.I.: Teleportation and dense coding via a multiparticle quantum channel of the GHZ-class. Quantum Information & Computation 2, 367 (2000)
Shimizu, K., Imoto, N., Mukai, T.: Dense coding in photonic quantum communication with enhanced information capacity. Phys. Rev. A 59(2), 1092 (1999)
Bose, S., Vedral, V., Knight, P.L.: Multiparticle generalization of entanglement swapping. Phys. Rev. A 57(2), 822 (1998)
Hao, J.C., Li, C.-F., Guo, G.-C.: Controlled dense coding using the Greenberger-Horne-Zeilinger state. Phys. Rev. A 63(5), 054301 (2001)
Braunstein, S.L., Kimble, H.J.: Dense coding for continuous variables. In: Quantum Information with Continuous Variables, pp 95–103. Springer, Berlin (2000)
Liu, X.S., Long, G.L., Tong, D.M., Li, F.: General scheme for superdense coding between multiparties. Phys. Rev. A 65(2), 022304 (2002)
Das, T., Prabhu, R., Sen(De), A., Sen, U.: Distributed quantum dense coding with two receivers in noisy environments. Phys. Rev. A 92, 052330 (2015)
Li, X. -H., Ghose, S.: Hyperentangled bell-state analysis and hyperdense coding assisted by auxiliary entanglement. Phys. Rev. A 96, 020303 (2017)
Gisin, N., Ribordy, G., Tittel, W., Zbinden, H.: Quantum cryptography. Reviews of Modern Physics 74(1), 145 (2002)
Gao, F., Wen, Q. -Y., Zhu, F. -C.: Teleportation attack on the qsdc protocol with a random basis and order. Chinese Physics B 17(9), 3189 (2008)
Schauer, S., Suda, M.: A novel attack strategy on entanglement swapping qkd protocols. International Journal of Quantum Information 6(04), 841–858 (2008)
Gao, F., Qin, S.J., Guo, F., Wen, Q. -Y.: Dense-coding attack on three-party quantum key distribution protocols. IEEE Journal of Quantum Electronics 47(5), 630–635 (2011)
Gao, F., Guo, F., Wen, Q. -Y., Zhu, F. -C.: Revisiting the security of quantum dialogue and bidirectional quantum secure direct communication. Science in China Series G: Physics Mechanics and Astronomy 51(5), 559–566 (2008)
Mohamed Halip, N.H., Mokhtar, M., Buhari, A.: Simulation of bennet and brassard 84 Protocol with Eve’s attacks. In: 2014 IEEE 5th International Conference on Photonics (ICP), pp. 29–31 (2014)
Huttner, B., Imoto, N., Gisin, N., Mor, T.: Quantum cryptography with coherent states. Phys. Rev. A 51(3), 1863 (1995)
Brassard, G., Lütkenhaus, N., Mor, T., Sanders, B.C.: Limitations on practical quantum cryptography. Phys. Rev. Lett. 85(6), 1330 (2000)
Guo, Q., Zhai, S., Cheng, L. -Y., Wang, H. -F., Zhang, S.: Counterfactual quantum cloning without transmitting any physical particles. Phys. Rev. A 96, 052335 (2017)
Rui, P., Zhang, W., Liao, Y., Zhang, Z.: Economical phase-covariant quantum telecloning of a single polarization photon via quantum nondemolition detection. The European Physical Journal D 71(5), 107 (2017)
Bartkiewicz, K., Lemr, K., Černoch, A., Soubusta, J., Miranowicz, A.: Experimental eavesdropping based on optimal quantum cloning. Phys. Rev Lett. 110, 173601 (2013)
Bartkiewicz, K., Černoch, A., Lemr, K., Soubusta, J., Stobiń, ska, M.: Efficient amplification of photonic qubits by optimal quantum cloning. Phys. Rev A 89, 062322 (2014)
Cerf, N.J.: Acta Phys. Slov. 48, 115 (1998)
Cerf, N.J.: Pauli cloning of a quantum bit. Phys. Rev. Lett 84(19), 4497 (2000)
Cerf, N.J.: J. Mod. Opt. 47, 187 (2000)
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The authors gratefully acknowledge the support from the National Natural Science Foundation of China through Grants No. 61622103, 61671083 and No.61701035.
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Zhang, YX., Cao, C., Wang, TJ. et al. The Study of Security During Quantum Dense Coding in High-Dimensions. Int J Theor Phys 59, 1957–1965 (2020). https://doi.org/10.1007/s10773-019-04334-x
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DOI: https://doi.org/10.1007/s10773-019-04334-x