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Published in: Quantum Information Processing 10/2019

01-10-2019

New quantum key agreement protocols based on Bell states

Authors: Yu-Guang Yang, Bo-Ran Li, Dan Li, Yi-Hua Zhou, Wei-Min Shi

Published in: Quantum Information Processing | Issue 10/2019

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Abstract

We present a new two-party quantum key agreement (QKA) protocol based on Bell states. The participant transmits Bell states directly by inserting decoy photons in them randomly. The protocol is secure against the outsider attack and participant attack. Finally, it is generalized to multi-party QKA based on Bell states.

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Literature
1.
go back to reference 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, pp. 175–179. IEEE, New York (1984) 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, pp. 175–179. IEEE, New York (1984)
4.
go back to reference Boström, K., Felbinger, T.: Deterministic secure direct communication using entanglement. Phys. Rev. Lett. 89, 187902 (2002)ADSCrossRef Boström, K., Felbinger, T.: Deterministic secure direct communication using entanglement. Phys. Rev. Lett. 89, 187902 (2002)ADSCrossRef
5.
go back to reference 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)ADSCrossRef 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)ADSCrossRef
7.
go back to reference Karlsson, A., Koashi, M., Imoto, N.: Quantum entanglement for secret sharing and secret splitting. Phys. Rev. A 59, 162–168 (1999)ADSCrossRef Karlsson, A., Koashi, M., Imoto, N.: Quantum entanglement for secret sharing and secret splitting. Phys. Rev. A 59, 162–168 (1999)ADSCrossRef
8.
go back to reference Dušek, M., Haderka, O., Hendrych, M., Myska, R.: Quantum identification system. Phys. Rev. A 60, 149–156 (1999)ADSCrossRef Dušek, M., Haderka, O., Hendrych, M., Myska, R.: Quantum identification system. Phys. Rev. A 60, 149–156 (1999)ADSCrossRef
9.
go back to reference Yang, Y.G., Wen, Q.Y.: An efficient two-party quantum private comparison protocol with decoy photons and two-photon entanglement. J. Phys. A: Math. Theor. 42(5), 055305 (2009)ADSMathSciNetMATHCrossRef Yang, Y.G., Wen, Q.Y.: An efficient two-party quantum private comparison protocol with decoy photons and two-photon entanglement. J. Phys. A: Math. Theor. 42(5), 055305 (2009)ADSMathSciNetMATHCrossRef
10.
11.
go back to reference Chen, X.B., Xu, G., Niu, X.X., Wen, Q.Y., Yang, Y.X.: An efficient protocol for the private comparison of equal information based on the triplet entangled state and single particle measurement. Opt. Commun. 283(7), 1561–1565 (2010)ADSCrossRef Chen, X.B., Xu, G., Niu, X.X., Wen, Q.Y., Yang, Y.X.: An efficient protocol for the private comparison of equal information based on the triplet entangled state and single particle measurement. Opt. Commun. 283(7), 1561–1565 (2010)ADSCrossRef
12.
go back to reference Yang, Y.-G., Liu, Z.-C., Li, J., Chen, X.-B., Zuo, H.-J., Zhou, Y.-H., Shi, W.-M.: Theoretically extensible quantum digital signature with starlike cluster states. Quantum Inf. Process. 16(1), 1–15 (2017)MATHCrossRef Yang, Y.-G., Liu, Z.-C., Li, J., Chen, X.-B., Zuo, H.-J., Zhou, Y.-H., Shi, W.-M.: Theoretically extensible quantum digital signature with starlike cluster states. Quantum Inf. Process. 16(1), 1–15 (2017)MATHCrossRef
13.
go back to reference Yang, Y.-G., Lei, H., Liu, Z.-C., Zhou, Y.-H., Shi, W.-M.: Arbitrated quantum signature scheme based on cluster states. Quantum Inf. Process. 15(6), 2487–2497 (2016)ADSMathSciNetMATHCrossRef Yang, Y.-G., Lei, H., Liu, Z.-C., Zhou, Y.-H., Shi, W.-M.: Arbitrated quantum signature scheme based on cluster states. Quantum Inf. Process. 15(6), 2487–2497 (2016)ADSMathSciNetMATHCrossRef
14.
go back to reference Jiang, D.-H., Xu, Y.-L., Xu, G.-B.: Arbitrary quantum signature based on local indistinguishability of orthogonal product states. Int. J. Theor. Phys. 58(3), 1036–1045 (2019)MathSciNetMATHCrossRef Jiang, D.-H., Xu, Y.-L., Xu, G.-B.: Arbitrary quantum signature based on local indistinguishability of orthogonal product states. Int. J. Theor. Phys. 58(3), 1036–1045 (2019)MathSciNetMATHCrossRef
15.
go back to reference Wang, T.-Y., Cai, X.Q., Ren, Y.L., Zhang, R.L.: Security of quantum digital signature. Sci. Rep. 5, 9231 (2015)CrossRef Wang, T.-Y., Cai, X.Q., Ren, Y.L., Zhang, R.L.: Security of quantum digital signature. Sci. Rep. 5, 9231 (2015)CrossRef
16.
go back to reference Gao, F., Liu, B., Huang, W., Wen, Q.Y.: Postprocessing of the oblivious key in quantum private query. IEEE. J. Sel. Top. Quant. 21, 6600111 (2015) Gao, F., Liu, B., Huang, W., Wen, Q.Y.: Postprocessing of the oblivious key in quantum private query. IEEE. J. Sel. Top. Quant. 21, 6600111 (2015)
17.
go back to reference 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)ADSCrossRef 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)ADSCrossRef
18.
go back to reference Yang, Y.-G., Liu, Z.-C., Chen, X.-B., Zhou, Y.-H., Shi, W.-M.: Robust QKD-based private database queries based on alternative sequences of single-qubit measurements. Sci. Chin. Phys. Mech. Astron. 60(12), 120311 (2017)ADSCrossRef Yang, Y.-G., Liu, Z.-C., Chen, X.-B., Zhou, Y.-H., Shi, W.-M.: Robust QKD-based private database queries based on alternative sequences of single-qubit measurements. Sci. Chin. Phys. Mech. Astron. 60(12), 120311 (2017)ADSCrossRef
19.
go back to reference Yang, Y.-G., Liu, Z.-C., Li, J., Chen, X.-B., Zuo, H.-J., Zhou, Y.-H., Shi, W.-M.: Quantum private query with perfect user privacy against a joint-measurement attack. Phys. Lett. A 380(48), 4033–4038 (2016)ADSMATHCrossRef Yang, Y.-G., Liu, Z.-C., Li, J., Chen, X.-B., Zuo, H.-J., Zhou, Y.-H., Shi, W.-M.: Quantum private query with perfect user privacy against a joint-measurement attack. Phys. Lett. A 380(48), 4033–4038 (2016)ADSMATHCrossRef
20.
go back to reference Yang, Y.-G., Liu, Z.C., Chen, X.B., Cao, W.F., Zhou, Y.H., Shi, W.M.: Novel classical post-processing for quantum key distribution-based quantum private query. Quantum Inf. Process. 15, 3833–3840 (2016)ADSMathSciNetMATHCrossRef Yang, Y.-G., Liu, Z.C., Chen, X.B., Cao, W.F., Zhou, Y.H., Shi, W.M.: Novel classical post-processing for quantum key distribution-based quantum private query. Quantum Inf. Process. 15, 3833–3840 (2016)ADSMathSciNetMATHCrossRef
21.
go back to reference Gao, F., Liu, B., Wen, Q.-Y.: Flexible quantum private queries based on quantum key distribution. Opt. Exp. 20, 17411–17420 (2012)ADSCrossRef Gao, F., Liu, B., Wen, Q.-Y.: Flexible quantum private queries based on quantum key distribution. Opt. Exp. 20, 17411–17420 (2012)ADSCrossRef
22.
go back to reference Yang, Y.-G., Sun, S.-J., Xu, P., Tian, J.: Flexible protocol for quantum private query based on B92 protocol. Quantum Inf. Process. 13, 805–813 (2014)ADSMathSciNetCrossRef Yang, Y.-G., Sun, S.-J., Xu, P., Tian, J.: Flexible protocol for quantum private query based on B92 protocol. Quantum Inf. Process. 13, 805–813 (2014)ADSMathSciNetCrossRef
23.
go back to reference Gao, F., Qin, S.J., Huang, W., Wen, Q.Y.: Quantum private query: a new kind of practical quantum cryptographic protocols. Sci. China-Phys. Mech. Astron. 62, 070301 (2019)CrossRef Gao, F., Qin, S.J., Huang, W., Wen, Q.Y.: Quantum private query: a new kind of practical quantum cryptographic protocols. Sci. China-Phys. Mech. Astron. 62, 070301 (2019)CrossRef
24.
go back to reference Yang, Y.-G., Guo, X.-P., Xu, G., Chen, X.-B., Li, J., Zhou, Y.-H., Shi, W.-M.: Reducing the communication complexity of quantum private database queries by subtle classical post-processing with relaxed quantum ability. Comput. Secur. 81, 15–24 (2019)CrossRef Yang, Y.-G., Guo, X.-P., Xu, G., Chen, X.-B., Li, J., Zhou, Y.-H., Shi, W.-M.: Reducing the communication complexity of quantum private database queries by subtle classical post-processing with relaxed quantum ability. Comput. Secur. 81, 15–24 (2019)CrossRef
26.
go back to reference Zhou, N., Zeng, G., Xiong, J.: Quantum key agreement protocol. Electron. Lett. 40(18), 1149 (2004)CrossRef Zhou, N., Zeng, G., Xiong, J.: Quantum key agreement protocol. Electron. Lett. 40(18), 1149 (2004)CrossRef
27.
28.
go back to reference 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)ADSMathSciNetMATHCrossRef 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)ADSMathSciNetMATHCrossRef
29.
go back to reference 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)ADSMathSciNetMATHCrossRef 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)ADSMathSciNetMATHCrossRef
30.
go back to reference Liu, W.-J., Xu, Y., Yang, C.-N., Gao, P.-P., Yu, W.-B.: An efficient and secure arbitrary N-party quantum key agreement protocol using Bell states. Int. J. Theor. Phys. 57, 195–207 (2018)MathSciNetMATHCrossRef Liu, W.-J., Xu, Y., Yang, C.-N., Gao, P.-P., Yu, W.-B.: An efficient and secure arbitrary N-party quantum key agreement protocol using Bell states. Int. J. Theor. Phys. 57, 195–207 (2018)MathSciNetMATHCrossRef
31.
go back to reference Chong, S.K., Hwang, T.: Quantum key agreement protocol based on BB84. Opt. Commun. 283, 1192–1195 (2010)ADSCrossRef Chong, S.K., Hwang, T.: Quantum key agreement protocol based on BB84. Opt. Commun. 283, 1192–1195 (2010)ADSCrossRef
32.
33.
go back to reference 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)MathSciNetMATHCrossRef 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)MathSciNetMATHCrossRef
34.
go back to reference 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)ADSMathSciNetMATHCrossRef 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)ADSMathSciNetMATHCrossRef
35.
go back to reference 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)ADSMathSciNetMATHCrossRef 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)ADSMathSciNetMATHCrossRef
36.
38.
go back to reference 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)MATHCrossRef 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)MATHCrossRef
40.
go back to reference Wang, S.-S., Xu, G.-B., Liang, X.-Q., Wu, Y.-L.: Multiparty quantum key agreement with four-qubit symmetric W state. Int. J. Theor. Phys. 57(12), 3716–3726 (2018)MathSciNetMATHCrossRef Wang, S.-S., Xu, G.-B., Liang, X.-Q., Wu, Y.-L.: Multiparty quantum key agreement with four-qubit symmetric W state. Int. J. Theor. Phys. 57(12), 3716–3726 (2018)MathSciNetMATHCrossRef
41.
go back to reference Zhou, N.-R., Min, S.-Q., Chen, H.-Y., Gong, L.-H.: Three-party quantum key agreement protocol with seven-qubit entangled states. Int. J. Theor. Phys. 57, 3505–3513 (2018)MATHCrossRef Zhou, N.-R., Min, S.-Q., Chen, H.-Y., Gong, L.-H.: Three-party quantum key agreement protocol with seven-qubit entangled states. Int. J. Theor. Phys. 57, 3505–3513 (2018)MATHCrossRef
42.
go back to reference Cabello, A.: Quantum key distribution in the Holevo limit. Phys. Rev. Lett. 85, 5635–5638 (2000)ADSCrossRef Cabello, A.: Quantum key distribution in the Holevo limit. Phys. Rev. Lett. 85, 5635–5638 (2000)ADSCrossRef
43.
go back to reference Zhao, Q.L., Li, X.Y.: A bargmann system and the involutive solutions associated with a new 4-order lattice hierarchy. Anal. Math. Phys. 6(3), 237–254 (2016)MathSciNetMATHCrossRef Zhao, Q.L., Li, X.Y.: A bargmann system and the involutive solutions associated with a new 4-order lattice hierarchy. Anal. Math. Phys. 6(3), 237–254 (2016)MathSciNetMATHCrossRef
45.
go back to reference Zhang, J.K., Wu, X.J., Xing, L.S., Zhang, C.: Bifurcation analysis of five-level cascaded H-bridge inverter using proportional-resonant plus time-delayed feedback. Int. J. Bifurc. Chaos. 26(11), 1630031 (2016)MathSciNetMATHCrossRef Zhang, J.K., Wu, X.J., Xing, L.S., Zhang, C.: Bifurcation analysis of five-level cascaded H-bridge inverter using proportional-resonant plus time-delayed feedback. Int. J. Bifurc. Chaos. 26(11), 1630031 (2016)MathSciNetMATHCrossRef
46.
go back to reference Liang, X., Gao, F., Zhou, C.-B., Wang, Z., Yang, X.-J.: An anomalous diffusion model based on a new general fractional operator with the Mittag-Leffler function of Wiman type. Adv. Differ. Equ. 2018(25) (2018) Liang, X., Gao, F., Zhou, C.-B., Wang, Z., Yang, X.-J.: An anomalous diffusion model based on a new general fractional operator with the Mittag-Leffler function of Wiman type. Adv. Differ. Equ. 2018(25) (2018)
47.
go back to reference Wang, J., Liang, K., Huang, X., Wang, Z., Shen, H.: Dissipative fault-tolerant control for nonlinear singular perturbed systems with Markov jumping parameters based on slow state feedback. Appl. Math. Comput. 328, 247–262 (2018)MathSciNetMATH Wang, J., Liang, K., Huang, X., Wang, Z., Shen, H.: Dissipative fault-tolerant control for nonlinear singular perturbed systems with Markov jumping parameters based on slow state feedback. Appl. Math. Comput. 328, 247–262 (2018)MathSciNetMATH
48.
go back to reference Cui, Y.J.: Uniqueness of solution for boundary value problems for fractional differential equations. Appl. Math. Lett. 51, 48–54 (2016)MathSciNetMATHCrossRef Cui, Y.J.: Uniqueness of solution for boundary value problems for fractional differential equations. Appl. Math. Lett. 51, 48–54 (2016)MathSciNetMATHCrossRef
49.
go back to reference Meng, X.Z., Zhao, S.N., Feng, T., Zhang, T.H.: Dynamics of a novel nonlinear stochastic Sis epidemic model with double epidemic hypothesis. J. Math. Anal. Appl. 433(1), 227–242 (2016)MathSciNetMATHCrossRef Meng, X.Z., Zhao, S.N., Feng, T., Zhang, T.H.: Dynamics of a novel nonlinear stochastic Sis epidemic model with double epidemic hypothesis. J. Math. Anal. Appl. 433(1), 227–242 (2016)MathSciNetMATHCrossRef
50.
go back to reference Yin, C., Cheng, Y.H., Zhong, S.M., Bai, Z.B.: Fractional-order switching type control law design for adaptive sliding mode technique of 3d fractional-order nonlinear systems. Complexity 21(6), 363–373(2016)MathSciNetCrossRef Yin, C., Cheng, Y.H., Zhong, S.M., Bai, Z.B.: Fractional-order switching type control law design for adaptive sliding mode technique of 3d fractional-order nonlinear systems. Complexity 21(6), 363–373(2016)MathSciNetCrossRef
51.
52.
go back to reference Liu, F., Chen, T., Wu, H.X.: A note on the endpoint regularity of the Hardy-littlewood maximal functions. Bull. Aust. Math. Soc. 94(1), 121–130 (2016)MathSciNetMATHCrossRef Liu, F., Chen, T., Wu, H.X.: A note on the endpoint regularity of the Hardy-littlewood maximal functions. Bull. Aust. Math. Soc. 94(1), 121–130 (2016)MathSciNetMATHCrossRef
53.
go back to reference Zhou, J.P., Sang, C.Y., Li, X., Fang, M.Y., Wang, Z.: H∞ consensus for nonlinear stochastic multi-agent systems with time delay. Appl. Math. Comput. 325, 41–58 (2018)MathSciNet Zhou, J.P., Sang, C.Y., Li, X., Fang, M.Y., Wang, Z.: H consensus for nonlinear stochastic multi-agent systems with time delay. Appl. Math. Comput. 325, 41–58 (2018)MathSciNet
54.
go back to reference Liu, F., Wang, F.: Entropy-expansiveness of geodesic flows on closed manifolds without conjugate points. Acta Math. Sin. (Engl. Ser.). 32(4), 507–520 (2016)MathSciNetMATHCrossRef Liu, F., Wang, F.: Entropy-expansiveness of geodesic flows on closed manifolds without conjugate points. Acta Math. Sin. (Engl. Ser.). 32(4), 507–520 (2016)MathSciNetMATHCrossRef
55.
go back to reference Cui, Y.J.: Existence of solutions for coupled integral boundary value problem at resonance. Publ. Math. Debr. 89(1–2), 73–88 (2016)MathSciNetMATHCrossRef Cui, Y.J.: Existence of solutions for coupled integral boundary value problem at resonance. Publ. Math. Debr. 89(1–2), 73–88 (2016)MathSciNetMATHCrossRef
56.
go back to reference Cui, Y.J., Zou, Y.M.: Existence of solutions for second-order integral boundary value problems. Nonlinear Anal. Modell. Control. 21(6), 828–838 (2016)MathSciNetMATHCrossRef Cui, Y.J., Zou, Y.M.: Existence of solutions for second-order integral boundary value problems. Nonlinear Anal. Modell. Control. 21(6), 828–838 (2016)MathSciNetMATHCrossRef
57.
go back to reference Dong, H.H., Guo, B.Y., Yin, B.S.: Generalized fractional supertrace identity for Hamiltonian structure of Nls-Mkdv hierarchy with self-consistent sources. Anal. Math. Phys. 6(2), 199–209 (2016)MathSciNetMATHCrossRef Dong, H.H., Guo, B.Y., Yin, B.S.: Generalized fractional supertrace identity for Hamiltonian structure of Nls-Mkdv hierarchy with self-consistent sources. Anal. Math. Phys. 6(2), 199–209 (2016)MathSciNetMATHCrossRef
58.
go back to reference Liu, F., Wu, H.X.: L-p bounds for marcinkiewicz integrals associated to homogeneous mappings. Monatshefte Fur Mathematik. 181(4), 875–906 (2016)MathSciNetMATHCrossRef Liu, F., Wu, H.X.: L-p bounds for marcinkiewicz integrals associated to homogeneous mappings. Monatshefte Fur Mathematik. 181(4), 875–906 (2016)MathSciNetMATHCrossRef
59.
go back to reference Li, X.P., Lin, X.Y., Lin, Y.Q.: Lyapunov-Type conditions and stochastic differential equations driven by Gbrownian motion. J. Math. Anal. Appl. 439(1), 235–255 (2016)MathSciNetMATHCrossRef Li, X.P., Lin, X.Y., Lin, Y.Q.: Lyapunov-Type conditions and stochastic differential equations driven by Gbrownian motion. J. Math. Anal. Appl. 439(1), 235–255 (2016)MathSciNetMATHCrossRef
60.
go back to reference Liu, F., Zhang, D.Q.: Multiple singular integrals and maximal operators with mixed homogeneity along compound surfaces. Math. Inequal. Appl. 19(2), 499–522 (2016)MathSciNetMATH Liu, F., Zhang, D.Q.: Multiple singular integrals and maximal operators with mixed homogeneity along compound surfaces. Math. Inequal. Appl. 19(2), 499–522 (2016)MathSciNetMATH
61.
go back to reference Zhao, Y., Zhang, W.H.: Observer-based controller design for singular stochastic Markov jump systems with state dependent noise. J. Syst. Sci. Complex. 29(4), 946–958 (2016)MathSciNetMATHCrossRef Zhao, Y., Zhang, W.H.: Observer-based controller design for singular stochastic Markov jump systems with state dependent noise. J. Syst. Sci. Complex. 29(4), 946–958 (2016)MathSciNetMATHCrossRef
62.
go back to reference Ma, H.J., Jia, Y.M.: Stability analysis for stochastic differential equations with infinite Markovian switchings. J. Math. Anal. Appl. 435(1), 593–605 (2016)MathSciNetMATHCrossRef Ma, H.J., Jia, Y.M.: Stability analysis for stochastic differential equations with infinite Markovian switchings. J. Math. Anal. Appl. 435(1), 593–605 (2016)MathSciNetMATHCrossRef
63.
go back to reference Hu, Q.Y., Yuan, L.: A plane wave method combined with local spectral elements for nonhomogeneous Helmholtz equation and time-harmonic Maxwell equations. Adv. Comput. Math. 44(1), 245–275 (2018)MathSciNetMATHCrossRef Hu, Q.Y., Yuan, L.: A plane wave method combined with local spectral elements for nonhomogeneous Helmholtz equation and time-harmonic Maxwell equations. Adv. Comput. Math. 44(1), 245–275 (2018)MathSciNetMATHCrossRef
64.
go back to reference Zhang, T.Q., Ma, W.B., Meng, X.Z., Zhang, T.H.: Periodic solution of a prey-predator model with nonlinear state feedback control. Appl. Math. Comput. 266, 95–107 (2015)MathSciNetMATH Zhang, T.Q., Ma, W.B., Meng, X.Z., Zhang, T.H.: Periodic solution of a prey-predator model with nonlinear state feedback control. Appl. Math. Comput. 266, 95–107 (2015)MathSciNetMATH
65.
go back to reference Liu, F., Zhang, D.Q.: Parabolic marcinkiewicz integrals associated to polynomials compound curves and extrapolation. Bull. Korean Math. Soc. 52(3), 771–788 (2015)MathSciNetMATHCrossRef Liu, F., Zhang, D.Q.: Parabolic marcinkiewicz integrals associated to polynomials compound curves and extrapolation. Bull. Korean Math. Soc. 52(3), 771–788 (2015)MathSciNetMATHCrossRef
66.
go back to reference Ling, S.T., Cheng, X.H., Jiang, T.S.: An algorithm for coneigenvalues and coneigenvectors of quaternion matrices. AACA 25(2), 377–384 (2015)MathSciNetMATHCrossRef Ling, S.T., Cheng, X.H., Jiang, T.S.: An algorithm for coneigenvalues and coneigenvectors of quaternion matrices. AACA 25(2), 377–384 (2015)MathSciNetMATHCrossRef
67.
go back to reference Liu, F., Wu, H.X., Zhang, D.Q.: L-p bounds for parametric marcinkiewicz integrals with mixed homogeneity. Math. Inequal. Appl. 18(2), 453–469 (2015)MathSciNetMATH Liu, F., Wu, H.X., Zhang, D.Q.: L-p bounds for parametric marcinkiewicz integrals with mixed homogeneity. Math. Inequal. Appl. 18(2), 453–469 (2015)MathSciNetMATH
68.
go back to reference Gao, M., Sheng, L., Zhang, W.H.: Stochastic H-2/H-infinity control of nonlinear systems with time-delay and state-dependent noise. Appl. Math. Comput. 266, 429–440 (2015)MathSciNetMATH Gao, M., Sheng, L., Zhang, W.H.: Stochastic H-2/H-infinity control of nonlinear systems with time-delay and state-dependent noise. Appl. Math. Comput. 266, 429–440 (2015)MathSciNetMATH
69.
go back to reference Li, Y.X., Huang, X., Song, Y.W., Lin, J.N.: A new fourth-order memristive chaotic system and its generation. Int. J. Bifurcation Chaos. 25(11), 1550151 (2015)ADSMathSciNetCrossRef Li, Y.X., Huang, X., Song, Y.W., Lin, J.N.: A new fourth-order memristive chaotic system and its generation. Int. J. Bifurcation Chaos. 25(11), 1550151 (2015)ADSMathSciNetCrossRef
70.
go back to reference Xu, X.X.: A deformed reduced semi-discrete Kaup-Newell equation, the related integrable family and darboux transformation. Appl. Math. Comput. 251, 275–283 (2015)MathSciNetMATH Xu, X.X.: A deformed reduced semi-discrete Kaup-Newell equation, the related integrable family and darboux transformation. Appl. Math. Comput. 251, 275–283 (2015)MathSciNetMATH
71.
go back to reference Liu, F.: Rough maximal functions supported by subvarieties on Triebel-Lizorkin spaces, Revista de la Real Academia de Ciencias Exactas. Fisicas y Nat. Ser. A. Math. 112(2), 593–614 (2018) Liu, F.: Rough maximal functions supported by subvarieties on Triebel-Lizorkin spaces, Revista de la Real Academia de Ciencias Exactas. Fisicas y Nat. Ser. A. Math. 112(2), 593–614 (2018)
72.
go back to reference Wang, W., Zhang, T.Q.: Caspase-1-mediated pyroptosis of the predominance for driving CD4++ T cells death: a nonlocal spatial mathematical model. Bull. Math. Biol. 80(3), 540–582 (2018)MathSciNetMATHCrossRef Wang, W., Zhang, T.Q.: Caspase-1-mediated pyroptosis of the predominance for driving CD4++ T cells death: a nonlocal spatial mathematical model. Bull. Math. Biol. 80(3), 540–582 (2018)MathSciNetMATHCrossRef
73.
go back to reference Li, H.J., Zhu, Y.L., Liu, J., Wang, Y.: Consensus of second-order delayed nonlinear multi-agent systems via node-based distributed adaptive completely intermittent protocols. Appl. Math. Comput. 326, 1–15 (2018)MathSciNetMATHCrossRef Li, H.J., Zhu, Y.L., Liu, J., Wang, Y.: Consensus of second-order delayed nonlinear multi-agent systems via node-based distributed adaptive completely intermittent protocols. Appl. Math. Comput. 326, 1–15 (2018)MathSciNetMATHCrossRef
74.
go back to reference Cui, Y.J., Ma, W.J., Sun, Q., Su, X.W.: New uniqueness results for boundary value problem of fractional differential equation. Nonlinear Anal. Modell. Control. 23(1), 31–39 (2018)MathSciNetMATHCrossRef Cui, Y.J., Ma, W.J., Sun, Q., Su, X.W.: New uniqueness results for boundary value problem of fractional differential equation. Nonlinear Anal. Modell. Control. 23(1), 31–39 (2018)MathSciNetMATHCrossRef
75.
go back to reference Liu, F., Mao, S.Z.: L-p bounds for nonisotropic marcinkiewicz integrals associated to surfaces. J. Aust. Math. Soc. 99(3), 380–398 (2015)MathSciNetMATHCrossRef Liu, F., Mao, S.Z.: L-p bounds for nonisotropic marcinkiewicz integrals associated to surfaces. J. Aust. Math. Soc. 99(3), 380–398 (2015)MathSciNetMATHCrossRef
76.
go back to reference Tramontana, F., Elsadany, A.A., Xin, B.G., Agiza, H.N.: Local stability of the cournot solution with increasing heterogeneous competitors. Nonlinear Anal. Real World Appl. 26, 150–160 (2015)MathSciNetMATHCrossRef Tramontana, F., Elsadany, A.A., Xin, B.G., Agiza, H.N.: Local stability of the cournot solution with increasing heterogeneous competitors. Nonlinear Anal. Real World Appl. 26, 150–160 (2015)MathSciNetMATHCrossRef
77.
go back to reference Cui, Y.J., Ma, W.J., Wang, X.Z., Su, X.W.: Uniqueness theorem of differential system with coupled integral boundary conditions. Electron. J. Qual. Theory Differ. Equ. (9), 1–10 (2018)MathSciNetMATHCrossRef Cui, Y.J., Ma, W.J., Wang, X.Z., Su, X.W.: Uniqueness theorem of differential system with coupled integral boundary conditions. Electron. J. Qual. Theory Differ. Equ. (9), 1–10 (2018)MathSciNetMATHCrossRef
78.
go back to reference Tan, C., Zhang, W.H.: On observability and detectability of continuous-time stochastic Markov jump systems. J. Syst. Sci. Complex. 28(4), 830–847 (2015)MathSciNetMATHCrossRef Tan, C., Zhang, W.H.: On observability and detectability of continuous-time stochastic Markov jump systems. J. Syst. Sci. Complex. 28(4), 830–847 (2015)MathSciNetMATHCrossRef
79.
go back to reference Yan, Z.G., Zhang, G.S., Wang, J.K., Zhang, W.H.: State and output feedback finite-time guaranteed cost control of linear it stochastic systems. J. Syst. Sci. Complex. 28(4), 813–829 (2015)MathSciNetMATHCrossRef Yan, Z.G., Zhang, G.S., Wang, J.K., Zhang, W.H.: State and output feedback finite-time guaranteed cost control of linear it stochastic systems. J. Syst. Sci. Complex. 28(4), 813–829 (2015)MathSciNetMATHCrossRef
80.
go back to reference Li, L., Wang, Z., Li, Y.X., Shen, H., Lu, J.W.: Hopf bifurcation analysis of a complex-valued neural network model with discrete and distributed delays. Appl. Math. Comput. 330, 152–169 (2018)MathSciNetMATH Li, L., Wang, Z., Li, Y.X., Shen, H., Lu, J.W.: Hopf bifurcation analysis of a complex-valued neural network model with discrete and distributed delays. Appl. Math. Comput. 330, 152–169 (2018)MathSciNetMATH
81.
go back to reference Jiang, D.-H., Wang, X.-J., Xu, G.-B., Lin, J.-Q.: A denoising-decomposition model combining TV minimisation and fractional derivatives. East Asia J. Appl. Math. 8, 447–462 (2018)CrossRef Jiang, D.-H., Wang, X.-J., Xu, G.-B., Lin, J.-Q.: A denoising-decomposition model combining TV minimisation and fractional derivatives. East Asia J. Appl. Math. 8, 447–462 (2018)CrossRef
Metadata
Title
New quantum key agreement protocols based on Bell states
Authors
Yu-Guang Yang
Bo-Ran Li
Dan Li
Yi-Hua Zhou
Wei-Min Shi
Publication date
01-10-2019
Publisher
Springer US
Published in
Quantum Information Processing / Issue 10/2019
Print ISSN: 1570-0755
Electronic ISSN: 1573-1332
DOI
https://doi.org/10.1007/s11128-019-2434-z

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