Abstract
We have proposed two deterministic remote state preparation schemes via the χ state as the entangled channel in ideal environment. In this paper, we re-investigate the schemes in seven types of noises: amplitude-damping, phase-damping, Pauli (bit-flip, phase-flip, bit-phase flip, depolaring) and collective dephasing noise. The fidelity is used to measure how close the output state with the initial state are. It is found that the fidelities are dependent on the amplitude factor, phase factor and noise parameter. Interestingly, the fidelity is irrelated to the participators’ measurement results except in the amplitude-damping and collective dephasing noise. When the prepared states are the specific two- and three-qubit states, the fidelity is periodic in the collective dephasing noise and monotonous in other noises. Moreover, the average fidelity and state-independent average fidelity are calculated to quantify the effect of noise. Among the amplitude-damping, phase-damping and Pauli noises, the Pauli noise has the greatest impact and the phase-damping noise has the smallest impact.
Similar content being viewed by others
References
Bennett, C.H., Brassard, G., Crpeau, C., Jozsa, R., Peres, A., Wootters, W.K.: Phys. Rev. Lett. 70, 1895 (1993)
Furusawa, A., Sorensen, J.L., Braunstein, S.L., Fuchs, C.A., Kimble, H.J., Polzik, E.S.: Science 282, 706 (1998)
Chen, X.B., Xu, G., Yang, Y.X., Wen, Q.Y.: Opt. Commun. 283, 4802 (2010)
Chen, Y.X., Du, J., Liu, S.Y., Wang, X.H.: Quantum Inf. Process. 16, 201 (2017)
Lo, H.K.: Phys. Rev. A 62, 012313 (2000)
Pati, A.K.: Phys. Rev. A 63, 14302 (2000)
Bennett, C.H., DiVincenzo, D.P., Shor, P.W., Smolin, J.A., Terhal, B.M., Wootters, W.K.: Phys. Rev. Lett. 87, 077902 (2001)
Berry, D.W., Sanders, B.C.: Phys. Rev. Lett. 90, 057901 (2003)
Gong, L.H., Song, H.C., He, C.S., Liu, Y., Zhou, N.R.: Phys. Scr. 89, 035101 (2014)
Xu, G., Chen, X.B., Duo, Z., Li, Z.P., Yang, Y.X.: Quantum Inf. Process. 14, 2959 (2015)
Chen, X.B., Tang, X., Xu, G., Dou, Z., Chen, Y.L., Yang, Y.X.: Quantum Inf. Process. 17, 225 (2018)
Ma, S.Y., Chen, X.B., Luo, M.X., Niu, X.X., Yang, Y.X.: Opt. Commun. 283, 497 (2010)
Xu, G., Chen, X.B., Li, J., Wang, C., Yang, Y.X., Li, Z.P.: Quantum Inf. Process. 14, 4297 (2015)
Li, J., Chen, X.B., Xu, G., Yang, Y.X., Li, Z.P.: IEEE Commun. Lett. 19, 115 (2015)
Li, J., Chen, X.B., Sun, X.M., Li, Z.P., Yang, Y.X.: Sci. China-Inf. Sci. 59, 042301 (2016)
Ma, S.Y., Chen, X.B., Luo, M.X., Zhang, R., Yang, Y.X.: Opt. Commun. 284, 4088 (2011)
Ma, S.Y., Tang, P., Chen, X.B., Yang, Y.X.: Int. J. Theor. Phys. 52, 968 (2013)
Ma, S.Y., Luo, M.X., Chen, X.B., Yang, Y.X.: Quantum Inf. Process. 13, 1951 (2014)
Ma, S.Y., Luo, M.X.: Chin. Phys. B 23, 090308 (2014)
Wang, Z.Y., Liu, Y.M., Zuo, X.Q., Zhang, Z.J.: Commun. Theor. Phys. 52, 235 (2009)
Chen, X.B., Ma, S.Y., Su, Y., Zhang, R., Yang, Y.X.: Quantum Inf. Process. 11, 1653 (2012)
Wang, C., Zeng, Z., Li, X.H.: Quantum Inf. Process. 14, 1077 (2015)
Gao, C., Ma, S.Y., Chen, W.L.: Int. J. Theor. Phys. 55, 2643 (2016)
Ma, S.Y., Chen, W.L., Qu, Z.G., Tang, P.: Int. J. Theor. Phys. 56, 1653 (2017)
Chen, X.B., Sun, Y.R., Xu, G., Jia, H.Y., Qu, Z.G., Yang, Y.X.: Quantum Inf. Process. 16, 244 (2017)
Su, Y., Chen, X.B., Yang, Y.X.: Int. J. Quantum Inf. 10, 1250006 (2012)
Zhang, Z.H., Shu, L., Mo, Z.W., Zheng, J., Ma, S.Y., Luo, M.X.: Quantum Inf. Process. 13, 1979 (2014)
Choudhury, B.S., Dhara, A.: Quantum Inf. Process. 14, 373 (2015)
Xu, G., Chen, X.B., Dou, Z., Li, J., Liu, X., Li, Z.P.: Entropy 18, 267 (2016)
Zhan, Y.B., Ma, P.C.: Quantum Inf. Process. 12, 997 (2013)
Chen, N., Quan, D.X., Yang, H., Pei, C.X.: Quantum Inf. Process. 15, 1719 (2016)
Wang, H.B., Zhou, X.Y., An, X.X., Cui, M.M., Fu, D.S.: Int. J. Theor. Phys. 55, 3588 (2016)
Zhang, P., Li, X., Ma, S.Y., Qu, Z.G.: Commun. Theor. Phys. 67, 498 (2017)
Ma, S.Y., Gao, C., Zhang, P., Qu, Z.G.: Quantum Inf. Process. 16, 93 (2017)
Qu, Z.G., Wu, S.Y., Wang, M.M., Sun, L., Wang, X.J.: Quantum Inf. Process. 16, 306 (2017)
Su, L., Wu, S.Y., Qu, Z.G., Wang, M.M., Wang, X.J.: Quantum Inf. Process. 17, 283 (2018)
Adepoju, A.G., Falaye, B.J., Sun, G.H., Camacho-Nieto, O., Dong, S.H.: Phys. Lett. A 381, 581 (2017)
Wang, M.M., Qu, Z.G., Wang, W., Chen, J.G.: Quantum Inf. Process. 16, 140 (2017)
Shukla, C., Thapliyal, K., Pathak, A.: Quantum Inf. Process. 16, 205 (2017)
Xiang, G.Y., Li, J., Yu, B., Guo, G.C.: Phys. Rev. A 72, 012315 (2005)
Mikami, H., Kobayashi, T.: Phys. Rev. A 75, 022325 (2007)
Barreiro, J.T., Wei, T.C.: Phys. Rev. Lett. 105, 030407 (2010)
Erhard, M., Qassim, H., Mand, H., Karimi, E., Boyd, R.W.: Phys. Rev. A 92, 022321 (2015)
Gong, L.H., Li, J.F., Zhou, N.R.: Laser Phys. Lett. 15, 105204 (2018)
Gong, L.H., Tian, C., Li, J.F., Zou, X.F.: Quantum Inf. Process. 17, 331 (2018)
Fortes, R., Rigolin, G.: Phys. Rev. A 92, 012338 (2015)
Acknowledgements
This work is supported by the National Natural Science Foundation of China (Nos. 61201253, 61572246), Open Foundation of State Key Laboratory of Networking and Switching Technology (Beijing University of Posts and Telecommunications) (No.SKLNST-2018-1-16), Foundation of Science and Technology on Information Assurance Laboratory (No. KJ-17-003), the program for science and technology innovation research team in universities of Henan province (No. 18IRTSTHN014).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Zhang, P., Ma, S. & Gong, L. Deterministic Remote Preparation via the χ State in Noisy Environment. Int J Theor Phys 58, 2795–2809 (2019). https://doi.org/10.1007/s10773-019-04164-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10773-019-04164-x