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Entanglement and nonlocality dynamics of a Bell state and the GHZ state in a noisy environment

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Abstract

We investigate the entanglement and nonlocality dynamics of a two-qubit Bell state and the three-qubit Greenberger–Home–Zeilinger (GHZ) state in a noisy environment by solving analytically a master equation in the Lindblad form. In the case of the Bell state, we obtain the analytic expressions of the concurrence and the maximal violation of the Clauser–Horne–Shimony–Holt inequality of the evolution state. In the case of the three-qubit GHZ state, we obtain the analytic formula of the genuinely multipartite concurrence of the evolution state. Usually, it is difficult to give the analytic expression of the maximum violation of the Svetlichny inequality for a general three-qubit state, but we find the analytic expression for a class of three-qubit states whose correlation matrices are of a special form. We use this result to obtain the analytic expression of the maximum violation of the Svetlichny inequality of the evolution state when parameters in the master equation meet certain conditions.

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Acknowledgements

This work is supported by Key Research and Development Project of Guang dong Province under Grant No. 2020B0303300001 and the Guangdong Basic and Applied Basic Research Foundation under Grant No. 2020B1515310016. We appreciate Chang-Yue Zhang for her useful discussion.

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Authors and Affiliations

  1. Department of Mathematics, South China University of Technology, Guangzhou, 510641, People’s Republic of China

    Yue-Qiu Chen, Hao Shu & Zhu-Jun Zheng

  2. Laboratory of Quantum Science and Engineering, South China University of Technology, Guangzhou, 510641, People’s Republic of China

    Yue-Qiu Chen, Hao Shu & Zhu-Jun Zheng

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  1. Yue-Qiu Chen
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  2. Hao Shu
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  3. Zhu-Jun Zheng
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Correspondence to Zhu-Jun Zheng.

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Chen, YQ., Shu, H. & Zheng, ZJ. Entanglement and nonlocality dynamics of a Bell state and the GHZ state in a noisy environment. Quantum Inf Process 20, 323 (2021). https://doi.org/10.1007/s11128-021-03263-1

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