\begin{document}$0.78 \lt F \lt 1$\end{document}, the maximum value \begin{document}${S_m}$\end{document} of testing quantum nonlocality will gradually transition from \begin{document}${S_m} \gt 2$\end{document} to \begin{document}${S_m} \lt 2$\end{document} with the increase of the evolution time of the two “X” states, and the research on the quantum nonlocality test cannot be successfully carried out. In the amplitude damping environment, the “X” state obtained by the local transformation operation has a longer evolution time for successfully testing quantum nonlocality when \begin{document}$F \gt 0.78$\end{document}. In particular, when \begin{document}$F = 1$\end{document}, the “X” state with the density matrix \begin{document}${\rho _W}$\end{document} cannot successfully test the quantum nonlocality after the evolution time \begin{document}$\varGamma t \gt 0.22$\end{document}. For the “X” state with density matrix \begin{document}${\tilde \rho _W}$\end{document}, the quantum nonlocality testing cannot be performed until the evolution time \begin{document}$\varGamma t \gt 0.26$\end{document}. These results show that the local transformation operation of the “X” state is more conducive to the quantum nonlocality testing based on the CHSH inequality. Finally, the fidelity ranges of successfully testing the quantum nonlocality of the two “X” states in phase and amplitude damping environments are given in detail. The results show that on the premise of the successful testing of quantum nonlocality , the two types of “X” states evolving in the phase damping environment have a large range of valid fidelity. Meanwhile, for the same evolution time, the local transformation operation is helpful in improving the fidelity range of quantum nonlocality test in amplitude damping environment for “X” state with density matrix \begin{document}${\rho _W}$\end{document}."> - 必威体育下载

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    Zeng Bai-Yun, Gu Peng-Yu, Jiang Shi-Min, Jia Xin-Yan, Fan Dai-He
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    • Abstract views:2935
    • PDF Downloads:55
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    Publishing process
    • Received Date:20 November 2022
    • Accepted Date:07 December 2022
    • Available Online:26 December 2022
    • Published Online:05 March 2023

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