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Research on whether quantum states retain quantum non-local correlation properties after evolving in non-Markovian environments has significant applications in the field of quantum information. This article presents the evolution results of the density matrix of quantum states over time in various non-Markovian environments. Specifically, we examine two types of non-Markovian phase damping environments: Random Telegraph (RT) noise and Ornstein-Uhlenbeck (OU) noise, as well as a nonMarkovian amplitude damping (AD) environment. By utilizing the Clauser-Horne-Shimony-Holt (CHSH) inequality, the quantum non-local correlation testing of the Werner state following its evolution in these nonMarkovian environments is studied. The results show significant differences in the quantum non-local correlation testing results of the Werner state after evolving in different non-Markovian environments. Notably, the Werner state displays information backflow in the RT noise environment and the AD environment, resulting in periodic oscillations in its quantum non-local correlation testing. This suggests that under certain conditions, the quantum state can transition from a state devoid of quantum non-local correlation back to a state possessing such correlation as evolution time progresses. The results also show that the Werner state exhibits information backflow phenomena in both RT noise and AD environments, leading to periodic oscillations in its quantum non-local correlation testing. Furthermore, these periods are inversely proportional to certain parameters, such as $\sqrt{\left(\frac{2 \gamma}{a}\right)^2-1}$ and $\sqrt{2 \frac{\Gamma}{\gamma}-\left(\frac{\Gamma}{\gamma}\right)^2}$. In contrast, in the OU noise environment, no information backflow is observed, leading to a decrease in the value of the quantum non-local correlation test with increasing evolution time. In most AD and OU noise environments, there exists a specific maximum evolution time $\gamma t_{\max }$ within which successful quantum non-local correlation testing can be conducted. This maximum evolution time $\gamma t_{\max }$ varies nonlinearly with increasing fidelity and inversely with increasing $\Gamma / \gamma$ parameters. In comparison, the maximum evolution time for successful quantum non-local correlation testing in the OU noise environment surpasses that in the AD environment under the same conditions, indicating that the AD environment exerts a more pronounced weakening effect on the quantum non-local correlation properties of the Werner state.
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Keywords:
- Quantum non-local correlation /
- Werner state /
- non-Markovian environment /
- CHSH inequality /
- phase damping /
- amplitude damping
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