基于镜像态判别在PT和反PT对称系统中的语境性恢复
Recovery of contextuality based on mirror-like state discrimination in PT- and anti-PT-symmetric systems
AI总结：
本研究系统探讨PT和反PT对称系统中基于镜像态判别的语境性动力学，发现对称未破缺时语境性周期性振荡且PT系统中MED和MCD均能恢复超过初始值，APT系统仅MCD有此现象，破缺时成功概率稳定于1/3。
摘要：
在过去的几十年中，对宇称-时间（PT）和反宇称-时间（APT）系统的研究引起了前所未有的关注，展示了它们各种有趣的特征以及在扩展规范厄米量子力学方面的巨大潜力。然而，尽管对这一新的物理学领域投入了大量努力，非厄米动力学中的语境性仍然是一个未探索的区域，无论是在PT对称还是APT对称系统中。由于语境性也已被证明是量子态判别（QSD）任务的核心资源，我们在此系统地研究了通过QSD在两个系统中的语境性的新表现，以镜像对称三态最小误差判别（MED）和最大置信度判别（MCD）场景作为两个例子。对两个场景和八个区域（每个场景四个区域）中语境性的时间演化进行了全面比较和分析，同时考虑了初始状态的差异。在对称性未破缺区域，我们的模拟显示MED和MCD场景中语境性均出现周期性振荡，其周期与状态无关但与系统的非厄米性相关。MED和MCD在PT系统中均显示出超过初始值的非平凡语境性恢复，而这种恢复在APT系统中仅存在于MCD。在对称性破缺区域，两个场景的成功概率首先从快速衰减开始，最终稳定在1/3的恒定值。仅在PT系统的MCD场景中发现非平凡性，其中恢复的语境性超过其初始值。
英文摘要：
In the past decades, researches on parity-time (PT) and anti-parity-time(APT) systems have garnered unprecedented attention, showcasing their various intriguing characteristics and promising potentiality in extending canonical Hermitian quantum mechanics. However, despite significant endeavors devoted to this new field of physics, non-Hermitian dynamics of contextuality still remains an uncharted region, either in PT-symmetry or APT-symmetry systems. Since contextuality has also been proven to be the core resource for quantum state discrimination (QSD) tasks, here we systematically investigate the novel performance of contextuality through QSD in both systems, taking mirror-symmetric three-state minimum error discrimination (MED) and maximum confidence discrimination (MCD) scenarios as two examples. The time evolution of contextuality in two scenarios and eight regimes (four regimes for each scenario) are comprehensively compared and analyzed, with the difference of initial states also considered. In the symmetry-unbroken regimes, our simulation shows periodic oscillations of contextuality for both MED and MCD scenarios, the period of which is state-independent but related to non-Hermiticity of the system. Both MED and MCD shows non-trivial recovery of contextuality exceeding its initial value in PT system, which is only existent for MCD in APT system. In the symmetry-broken regimes, the success probabilities of both scenarios start from a prompt decay at first, ending up with a stable value which is constantly 1/3. Non-triviality is found only for MCD scenario in PT system, where the recovered contextuality exceeds its initial value.
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