Non-Hermitian systems with parity-time ($\mathcal{PT}$) symmetry give rise to exceptional points (EPs) with exceptional properties that arise due to the coalescence of eigenvectors. Such systems have been extensively explored in the classical domain, where second- or higher-order EPs have been proposed or realized. In contrast, quantum information studies of $\mathcal{PT}$-symmetric systems have been confined to systems with a two-dimensional Hilbert space. Here, by using a single-photon interferometry setup, we simulate the quantum dynamics of a four-dimensional $\mathcal{PT}$-symmetric system across a fourth-order exceptional point. By tracking the coherent, nonunitary evolution of the density matrix of the system in $\mathcal{PT}$-symmetry unbroken and broken regions, we observe the entropy dynamics for both the entire system, and the gain and loss subsystems. Our setup is scalable to the higher-dimensional $\mathcal{PT}$-symmetric systems, and our results point towards the rich dynamics and critical properties.

中文翻译：

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高维奇偶时间对称系统中的量子信息动力学

具有校验时间的非赫米特系统（$\mathcal{PT}$）对称会产生具有特征的异常点（EP），这些异常点是由于特征向量的合并而产生的。在经典领域中已经广泛地探索了这样的系统，其中已经提出或实现了二阶或更高阶的EP。相反，量子信息研究$\mathcal{PT}$对称系统仅限于具有二维希尔伯特空间的系统。在这里，通过使用单光子干涉仪设置，我们模拟了四维的量子动力学$\mathcal{PT}$四阶例外点的对称系统。通过跟踪系统密度矩阵的相干，非unit演化$\mathcal{PT}$-对称的连续区域和不连续区域，我们观察到整个系统以及增益和损耗子系统的熵动力学。我们的设置可扩展到更高维度$\mathcal{PT}$不对称系统，我们的结果指向了丰富的动力学和关键特性。