The effect of PT-symmetry breaking in coupled systems with balanced gain and loss has recently attracted considerable attention and has been demonstrated in various photonic, electrical and mechanical systems in the classical regime. Here we generalize the definition of PT symmetry to finite-dimensional open quantum systems, which are described by a Markovian master equation. Specifically, we show that the invariance of this master equation under a certain symmetry transformation implies the existence of stationary states with preserved and broken parity symmetry. As the dimension of the Hilbert space grows, the transition between these two limiting phases becomes increasingly sharp and the classically expected PT-symmetry breaking transition is recovered. This quantum-to-classical correspondence allows us to establish a common theoretical framework to identify and accurately describe PT-symmetry breaking effects in a large variety of physical systems, operated both in the classical and quantum regimes.

中文翻译：

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PT对称性在开放量子系统中的出现

PT对称性在具有平衡增益和损耗的耦合系统中的破坏效应最近引起了相当大的关注，并且已经在经典状态下的各种光子，电气和机械系统中得到了证明。在这里，我们将PT对称性的定义推广到有限维开放量子系统，这由马尔可夫主方程描述。具体来说，我们表明该主方程在一定对称性变换下的不变性意味着存在奇偶对称性保持不变和破碎的平稳状态。随着希尔伯特空间维数的增长，这两个极限相位之间的过渡变得越来越尖锐，并且恢复了经典的PT对称断裂过渡。