关于经典和量子非马尔可夫性的讲义
Lecture notes on classical and quantum non-Markovianity
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中文总结 AI 辅助
为熟悉量子力学和概率论的研究生介绍非马尔可夫量子过程，聚焦基于量子通道可分性和单调递减态可区分性的两种量子马尔可夫性表征，强调经典与量子概念对应关系。
中文摘要 AI 辅助
近几十年来，对非马尔可夫量子过程的研究引起了广泛关注，产生了几种相互竞争的量子非马尔可夫性概念。这些笔记是为熟悉量子力学和概率论的研究生介绍该主题。由于文献众多，我们聚焦于基于量子通道可分性和单调递减态可区分性的两种突出的量子马尔可夫性表征。文中始终强调经典概念（随机矩阵、查普曼 - 柯尔莫哥洛夫方程）与其量子类似物（动力学映射、CP - 可分性）之间的对应关系。
英文摘要
The study of non-Markovian quantum processes has attracted significant interest in recent decades, giving rise to several competing notions of quantum non-Markovianity. These notes serve as an introduction to the topic for graduate students familiar with quantum mechanics and probability theory. Owing to the vastness of the literature, we focus on two prominent characterizations of quantum Markovianity based on the divisibility of quantum channels and monotonically decreasing state distinguishability. The correspondence between classical concepts (stochastic matrices, Chapman-Kolmogorov equation) and their quantum analogs (dynamical maps, CP-divisibility) is emphasized throughout.
