AI 中文总结
该研究建立了可操作量子非马尔可夫性与广义洛施密特回声的联系，确定了系统马尔可夫行为的条件及广义回声对系统-环境信息交换的识别作用，并以自旋环境为例进行了阐释。
AI 中文摘要
非马尔可夫性可通过开展一系列连续测量并分析相应结果统计量与马尔可夫概率结构的偏离来表征。考虑一个通过退相位相互作用与其环境耦合的系统，我们证明联合结果概率可由一组双时间环境关联函数表示。这些关联函数的定义涉及具有不同哈密顿量的正向和反向传播子，与近期引入的标准洛施密特回声的广义形式相关[Cormick和Budini，《物理快报A》593卷，132011页（2026年）]。该结果建立了可操作（基于测量）方式定义的量子非马尔可夫性与通过动力学扰动敏感性研究的复杂量子动力学之间的坚实联系。我们找到了保证系统呈现马尔可夫行为的条件，还确定了广义回声如何能识别系统与环境之间的信息交换。我们以实现这些不同动力学 regime 的自旋环境为例阐释了我们的想法。
英文摘要
Non-Markovianity can be characterized by performing a series of successive measurements and analyzing departures of the corresponding outcome statistics from a Markovian probabilistic structure. Considering a system coupled with its environment via a dephasing interaction, we show that joint outcome probabilities can be written in terms of a set of two-time environment correlations. Their definition involves forward and backward propagators with different Hamiltonians, associated with a recently introduced generalization of standard Loschmidt echoes [Cormick and Budini, Phys. Lett. A 593, 132011 (2026)]. This result establishes a solid connection between quantum non-Markovianity defined in an operational (measurement-based) way and complex quantum dynamics studied through their sensitivity to dynamical perturbations. We find conditions that guarantee a Markovian (system) behavior and also determine how the generalized echoes can identify information exchanges between the system and its environment. We illustrate our ideas considering examples of spin environments that realize these different dynamical regimes.
Comments13 pages, 2 figures
