The non-Markovianity of an arbitrary open quantum system is analyzed in reference to the multi-time statistics given by its monitoring at discrete times. On the one hand, we exploit the hierarchy of inhomogeneous transfer tensors (TTs), which provides us with relevant information about the role of correlations between the system and the environment in the dynamics. The connection between the TT hierarchy and the CP-divisibility property is then investigated, by showing to what extent quantum Markovianity can be linked to a description of the open-system dynamics by means of the composition of one-step TTs only. On the other hand, we introduce the set of stochastic TT transformations associated with local measurements on the open system at different times and conditioned on the measurement outcomes. The use of the TT formalism accounts for different kinds of memory effects in the multi-time statistics and allows us to compare them on a similar footing with the memory effects present in non-monitored non-Markovian dynamics, as we illustrate on a spin-boson case study.

任意开放量子系统的非马尔可夫性是参照其在离散时间的监测给出的多时间统计来分析的。一方面，我们利用了非齐次传递张量（TT）的层次结构，它为我们提供了有关系统与环境之间的相关性在动力学中的作用的相关信息。然后研究了 TT 层次结构和 CP 可分性之间的联系，通过仅通过一步 TT 的组合显示量子马尔可夫性在多大程度上可以与开放系统动力学的描述联系起来。另一方面，我们引入了一组与开放系统上不同时间的局部测量相关的随机 TT 变换，并以测量结果为条件。