Quantum non-Markovianity of a quantum noisy channel is typically identified with information backflow or, more generally, with departure of the intermediate map from complete positivity. But here, we also indicate certain non-Markovian channels that cannot be witnessed by the CP-divisibility criterion. In complex systems, non-Markovianity becomes more involved on account of subsystem dynamics. Here we study various facets of non-Markovian evolution, in the context of coined quantum walks, with particular stress on disambiguating the internal vs. environmental contributions to non-Markovian backflow. For the above problem of disambiguation, we present a general power-spectral technique based on a distinguishability measure such as trace-distance or correlation measure such as mutual information. We also study various facets of quantum correlations in the transition from quantum to classical random walks, under the considered non-Markovian noise models. The potential for the application of this analysis to the quantum statistical dynamics of complex systems is indicated.

中文翻译：

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非马尔可夫进化：量子行走视角

量子噪声通道的量子非马尔可夫性通常用信息回流来识别，或者更一般地，用中间图偏离完全正性来识别。但是在这里，我们还指出了某些非马尔可夫通道，这些通道不能被 CP 可分性标准见证。在复杂系统中，由于子系统动力学，非马尔可夫性变得更加重要。在这里，我们在创造量子游走的背景下研究了非马尔可夫进化的各个方面，特别强调消除对非马尔可夫回流的内部与环境贡献。对于上述消歧问题，我们提出了一种通用的功率谱技术，该技术基于可区分性度量（例如迹距离）或相关性度量（例如互信息）。在考虑的非马尔可夫噪声模型下，我们还研究了从量子到经典随机游走过渡过程中量子相关性的各个方面。指出了将该分析应用于复杂系统的量子统计动力学的潜力。