1] Key Laboratory of Quantum Information, University of Science and Technology of China, CAS, Hefei, 230026, China [2].
1] Physikalisches Institut, Universität Freiburg, Hermann-Herder-Straße 3, D-79104 Freiburg, Germany [2].
Sci Rep. 2014 Sep 11;4:6327. doi: 10.1038/srep06327.
The modeling and analysis of the dynamics of complex systems often requires to employ non-Markovian stochastic processes. While there is a clear and well-established mathematical definition for non-Markovianity in the case of classical systems, the extension to the quantum regime recently caused a vivid debate, leading to many different proposals for the characterization and quantification of memory effects in the dynamics of open quantum systems. Here, we derive a mathematical representation for the non-Markovianity measure based on the exchange of information between the open system and its environment, which reveals the locality and universality of non-Markovianity in the quantum state space and substantially simplifies its numerical and experimental determination. We further illustrate the application of this representation by means of an all-optical experiment which allows the measurement of the degree of memory effects in a photonic quantum process with high accuracy.
复杂系统动力学的建模和分析通常需要采用非马尔可夫随机过程。虽然在经典系统的情况下，对于非马尔可夫性有明确和成熟的数学定义，但最近将其扩展到量子领域引发了激烈的争论，导致对开放量子系统动力学中记忆效应的特征化和量化提出了许多不同的建议。在这里，我们基于开放系统与其环境之间的信息交换，推导出基于非马尔可夫性度量的数学表示，揭示了量子态空间中非马尔可夫性的局域性和通用性，并大大简化了其数值和实验确定。我们进一步通过全光学实验说明了这种表示的应用，该实验允许以高精度测量光子量子过程中的记忆效应程度。
