论文标题
通过Fisher信息来表征（非）马克维亚语
Characterizing (non-)Markovianity through Fisher Information
论文作者
论文摘要
一个非分离的物理系统通常会将信息丢失给其环境，而当这种损失不可逆时，据说进化是马尔可夫人。通过监视信息量化符（例如物理状态之间的距离）如何演变来研究非马克维亚效应。在这里，我们表明，在这种情况下，Fisher Information指标是研究的自然对象。我们从数学和操作的角度完全表征了其合同性特性与马克维亚性之间的关系。我们证明，对于经典和量子动力学，马尔可维亚性等于在一组状态的所有点上的费舍尔度量的单调收缩。同时，除非将特定的物理后处理应用于动力学，否则基于Fisher距离扩张的非马克维亚性目击者不能检测所有非马克维亚的演变。最后，我们首次表明，在任何时候，状态之间的非马克维亚距离扩张对应于有关时间0动态的初始状态的回程，这是通过贝叶斯的回顾。
A non-isolated physical system typically loses information to its environment, and when such loss is irreversible the evolution is said to be Markovian. Non-Markovian effects are studied by monitoring how information quantifiers, such as the distance between physical states, evolve in time. Here we show that the Fisher information metric emerges as a natural object to study in this context; we fully characterize the relation between its contractivity properties and Markovianity, both from the mathematical and operational point of view. We prove, both for classical and quantum dynamics, that Markovianity is equivalent to the monotonous contraction of the Fisher metric at all points of the set of states. At the same time, operational witnesses of non-Markovianity based on the dilation of the Fisher distance cannot, in general, detect all non-Markovian evolutions, unless specific physical postprocessing is applied to the dynamics. Finally, we show for the first time that non-Markovian dilations of Fisher distance between states at any time correspond to backflow of information about the initial state of the dynamics at time 0, via Bayesian retrodiction.
