Equivalence between non-Markovian dynamics and correlation backflows

Abstract

The information encoded into an open quantum system that evolves under a Markovian dynamics is always monotonically non-increasing. Nonetheless, for a given quantifier of the information contained in the system, it is in general not clear if for all non-Markovian dynamics it is possible to observe a non-monotonic evolution of this quantity, namely a backflow. We address this problem by considering correlations of finite-dimensional bipartite systems. For this purpose, we consider a class of correlation measures and prove that if the dynamics is non-Markovian there exists at least one element from this class that provides a correlation backflow. Moreover, we provide a set of initial probe states that accomplish this witnessing task. This result provides the first one-to-one relation between non-Markovian quantum dynamics and correlation backflows. Finally, we introduce a measure of non-Markovianity.

On the connection between microscopic description and memory effects in open quantum system dynamics

“…Role and relevance of correlations with ancillary degrees of freedom in the characterization of non-Markovian dynamics has also been the object of many recent investigations [31][32][33][34]. In the present contribution, we instead concentrate on the role of the correlations between system and environment arising due to the microscopic interaction.…”

Entropic bounds on information backflow

“…In the approach based on TD, its increase in time signifies a backflow of information to the open system, resulting in an enhanced reduced-state distinguishability and representing the distinctive trait of memory effects in the dynamics. The revivals of distinguishability are related to the establishment of system-environment correlations and changes in the environmental state [19][20][21][22][23], which then appear to be the basic elements ruling the non-Markovian character of open-system dynamics, though the precise assessment of their role is still under vivid debate [24][25][26][27][28][29][30].…”

Entropic Bounds on Information Backflow

“…In the approach based on TD, its increase in time signifies a backflow of information to the open system, resulting in an enhanced reduced-state distinguishability and representing the distinctive trait of memory effects in the dynamics. The revivals of distinguishability are related to the establishment of system-environment correlations and changes in the environmental state depending on the initial system state [20][21][22][23][24], though the precise assessment of their role is still under vivid debate [25][26][27][28][29][30].…”