# Equivalence between non-Markovian dynamics and correlation backflows

## TL;DR

This paper establishes a direct link between non-Markovian quantum dynamics and correlation backflows, showing that non-Markovian behavior can always be witnessed through correlation measures in finite-dimensional systems.

## Contribution

It proves a one-to-one correspondence between non-Markovian dynamics and correlation backflows using specific correlation measures and initial states.

## Key findings

- Non-Markovian dynamics always exhibit correlation backflows with appropriate measures.
- A set of initial probe states can effectively witness non-Markovian behavior.
- First proof of a direct equivalence between non-Markovianity 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 dynamics of finite-dimensional quantum systems and correlation backflows.