# Witnessing non-Markovian dynamics through correlations

## TL;DR

This paper investigates how correlations between a system and an auxiliary system can be used to detect non-Markovian dynamics, analyzing different correlation measures and their effectiveness in witnessing memory effects in open quantum systems.

## Contribution

It demonstrates the effectiveness of correlation-based methods for witnessing non-Markovianity, highlighting the strengths and limitations of various correlation measures including entanglement, mutual information, and distinguishability.

## Key findings

- Correlation backflows can indicate non-Markovian dynamics.
- Entanglement and mutual information have specific strengths and limitations.
- Adding auxiliary systems enhances detection of non-Markovian effects.

## Abstract

Non-Markovian effects in an open-system dynamics are usually associated to information backflows from the environment to the system. However, the way these backflows manifest and how to detect them is unclear. A natural approach is to study the backflow in terms of the correlations the evolving system displays with another unperturbed system during the dynamics. In this work, we study the power of this approach to witness non-Markovian dynamics using different correlation measures. We identify simple dynamics where the failure of completely-positive divisibility is in one-to-one correspondence with a correlation backflow. We then focus on specific correlation measures, such as those based on entanglement and the mutual information, and identify their strengths and limitations. We conclude with a study of a recently introduced correlation measures based on state distinguishability and see how, for these measures, adding an extra auxiliary system enlarges the set of detectable non-Markovian dynamics.