# Precursors of non-Markovianity

## TL;DR

This paper introduces the concept of precursors of non-Markovianity, identifying necessary early-time properties of system-environment states that lead to non-Markovian dynamics, using a framework based on quantum state fidelity.

## Contribution

It defines and quantifies precursors of non-Markovianity through system-environment correlations and environmental changes, applicable via the Bures distance in various physical models.

## Key findings

- Precursors are necessary conditions for non-Markovian behavior.
- Quantitative assessment of correlations and environmental changes.
- Application to discrete and continuous variable collision models.

## Abstract

Using the paradigm of information backflow to characterize a non-Markovian evolution, we introduce so-called precursors of non-Markovianity, i.e. necessary properties that the system and environment state must exhibit at earlier times in order for an ensuing dynamics to be non-Markovian. In particular, we consider a quantitative framework to assess the role that established system-environment correlations together with changes in environmental states play in an emerging non-Markovian dynamics. By defining the relevant contributions in terms of the Bures distance, which is conveniently expressed by means of the quantum state fidelity, these quantities are well defined and easily applicable to a wide range of physical settings. We exemplify this by studying our precursors of non-Markovianity in discrete and continuous variable non-Markovian collision models.