# Entanglement revival can occur only when the system-environment state is not a Markov state

## TL;DR

This paper generalizes the concept of Markov states in multipartite quantum systems and establishes that entanglement revival requires the system-environment state to be non-Markovian, highlighting the nuanced relationship between non-Markovianity and quantum correlations.

## Contribution

It introduces a generalized definition of Markov states for multipartite systems and identifies a necessary condition for entanglement revival based on non-Markovianity.

## Key findings

- Entanglement revival occurs only when the system-environment state is not a Markov state.
- Classical environment models can still exhibit entanglement revival through non-Markovian dynamics.
- Non-Markovianity is not necessarily linked to non-classical correlations.

## Abstract

Markov states have been defined for tripartite quantum systems. In this paper, we generalize the definition of the Markov states to arbitrary multipartite case and find the general structure of an important subset of them, which we will call strong Markov states. In addition, we focus on an important property of the Markov states: If the initial state of the whole system-environment is a Markov state, then each localized dynamics of the whole system-environment reduces to a localized subdynamics of the system. This provides us a necessary condition for entanglement revival in an open quantum system: Entanglement revival can occur only when the system-environment state is not a Markov state. To illustrate (a part of) our results, we consider the case that the environment is modeled as classical. In this case, though the correlation between the system and the environment remains classical during the evolution, the change of the state of the system-environment, from its initial Markov state to a state which is not a Markov one, leads to the entanglement revival in the system. This shows that the non-Markovianity of a state is not equivalent to the existence of non-classical correlation in it, in general.