# The role of coherence during classical and quantum decoherence

## TL;DR

This paper investigates the fundamental role of quantum coherence in bipartite systems, analyzing its relation to quantum discord and classical correlations, and examining their dynamics under incoherent channels.

## Contribution

It clarifies the relationship between coherence and quantum discord, and explores how coherence dynamics reflect the behavior of correlations during decoherence processes.

## Key findings

- Coherence indicates the behavior of quantum discord and classical correlation before a critical time.
- Coherence freezing corresponds to the freezing of quantum discord and classical correlation.
- Coherence decay signals the decoherence of correlations.

## Abstract

The total correlations in a bipartite quantum system are measured by the quantum mutual information $\mathcal{I}$, which consists of quantum discord and classical correlation. However, recent results in quantum information shows that coherence, which is a part of total correlation, is more general and more fundamental than discord. The role of coherence in quantum resource theories is worthwhile to investigate. We first study the relation between quantum discord and coherence by reducing the difference between them. And then, we consider the dynamics of quantum discord, classical correlations and quantum coherence under incoherent quantum channels. We discover that coherence indicate the behavior of quantum discord (classical correlation) for times $t<\bar t$, and indicate the decoherence of classical correlation (quantum discord) for times $t>\bar t$. What is more, the coherence frozen and decay indicate the quantum discord and classical correlation frozen and decay respectively.