# Dynamics of quantum coherence in Bell-diagonal states under Markovian channels

## TL;DR

This paper investigates how quantum coherence in Bell-diagonal states evolves under various Markovian channels, revealing measure-dependent freezing phenomena and complex dynamics influenced by channel types and configurations.

## Contribution

It provides a detailed analysis of coherence dynamics in Bell-diagonal states under different Markovian channels, highlighting measure-dependent effects and multi-channel interactions.

## Key findings

- Frozen coherence occurs under certain conditions for $l_{1}$ norm.
- Coherence under depolarizing channels initially decreases then increases.
- Coherence dynamics vary with channel types and configurations.

## Abstract

We study the curves of coherence for the Bell-diagonal states including $l_{1}$-norm of coherence and relative entropy of coherence under the Markovian channels in the first subsystem once. For a special Bell-diagonal state under bit-phase flip channel, we find frozen coherence under $l_{1}$ norm occurs, but relative entropy of coherence decrease. It illustrates that the occurrence of frozen coherence depends on the type of the measure of coherence. We study the coherence evolution of Bell-diagonal states under Markovian channels in the first subsystem $n$ times and find coherence under depolarizing channel decreases initially then increases for small $n$ and tend to zero for large $n$. We discuss the dynamics of coherence of the Bell-diagonal state under two independent same type local Markovian channels. We depict the dynamic behaviors of relative entropy of coherence for Bell-diagonal state under the bi-side different Markovian channel. We depict the dynamic behaviors of relative entropy of coherence for Bell-diagonal state under the bi-side different Markovian channel.