Dynamics of coherence-induced state ordering under Markovian channels

TL;DR

This paper investigates how different Markovian channels affect the ordering of quantum states based on their coherence measures, revealing that most channels preserve the ordering except for specific cases with the bit flip channel.

Contribution

It provides a detailed analysis of the effects of four common Markovian channels on coherence-induced state ordering, highlighting which channels preserve or alter the ordering.

Findings

Amplitude damping, phase damping, and depolarizing channels do not change state ordering.

Bit flip channel can alter state ordering in certain cases.

The study covers multiple coherence measures including $l_1$ norm, relative entropy, geometric measure, and Tsallis entropy.

Abstract

We study the dynamics of coherence-induced state ordering under incoherent channels, particularly four specific Markovian channels: $-$ amplitude damping channel, phase damping channel, depolarizing channel and bit flit channel for single-qubit states. We show that the amplitude damping channel, phase damping channel, and depolarizing channel do not change the coherence-induced state ordering by $l_1$ norm of coherence, relative entropy of coherence, geometric measure of coherence, and Tsallis relative $\alpha$-entropies, while the bit flit channel does change for some special cases.