Entanglement-Coherence and Discord-Coherence analytical relations for X states

TL;DR

This paper derives analytical relations linking entanglement, discord, and coherence for X states under various noise channels, showing coherence as a fundamental resource necessary for entanglement and discord.

Contribution

It provides new analytical formulas connecting coherence with entanglement and discord for X states under common noise models.

Findings

Coherence is necessary for entanglement and discord in X states.

Analytical relations between these quantum correlations are established.

Results apply to states evolving under Bit Flip, Phase Damping, and Depolarizing channels.

Abstract

In this work we derive analytical relations between Entanglement and Coherence as well as between Discord and Coherence, for Bell-diagonal states and for X states, evolving under the action of several noise channels: Bit Flip, Phase Damping and Depolarizing. We demonstrate that for these families, Coherence is the fundamental correlation, that is: Coherence is necessary for the presence of Entanglement and Discord.