Quantum coherence, discord and correlation measures based on Tsallis relative entropy

TL;DR

This paper introduces three new Tsallis entropy-based quantum coherence measures that satisfy strong monotonicity, compares them with existing measures, and explores their applications in defining discord and correlation measures with explicit formulas and bounds.

Contribution

It proposes novel Tsallis coherence measures satisfying strong monotonicity, compares them with existing definitions, and extends their application to discord and correlation measures with explicit formulas and bounds.

Findings

Three new Tsallis coherence measures satisfying strong monotonicity.

Explicit formulas for discord and correlation measures on pure states.

Tight bounds on discord and correlation measures for any quantum state.

Abstract

Several ways have been proposed in the literature to define a coherence measure based on Tsallis relative entropy. One of them is defined as a distance between a state and a set of incoherent states with Tsallis relative entropy taken as a distance measure. Unfortunately, this measure does not satisfy the required strong monotonicity, but a modification of this coherence has been proposed that does. We introduce three new Tsallis coherence measures coming from a more general definition that also satisfy the strong monotonicity, and compare all five definitions between each other. Using three coherence measures that we discuss, one can also define a discord. Two of these have been used in the literature, and another one is new. We also discuss two correlation measures based on Tsallis relative entropy. We provide explicit expressions for all three discord and two correlation measure on pure states. Lastly, we provide tight upper and lower bounds on two discord and correlations measures on any quantum state, with the condition for equality.