Quantifying quantum coherence based on the Tsallis relative operator entropy

TL;DR

This paper introduces a new family of quantum coherence measures based on Tsallis relative operator entropy, extending existing inequalities and satisfying standard criteria for coherence quantification.

Contribution

It proposes novel coherence quantifiers derived from Tsallis entropy, unifying and generalizing existing measures with rigorous mathematical foundations.

Findings

The new measures satisfy all standard coherence criteria.

They include existing measures as special cases.

Examples illustrate the relations among different coherence measures.

Abstract

Coherence is a fundamental ingredient in quantum physics and a key resource in quantum information processing. The quantification of quantum coherence is of great importance. We present a family of coherence quantifiers based on the Tsallis relative operator entropy. Shannon inequality and its reverse one in Hilbert space operators derived by Furuta [Linear Algebra Appl. 381 (2004) 219] are extended in terms of the parameter of the Tsallis relative operator entropy. These quantifiers are shown to satisfy all the standard criteria for a well-defined measure of coherence and include some existing coherence measures as special cases. Detailed examples are given to show the relations among the measures of quantum coherence.