Quantifying coherence of quantum channels based on the generalized $\alpha$-$z$-relative R\'{e}nyi entropy

TL;DR

This paper introduces new coherence measures for quantum channels using the generalized $ ext{α}$-$ ext{z}$-relative Rényi entropy, providing explicit formulas and analyzing their properties.

Contribution

It proposes two novel coherence measures for quantum channels based on the generalized $ ext{α}$-$ ext{z}$-relative Rényi entropy, with detailed properties and explicit formulas.

Findings

Derived explicit formulas for coherence measures of specific quantum channels.

Analyzed properties of the proposed coherence measures.

Provided a new framework for quantifying quantum channel coherence.

Abstract

By using the Choi-Jamio{\l}kowski isomorphism, we propose a well-defined coherence measure of quantum channels based on the generalized $\alpha$-$z$-relative R\'{e}nyi entropy. In addition, we present an alternative coherence measure of quantum channels by quantifying the commutativity between the channels and the completely dephasing channels with the generalized $\alpha$-$z$-relative R\'{e}nyi entropy. Some elegant properties of the measures are illustrated in detail. Explicit formulas of these coherence measures are derived for some detailed typical quantum channels.