Coherence monotones of quantum channels based on two generalized quantum relative entropies

TL;DR

This paper introduces new coherence monotones for quantum channels using generalized quantum relative entropies, providing their properties, bounds, and explicit formulas for qubit unitary channels.

Contribution

It proposes two classes of coherence monotones based on unified and sandwiched Rényi relative entropies, with detailed properties and explicit calculations for specific channels.

Findings

Derived upper bounds for the coherence monotones.

Established properties of the coherence monotones.

Provided explicit formulas for qubit unitary channels.

Abstract

By using the Choi-Jamio{\l}kowski isomorphism, we propose two classes of coherence monotones of quantum channels based on the unified $(r,s)$-relative entropy and the sandwiched R\'{e}nyi relative entropy. Elegant properties of the coherence monotones for quantum channels are explored. Moreover, we present the upper bounds of the coherence monotones and derive the explicit formulas of the coherence monotones for qubit unitary channels.