Coherence generating power of unitary transformations via probabilistic average

TL;DR

This paper introduces a measure for the coherence generating power of quantum channels, especially unitaries, based on probabilistic averages, with explicit formulas and bounds derived, advancing understanding of quantum coherence dynamics.

Contribution

It provides an analytical formula for the coherence generating power of unitary channels using subentropy and establishes bounds for unital channels, with detailed examples.

Findings

Explicit formula for CGP of unitary channels in terms of subentropy

Upper bound for CGP of unital quantum channels

Analytical and example-based investigation of coherence generation

Abstract

We study the ability of a quantum channel to generate quantum coherence when it applies to incoherent states. Based on probabilistic averages, we define a measure of such coherence generating power (CGP) for a generic quantum channel, based on the average coherence generated by the quantum channel acting on a uniform ensemble of incoherent states. Explicit analytical formula of the CGP for any unitary channels are presented in terms of subentropy. An upper bound for CGP of unital quantum channels has been also derived. Detailed examples are investigated.