Set coherence: basis-independent quantification of quantum coherence

TL;DR

This paper introduces a basis-independent measure of quantum coherence for sets of states and measurements, providing operational meaning and connecting to resource theories, thus advancing the understanding of quantum coherence beyond individual states.

Contribution

It develops the concept of set coherence, offering basis-independent quantification and operational interpretation, which extends coherence analysis to sets of quantum systems.

Findings

Set coherence measures are operationally meaningful in discrimination tasks.

The measures capture the advantage of coherent sets over incoherent ones.

Connections are established between set coherence and resource-theoretic frameworks.

Abstract

The coherence of an individual quantum state can be meaningfully discussed only when referring to a preferred basis. This arbitrariness can however be lifted when considering sets of quantum states. Here we introduce the concept of set coherence for characterising the coherence of a set of quantum systems in a basis-independent way. We construct measures for quantifying set coherence of sets of quantum states as well as quantum measurements. These measures feature an operational meaning in terms of discrimination games and capture precisely the advantage offered by a given set over incoherent ones. Along the way, we also connect the notion of set coherence to various resource-theoretic approaches recently developed for quantum systems.