Quantum Coherence Dispersion

TL;DR

This paper introduces a measure of quantum coherence dispersion, revealing its maximum at intermediate entropy levels and linking it to complexity in quantum and non-equilibrium systems.

Contribution

It proposes a new quantifier for quantum coherence dispersion and explores its relation to complexity and non-equilibrium quantum systems.

Findings

Coherence dispersion is maximized at intermediate entropy levels.

The proposed measure captures features of complexity quantifiers.

Connections are made between quantum coherence dispersion and non-equilibrium systems.

Abstract

We investigate how quantum coherence can be distributed among the several off-diagonal elements of an arbitrary density matrix. An easily computable quantity that captures this variability notion is proposed and it is argued that it presents marked features of complexity quantifiers. It turns out that this coherence dispersion ($\Delta_{\rm c}$) is maximized for intermediate values of an appropriate entropy (the relative entropy of coherence), a prevalent signature of complexity quantifiers across different fields, from evolutionary biology to linguistics and information science. The final part of the manuscript is dedicated to the connection between the proposed framework and non-equilibrium systems in the quantum regime.