Basis-independent quantum coherence and its distribution

TL;DR

This paper introduces a basis-independent measure of quantum coherence, analyzing its distribution in multipartite systems and highlighting advantages over traditional basis-dependent methods through geometric and numerical insights.

Contribution

It proposes a basis-independent coherence measure using the maximally mixed state, enabling invariant analysis and distribution characterization in multipartite quantum systems.

Findings

Basis-independent coherence measure is invariant under unitary transformations.

Distribution of coherence can be decomposed into subsystem and correlation contributions.

Numerical examples demonstrate the effectiveness of the basis-independent approach.

Abstract

We analyze a basis-independent definition of quantum coherence. The maximally mixed state is used as the reference state, which allows for a way of defining coherence that is invariant under arbitrary unitary transformations. The basis-independent approach is applied to finding the distri- bution of the coherence within a multipartite system, where the contributions due to correlations between the subsystems and within each subsystem are isolated. The use of the square root of the Jensen-Shannon divergence allows for inequality relations to be derived between these quantities, giving a geometrical picture within the Hilbert space of the system. We describe the relationship between the basis-independent and the basis-dependent approaches, and argue that many advan- tages exist for the former method. The formalism is illustrated with several numerical examples which show that the states can be characterized in a simple and effective manner.