Quantum Coherence: Reciprocity and Distribution

TL;DR

This paper investigates the fundamental relationship between quantum coherence and mixedness, revealing a general reciprocity, and explores how coherence distributes in multipartite systems, especially in Dicke states, highlighting differences between normalized and unnormalized measures.

Contribution

It analytically and numerically demonstrates the reciprocity between coherence and mixedness and examines coherence distribution in multipartite systems, revealing differences based on measure normalization.

Findings

Reciprocity between coherence and mixedness is a general feature.

Normalized coherence measures violate additivity in Dicke states.

Unnormalized coherence measures satisfy additivity in Dicke states.

Abstract

Quantum coherence is the outcome of the superposition principle. Recently, it has been theorized as a quantum resource, and is the premise of quantum correlations in multipartite systems. It is therefore interesting to study the coherence content and its distribution in a multipartite quantum system. In this work, we show analytically as well as numerically the reciprocity between coherence and mixedness of a quantum state. We find that this trade-off is a general feature in the sense that it is true for large spectra of measures of coherence and of mixedness. We also study the distribution of coherence in multipartite systems by looking at monogamy-type relation--which we refer to as additivity relation--between coherences of different parts of the system. We show that for the Dicke states, while the normalized measures of coherence violate the additivity relation, the unnormalized ones satisfy the same.