Genuine Distributed Coherence

TL;DR

This paper introduces a new concept of genuine distributed coherence in quantum systems, providing a way to quantify and localize coherence across subsystems, with detailed analysis for bipartite pure states.

Contribution

It defines an entropic measure of genuine distributed coherence and establishes conditions for fully localizing coherence in bipartite pure states.

Findings

Identifies conditions for genuine distributed bipartite coherence.

Derives necessary and sufficient conditions for coherence localization.

Finds states with maximal genuine distributed coherence that are not globally maximally coherent.

Abstract

We introduce a notion of genuine distributed coherence. Such a notion is based on the possibility of concentrating on individual systems the coherence present in a distributed system, by making use of incoherent unitary transformations. We define an entropic quantifier of genuine distributed multipartite coherence for generic mixed states, and we focus on the bipartite pure-state case. In the latter case we derive necessary and sufficient conditions for the possibility of fully localizing the coherence, hence identifying the conditions for genuine distributed bipartite coherence. We analyze in detail the quantitative problem for the case of two-qubit pure states, identifying the states with the largest amount of genuine distributed coherence. Interestingly, such states do not have maximal global coherence nor maximal coherence rank.