Bipartite concurrence and localized coherence

TL;DR

This paper introduces a coherence measure that links bipartite concurrence with local coherence, providing an operational interpretation and extending the relation to mixed states.

Contribution

It establishes a novel connection between bipartite concurrence and local coherence, offering an alternative operational meaning and extending the framework to mixed states.

Findings

Bipartite concurrence equals the maximal difference between local coherence and average coherence.

The coherence measure precisely captures local coherence of pure states.

The relation extends to bipartite mixed states.

Abstract

Based on a proposed coherence measure, we show that the local coherence of a bipartite quantum pure state (coherence of its reduced density matrix) is exactly the same as the minimal average co- herence with all potential pure-state realizations under consideration. In particular, it is shown that bipartite concurrence of pure states just captures the maximal difference between local coherence and the average coherence of one subsystem induced by local operations on the other subsystem with the assistance of classical communications, which provides an alternative operational meaning for bipartite concurrence of pure states. The relation between concurrence and the proposed coherence measure can also be extended to bipartite mixed states.