Quantum coherence in multipartite systems

TL;DR

This paper explores the hierarchical structure of quantum correlations in multipartite systems, introduces a basis-free measure of quantum coherence, and examines how local and nonlocal unitaries create coherence.

Contribution

It introduces a basis-free quantum coherence measure equivalent to quantum discord and analyzes coherence creation by local and nonlocal unitaries in multipartite systems.

Findings

Basis-free quantum coherence equals quantum discord.

Nonlocal unitaries do not always outperform local unitaries in creating coherence.

Discusses additivity of quantum coherence in tripartite systems.

Abstract

Within the unified framework of exploiting the relative entropy as a distance measure of quantum correlations, we make explicit the hierarchical structure of quantum coherence, quantum discord and quantum entanglement in multipartite systems. On this basis, we introduce a new measure of quantum coherence, the basis-free quantum coherence and prove that this quantity is exactly equivalent to quantum discord. Furthermore, since the original relative entropy of coherence is a basis-dependent quantity, we investigate the local and nonlocal unitary creation of quantum coherence, focusing on the two-qubit unitary gates. Intriguingly, our results demonstrate that nonlocal unitary gates do not necessarily outperform the local unitary gates. Finally, the additivity relationship of quantum coherence in tripartite systems is discussed in detail, where the strong subadditivity of von Neumann entropy plays an essential role.