Relating quantum coherence and correlations with entropy-based measures

TL;DR

This paper explores how entropy-based measures of quantum coherence relate to quantum correlations like discord and entanglement, establishing bounds and characterizations that deepen understanding of quantum resource interrelations.

Contribution

It introduces a novel approach linking quantum correlated coherence with quantum discord and entanglement, providing bounds and characterizations for these quantum resources.

Findings

Quantum discord and entanglement are characterized by quantum correlated coherence.

Entanglement measure based on quantum correlated coherence is bounded by known entanglement measures.

For maximally correlated states, the entanglement measure equals the relative entropy of entanglement.

Abstract

Quantum coherence as an important quantum resource plays a key role in quantum theory. In this paper, using entropy-based measures, we investigate the relations between quantum correlated coherence, which is the coherence between subsystems [K. C. Tan, H. Kwon, C. Y. Park, and H. Jeong, Phys. Rev. A 94, 022329 (2016)], and two main kinds of quantum correlations as defined by quantum discord as well as quantum entanglement. In particular, we show that quantum discord and quantum entanglement can be well characterized by quantum correlated coherence. Moreover, we prove that the entanglement measure formulated by quantum correlated coherence is lower and upper bounded by the relative entropy of entanglement and the entanglement of formation, respectively, and equal to the relative entropy of entanglement for maximally correlated states.