Measuring Coherence with Entanglement Concurrence

TL;DR

This paper introduces a new convex roof quantum coherence measure called coherence concurrence, establishing a quantitative link between coherence and entanglement through concurrence measures.

Contribution

It proposes a novel coherence measure based on the generalized Gell-Mann matrices and proves its validity within the resource theory of coherence.

Findings

The coherence concurrence fulfills all resource theory requirements.

Any coherence can be converted into entanglement via incoherent operations.

The work establishes a quantitative operational connection between coherence and entanglement.

Abstract

Quantum coherence is a fundamental manifestation of the quantum superposition principle. Recently, Baumgratz \emph{et al}. [Phys. Rev. Lett. \textbf{113}, 140401 (2014)] presented a rigorous framework to quantify coherence from the view of theory of physical resource. Here we propose a new valid quantum coherence measure which is a convex roof measure, for a quantum system of arbitrary dimension, essentially using the generalized Gell-Mann matrices. Rigorous proof shows that the proposed coherence measure fulfills all the requirements dictated by the resource theory of quantum coherence measures. Moreover, strong links between the resource frameworks of coherence concurrence and entanglement concurrence is derived, which shows that any degree of coherence with respect to some reference basis can be converted to entanglement via incoherent operations. Our work provides a clear quantitative and operational connection between coherence and entanglement based on two kinds of concurrence. This new coherence measure, coherence concurrence, may be beneficial to the study of quantum coherence.