Entanglement irreversibility from quantum discord and quantum deficit

TL;DR

This paper explores the irreversibility of entanglement in quantum systems by relating it to quantum discord and quantum deficit, providing new insights into entanglement measures and their limitations.

Contribution

It establishes a connection between entanglement irreversibility and quantum correlations, and analytically characterizes several entanglement measures for a generalized family of states.

Findings

Entanglement of formation exceeds coherent information in most cases.

Entanglement cost is generally larger than entanglement of formation.

Irreversibility of entanglement under LOCC is demonstrated for a broad class of states.

Abstract

We relate the problem of irreversibility of entanglement with the recently defined measures of quantum correlation - quantum discord and one-way quantum deficit. We show that the entanglement of formation is always strictly larger than the coherent information and the entanglement cost is also larger in most cases. We prove irreversibility of entanglement under LOCC for a family of entangled states. This family is a generalization of the maximally correlated states for which we also give an analytic expression for the distillable entanglement, the relative entropy of entanglement, the distillable secret key and the quantum discord.