Relative entropy of entanglement for certain multipartite mixed states

TL;DR

This paper analytically determines the relative entropy of entanglement for specific multipartite mixed states, including permutation-invariant states and D"ur's bound entangled states, and explores their relation to other entanglement measures.

Contribution

It proves conjectures on REE for certain multipartite states and provides explicit formulas, extending results to multi-qudit states and relating REE to other entanglement measures.

Findings

Analytic expressions for REE of permutation-invariant states.

Validation of conjectures for D"ur's bound entangled states.

Extended relations between REE, robustness, and geometric entanglement.

Abstract

We prove conjectures on the relative entropy of entanglement (REE) for two families of multipartite qubit states. Thus, analytic expressions of REE for these families of states can be given. The first family of states are composed of mixture of some permutation-invariant multi-qubit states. The results generalized to multi-qudit states are also shown to hold. The second family of states contain D\"ur's bound entangled states. Along the way, we have discussed the relation of REE to two other measures: robustness of entanglement and geometric measure of entanglement, slightly extending previous results.