Relative Entropy of Entanglement and Restricted Measurements

TL;DR

This paper introduces measurement-restricted variants of the relative entropy of entanglement, demonstrating that all multipartite entangled states require a positive rate of non-local resource for their asymptotic creation.

Contribution

It develops new entanglement measures based on restricted measurements and proves the positivity of the regularized entropy of entanglement for all multipartite states.

Findings

Regularized entropy of entanglement is strictly positive for all multipartite entangled states.

Asymptotic creation of multipartite entangled states requires a non-zero non-local resource.

New variants of relative entropy of entanglement based on measurement restrictions.

Abstract

We introduce variants of relative entropy of entanglement based on the optimal distinguishability from unentangled states by means of restricted measurements. In this way, we are able to prove that the standard regularized entropy of entanglement is strictly positive for all multipartite entangled states. In particular, this implies that the asymptotic creation of a multipartite entangled state by means of local operations and classical communication always requires the consumption of a non-local resource at a strictly positive rate.