The joys of permutation symmetry: direct measurements of entanglement

TL;DR

This paper discusses how to transform direct measurements of entanglement into reliable verification tests by leveraging a recent theorem, addressing previous experimental limitations and assumptions.

Contribution

It introduces a method to turn direct entanglement measurements into verified entanglement tests using Renner's theorem.

Findings

Addresses unverified assumptions in previous experiments

Proposes a verification method based on a recent theorem

Enhances reliability of entanglement measurement techniques

Abstract

So-called direct measurements of entanglement are collective measurements on multiple copies of a (bipartite or multipartite) quantum system that directly provide one a value for some entanglement measure, such as the concurrence for bipartite states. Multiple copies are needed since the entanglement of a mixed state is not a linear function of the density matrix. Unfortunately, so far all experimental implementations of direct measurements made unverified assumptions about the form of the states, and, therefore, do not qualify as entanglement verification tests. I discuss how a direct measurement can be turned into a quantitative entanglement verification test by exploiting a recent theorem by Renner (R. Renner, Nature Physics 3, 645 (2007)).