Determining lower bounds on a measure of multipartite entanglement from few local observables

TL;DR

This paper presents a method to efficiently estimate a measure of multipartite entanglement using minimal local measurements, providing tight bounds and connecting to recent nonlinear witness frameworks.

Contribution

It introduces a novel approach to lower bound multipartite entanglement measures with few local observables, enhancing measurement efficiency and theoretical understanding.

Findings

Some bounds are tight and explicitly connected to recent nonlinear witnesses.

Only a few local measurements are needed to determine these bounds.

The method improves measurement efficiency for entanglement quantification.

Abstract

We introduce a method to lower bound an entropy-based measure of genuine multipartite entanglement via nonlinear entanglement witnesses. We show that some of these bounds are tight and explicitly work out their connection to a framework of nonlinear witnesses that were published recently. Furthermore we provide a detailed analysis of these lower bounds in the context of other possible bounds and measures. In exemplary cases we show that only a few local measurements are necessary to determine these lower bounds.