Experimental Examination of Entanglement Estimates

TL;DR

This paper introduces a new method to estimate both lower and upper bounds of genuine multipartite entanglement in mixed states using expectation values of Hermitian operators, simplifying experimental procedures.

Contribution

It extends previous entanglement estimation techniques to include upper bounds and identifies a class of operators requiring minimal measurements.

Findings

Successfully estimated entanglement bounds for various states

Demonstrated method's effectiveness with experimental data

Reduced measurement complexity for entanglement estimation

Abstract

Recently a proper genuine multipartite entanglement (GME) measure has been found for three-qubit pure states [see Xie and Eberly, Phys. Rev. Lett. 127, 040403 (2021)], but capturing useful entanglement measures for mixed states has remained an open challenge. So far, it requires not only a full tomography in experiments, but also huge calculational labor. A leading proposal was made by G\"uhne, Reimpell, and Werner [Phys. Rev. Lett. 98, 110502 (2007)], who used expectation values of entanglement witnesses to describe a lower bound estimation of entanglement. We provide here an extension that also gives genuine upper bounds of entanglement. This advance requires only the expectation value of {\em any} Hermitian operator. Moreover, we identify a class of operators $\A_1$ which not only give good estimates, but also require a remarkably small number of experimental measurements. In this note we define our approach and illustrate it by estimating entanglement measures for a number of pure and mixed states prepared in our recent experiments.