Estimating multipartite entanglement measures

TL;DR

This paper explores methods to estimate the three-tangle, a measure of multipartite entanglement, from experimental data, providing bounds that relate to characteristic curves and applying these to real experimental states.

Contribution

It introduces a new approach to estimate the convex-roof extended three-tangle from experimental data using characteristic curves, linking theory with practical measurements.

Findings

Lower bounds on three-tangle can be obtained from experimental data.

A non-zero lower bound is achieved if GHZ-fidelity exceeds 3/4.

The method is applied to recent experimental states producing GHZ states.

Abstract

We investigate the lower bound obtained from experimental data of a quantum state $\rho$, as proposed independently by G\"uhne et al. and Eisert et al. for mixed states of three qubits. The measure we consider is the convex-roof extended three-tangle. Our findings highlight an intimate relation to lower bounds obtained recently from so-called characteristic curves of a given entanglement measure. We apply the bounds to estimate the three-tangle present in recently performed experiments aimed at producing a three-qubit GHZ state. A non-vanishing lower bound is obtained if the GHZ-fidelity of the produced states is larger than 3/4.