Geometric measure of entanglement for pure multipartite states

TL;DR

This paper develops methods to compute the geometric measure of entanglement for specific classes of pure multipartite states, providing analytical formulas and identifying the maximally entangled three-qubit state.

Contribution

It introduces new computational techniques for the geometric entanglement measure in symmetric multiqubit and three-qubit states, including analytical formulas and a canonical form.

Findings

Derived analytical formulas for three-qubit states.

Identified the W state as the maximally entangled three-qubit state.

Provided methods for symmetric multiqubit states with non-negative amplitudes.

Abstract

We provide methods for computing the geometric measure of entanglement for two families of pure states with both experimental and theoretical interests: symmetric multiqubit states with non-negative amplitudes in the Dicke basis and symmetric three-qubit states. In addition, we study the geometric measure of pure three-qubit states systematically in virtue of a canonical form of their two-qubit reduced states, and derive analytical formulae for a three-parameter family of three-qubit states. Based on this result, we further show that the W state is the maximally entangled three-qubit state with respect to the geometric measure.