Duality and the geometric measure of entanglement of general multiqubit W states

TL;DR

This paper determines the closest product states for general multiqubit W states and uses this to compute their geometric measure of entanglement, revealing uniqueness in highly entangled cases.

Contribution

It introduces a duality approach between unit vectors and W states to calculate the geometric measure of entanglement for multiqubit states.

Findings

Nearest product states are essentially unique for highly entangled W states.

The geometric measure of entanglement can be explicitly calculated using this duality.

A unit vector in Euclidean space characterizes the closest product state.

Abstract

We find the nearest product states for arbitrary generalized W states of n qubits, and show that the nearest product state is essentially unique if the W state is highly entangled. It is specified by a unit vector in Euclidean n-dimensional space. We use this duality between unit vectors and highly entangled W states to find the geometric measure of entanglement of such states.