Universal behavior of the geometric entanglement measure of many-qubit W states

TL;DR

This paper demonstrates that for large N, the geometric entanglement of most W states depends only on a single parameter related to the minimal z component of the Bloch vector, simplifying their analysis and experimental estimation.

Contribution

It provides an analytical formula linking the geometric entanglement measure of large W states to a single Bloch vector parameter, streamlining their characterization.

Findings

Geometric entanglement depends on one variable for large N W states.

The formula relates maximal product overlap to the Bloch vector.

Experimental estimation of entanglement becomes easier with the derived relation.

Abstract

We show that when N>>1 the geometric entanglement measure of general N-qubit W states, except maximally entangled W states, is a one-variable function and depends only on the Bloch vector with the minimal z component. Hence one can prepare a W state with the required maximal product overlap by altering the Bloch vector of a single qubit. Next we compute analytically the geometric measure of large-scale W states by describing these systems in terms of very few parameters. The final formula relates two quantities, namely the maximal product overlap and the Bloch vector, that can be easily estimated in experiments.