The geometric measure of multipartite entanglement and the singular values of a hypermatrix

TL;DR

This paper introduces a polynomial equation characterizing the geometric measure of entanglement in multipartite states, extending bipartite matrix concepts, and provides solutions for specific three-qubit states.

Contribution

It generalizes the characteristic equation approach to multipartite entanglement and solves it explicitly for certain three-qubit states.

Findings

The geometric measure of multipartite entanglement satisfies a polynomial equation.

The polynomial equation extends the bipartite characteristic equation to multipartite systems.

Explicit solutions are obtained for a class of three-qubit states.

Abstract

It is shown that the geometric measure of entanglement of a pure multipartite state satisfies a polynomial equation, generalising the characteristic equation of the matrix of coefficients of a bipartite state. The equation is solved for a class of three-qubit states.