On the geometric measure of entanglement for pure states

TL;DR

This paper extends the calculation of the geometric measure of entanglement to broader classes of states by relaxing symmetry restrictions, enabling analysis of more complex and relevant quantum states.

Contribution

It introduces generalized methods for computing the geometric entanglement measure for less symmetric states, broadening applicability beyond highly symmetric cases.

Findings

Computed geometric entanglement for larger classes of states

Relaxed symmetry restrictions enable analysis of more complex states

Provided analytic solutions for generalized state coefficients

Abstract

The geometric measure of entanglement is the distance or angle between an entangled target state and the nearest unentangled state. Often one considers the geometric measure of entanglement for highly symmetric entangled states because it simplifies the calculations and allows for analytic solutions. Although some symmetry is required in order to deal with large numbers of qubits, we are able to loosen significantly the restrictions on the highly symmetric states considered previously, and consider several generalizations of the coefficients of both target and unentangled states. This allows us to compute the geometric entanglement measure for larger and more relevant classes of states.