Easy implementable algorithm for the geometric measure of entanglement

TL;DR

This paper introduces a straightforward algorithm for approximating the geometric measure of entanglement in multipartite mixed states, requiring only eigenproblem solutions and singular value decompositions, demonstrated on specific quantum states.

Contribution

The paper proposes a simple, implementable algorithm for estimating the geometric measure of entanglement applicable to any multipartite mixed state, using only basic linear algebra techniques.

Findings

Algorithm successfully applied to isotropic 3-qubit states

Effective on 3-qubit XX model with magnetic field

Provides upper bounds for entanglement measure

Abstract

We present an easy implementable algorithm for approximating the geometric measure of entanglement from above. The algorithm can be applied to any multipartite mixed state. It involves only the solution of an eigenproblem and finding a singular value decomposition, no further numerical techniques are needed. To provide examples, the algorithm was applied to the isotropic states of 3 qubits and the 3-qubit XX model with external magnetic field.