Entanglement measure for multipartite pure states and its numerical calculation

TL;DR

This paper introduces a new entanglement measure for multipartite pure states based on Shannon entropy, demonstrating its properties and providing a genetic algorithm for numerical computation, also extending to fermionic states.

Contribution

It proposes a novel entanglement measure for multipartite pure states, with properties and a genetic algorithm for numerical calculation, extending to fermionic states.

Findings

The measure is additive and monotone under LOCC.

It coincides with reduced von Neumann entropy for bipartite states.

A genetic algorithm effectively computes the measure numerically.

Abstract

The quantification and classification of quantum entanglement is a very important and still open question of quantum information theory. In this paper, we describe an entanglement measure for multipartite pure states (the minimum of Shannon's entropy of orthogonal measurements). This measure is additive, monotone under LOCC, and coincides with the reduced von Neumann entropy on bipartite states. A method for numerical calculation of this measure by genetic algorithms is also presented. Moreover, the minimization of entropy technique is extended to fermionic states.