Geometric measure of entanglement of multipartite mixed states

TL;DR

This paper extends the geometric measure of entanglement from pure to multipartite mixed states, characterizing the closest disentangled state and introducing the entanglement eigenvalue to quantify mixed state entanglement.

Contribution

It introduces a method to compute the geometric measure of entanglement for multipartite mixed states and defines the entanglement eigenvalue for such states.

Findings

Characterization of the nearest disentangled mixed state.

Introduction of the entanglement eigenvalue.

Relation between the nearest disentangled state and the entanglement eigenvalue.

Abstract

The geometric measure of entanglement of a pure state, defined by its distance to the set of pure separable states, is extended to multipartite mixed states. We characterize the nearest disentangled mixed state to a given mixed state with respect to this measure by a system of equations. The entanglement eigenvalue for a mixed state is introduced. For a given mixed state, we show that its nearest disentangled mixed state is associated with its entanglement eigenvalue.