A Riemannian Genuine Measure of Entanglement for Pure States

TL;DR

This paper introduces a new geometric measure of entanglement for pure quantum states based on geodesic distances, which satisfies key properties and outperforms existing measures in smoothness and discriminance.

Contribution

It proposes a novel Riemannian geometric entanglement measure for pure states that enhances the accuracy and robustness over previous measures.

Findings

The measure satisfies all properties of a genuine entanglement measure.

It demonstrates improved smoothness compared to existing measures.

It shows better discriminance among different pure states.

Abstract

While several measures exist for entanglement of multipartite pure states, a true entanglement measure for mixed states still eludes us. A deeper study of the geometry of quantum states may be the way to address this issue, on which context we come up with a measure for pure states based on a geodesic distance on the space of quantum states. Our measure satisfies all the desirable properties of a ``Genuine Measure of Entanglement" (GME), and in comparison with some of the other existing measures, shows better smoothness and discriminance.