A Riemannian Genuine Measure of Entanglement for 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.

This work was not complete and had some incorrect assumptions as it was pointed out by a few peers. An impoved version of ideas used here are presented as Sharp Geometric Measure