A Riemannian Genuine Measure of Entanglement for Pure States

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, in which context we present a measure for multipartite pure state entanglement (GBR) based on a geodesic distance in the space of quantum states. Our measure satisfies all the desirable properties of a “Genuine Measure of Entanglement” (GME), that exhibits some advantages over other GMEs.