Entanglement detection and lower bound of the convex-roof extension of the negativity

Abstract

We present a set of inequalities based on mean values of quantum mechanical observables similar to nonlinear entanglement witnesses for bipartite quantum systems. These inequalities give rise to sufficient and necessary conditions for separability of all bipartite pure states and even some mixed states. In terms of these mean values of quantum mechanical observables, a measurable lower bound of the convex-roof extension of the negativity is derived.