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

TL;DR

This paper introduces inequalities based on observable mean values that serve as both necessary and sufficient conditions for bipartite state separability and provides a measurable lower bound for the convex-roof extension of negativity.

Contribution

It proposes a new set of inequalities for entanglement detection and derives a measurable lower bound for negativity's convex-roof extension.

Findings

Inequalities serve as necessary and sufficient conditions for pure states.

Applicable to some mixed states for entanglement detection.

Provides a measurable lower bound for negativity.

Abstract

We present a set of inequalities based on mean values of quantum mechanical observables 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.