A characterization of optimal entanglement witnesses

TL;DR

This paper characterizes optimal entanglement witnesses using positive maps, introduces a method to verify their optimality, and presents new examples supporting a conjecture about their physical approximations leading to entanglement breaking maps.

Contribution

It provides a new characterization of optimal entanglement witnesses and a general method for checking their optimality, including the construction of new indecomposable examples.

Findings

New indecomposable optimal witnesses without spanning property.

Support for the conjecture that structural physical approximations lead to entanglement breaking maps.

A general method for verifying the optimality of entanglement witnesses.

Abstract

In this paper, we present a characterization of optimal entanglement witnesses in terms of positive maps and then provide a general method of checking optimality of entanglement witnesses. Applying it, we obtain new indecomposable optimal witnesses which have no spanning property. These also provide new examples which support a recent conjecture saying that the so-called structural physical approximations to optimal positive maps (optimal entanglement witnesses) give entanglement breaking maps (separable states).