Constructing new optimal entanglement witnesses

TL;DR

This paper introduces a new class of optimal indecomposable entanglement witnesses capable of detecting PPT entanglement, with implications for quantum state analysis and entanglement-breaking channels.

Contribution

It presents a novel construction of indecomposable atomic entanglement witnesses and maps, extending known results and supporting recent conjectures.

Findings

New class of indecomposable entanglement witnesses introduced

Witnesses are proven to be optimal and atomic

Structural physical approximations lead to entanglement breaking channels

Abstract

We provide a new class of indecomposable entanglement witnesses. In 4 x 4 case it reproduces the well know Breuer-Hall witness. We prove that these new witnesses are optimal and atomic, i.e. they are able to detect the "weakest" quantum entanglement encoded into states with positive partial transposition (PPT). Equivalently, we provide a new construction of indecomposable atomic maps in the algebra of 2k x 2k complex matrices. It is shown that their structural physical approximations give rise to entanglement breaking channels. This result supports recent conjecture by Korbicz et. al.