Constructing optimal entanglement witnesses. II

TL;DR

This paper introduces a new class of optimal entanglement witnesses and positive maps for large quantum systems, generalizing the Robertson map, with implications for entanglement detection and quantum channel design.

Contribution

It presents a novel construction of nondecomposable entanglement witnesses and positive maps for 4N x 4N systems, extending previous methods.

Findings

Constructed a class of optimal nondecomposable entanglement witnesses.

Showed that their physical approximations lead to entanglement breaking channels.

Generalized the Robertson map to higher-dimensional systems.

Abstract

We provide a class of optimal nondecomposable entanglement witnesses for 4N x 4N composite quantum systems or, equivalently, a new construction of nondecomposable positive maps in the algebra of 4N x 4N complex matrices. This construction provides natural generalization of the Robertson map. It is shown that their structural physical approximations give rise to entanglement breaking channels.