Structural approximations to positive maps and entanglement breaking channels

TL;DR

This paper investigates structural approximations of positive maps, demonstrating that many optimal approximations are entanglement breaking channels, which can be implemented through measurement and state-preparation, aiding in entanglement detection.

Contribution

It shows that optimal positive map approximations are entanglement breaking channels, enabling practical measurement-based entanglement detection methods.

Findings

Many approximations define entanglement breaking channels

These channels can be implemented via measurement and state-preparation

Findings facilitate simpler entanglement detection methods

Abstract

Structural approximations to positive, but not completely positive maps are approximate physical realizations of these non-physical maps. They find applications in the design of direct entanglement detection methods. We show that many of these approximations, in the relevant case of optimal positive maps, define an entanglement breaking channel and, consequently, can be implemented via a measurement and state-preparation protocol. We also show how our findings can be useful for the design of better and simpler direct entanglement detection methods.