PPT-inducing, distillation-prohibiting, and entanglement-binding quantum channels

TL;DR

This paper reviews entanglement degradation in quantum systems, focusing on PPT-inducing, distillation-prohibiting, and entanglement-binding channels, and clarifies their relationships with concrete examples.

Contribution

It introduces and analyzes PPT-inducing channels, their relation to distillation-prohibiting and entanglement-binding channels, and provides explicit examples.

Findings

PPT-inducing channels form a convex subset of distillation-prohibiting channels.

A relation between entanglement-binding and distillation-prohibiting channels is established.

An example of a distillation-prohibiting map not entanglement binding is provided.

Abstract

Entanglement degradation in open quantum systems is reviewed in the Choi-Jamio{\l}kowski representation of linear maps. In addition to physical processes of entanglement dissociation and entanglement annihilation, we consider quantum dynamics transforming arbitrary input states into those that remain positive under partial transpose (PPT-inducing channels). Such evolutions form a convex subset of distillation-prohibiting channels. A relation between the above channels and entanglement-binding ones is clarified. An example of the distillation-prohibiting map $\Phi\otimes\Phi$ is given, where $\Phi$ is not entanglement binding.