On quantum channels

TL;DR

This paper reviews and unifies various known and new results on quantum channels, focusing on their dual states, extremal maps, and state parameterizations, to deepen understanding of entanglement behavior in quantum information.

Contribution

It provides a unified presentation of results on quantum channels, including characterizations of extremal maps and new parameterizations based on state normal forms.

Findings

Dual states induce characterizations of extremal CP-maps

Normal forms lead to new parameterizations of quantum channels

Insights into entanglement behavior through channel analysis

Abstract

One of the most challenging open problems in quantum information theory is to clarify and quantify how entanglement behaves when part of an entangled state is sent through a quantum channel. Of central importance in the description of a quantum channel or completely positive map (CP-map) is the dual state associated to it. The present paper is a collection of well-known, less known and new results on quantum channels, presented in a unified way. We will show how this dual state induces nice characterizations of the extremal maps of the convex set of CP-maps, and how normal forms for states defined on a Hilbert space with a tensor product structure lead to interesting parameterizations of quantum channels.