Decomposing nuclear maps

TL;DR

This paper demonstrates that a strengthened form of the completely positive approximation property applies to all nuclear order zero maps, involving asymptotically order zero maps and convex combinations of order zero maps.

Contribution

It establishes that the strengthened approximation property holds universally for nuclear order zero maps, extending previous results.

Findings

The strengthened approximation property applies to all nuclear order zero maps.

Asymptotically order zero maps are involved in the approximation.

Convex combinations of order zero maps are used in the approximation process.

Abstract

We show that the strengthened version of the completely positive approximation property of Brown, Carri\'on, and White---where the downward maps are asymptotically order zero and the upward maps are convex combinations of order zero maps---is enjoyed by every nuclear order zero map.