Quantum channels with polytopic images and image additivity

TL;DR

This paper investigates quantum channels with polytopic images, characterizing their properties, including violations of additivity of minimal output entropy and conditions for universal image additivity, revealing their relation to entanglement breaking and classical-quantum channels.

Contribution

It provides a complete characterization of channels with polytopic images and introduces the concept of universally image additive channels, expanding understanding of quantum channel structures.

Findings

Channels with polytopic images can violate minimal output entropy additivity.

Universally image additive channels are a strict subset of entanglement breaking channels.

Classical-quantum channels are a subset of universally image additive channels.

Abstract

We study quantum channels with respect to their image, i.e., the image of the set of density operators under the action of the channel. We first characterize the set of quantum channels having polytopic images and show that additivity of the minimal output entropy can be violated in this class. We then provide a complete characterization of quantum channels $T$ that are universally image additive in the sense that for any quantum channel $S$, the image of $T \otimes S$ is the convex hull of the tensor product of the images of $T$ and $S$. These channels turn out to form a strict subset of entanglement breaking channels with polytopic images and a strict superset of classical-quantum channels.