Irreducibly $SU(2)$-covariant quantum channels of low rank

TL;DR

This paper characterizes low-rank $SU(2)$-covariant quantum channels, revealing their entanglement properties, limitations on degradability, and demonstrating significant additivity violations in their coherent information.

Contribution

It provides a complete description of low-rank $SU(2)$-covariant channels and explores their information-theoretic properties, including entanglement and additivity violations.

Findings

PPT property coincides with entanglement-breaking for these channels

Degradability is rare among these channels

Strong additivity violation of coherent information observed

Abstract

We investigate information theoretic properties of low rank (less than or equal to 3) quantum channels with $SU(2)$-symmetry, where we have a complete description. We prove that PPT property coincides with entanglement-breaking property and that degradability seldomly holds in this class. In connection with these results we will demonstrate how we can compute Holevo and coherent information of those channels. In particular, we exhibit a strong form of additivity violation of coherent information, which resembles the superactivation of coherent information of depolarizing channels.