Capacities of a two-parameter family of noisy Werner-Holevo channels

TL;DR

This paper introduces a two-parameter family of noisy quantum channels based on Werner-Holevo channels, analyzing their properties such as capacity, spectrum, and divisibility, extending their applicability to higher-dimensional qudits.

Contribution

It extends Werner-Holevo channels to higher dimensions using Lie algebra structures and explores their properties as noisy channels with reduced covariance.

Findings

Channels interpolate between identity and Werner-Holevo channels

Spectrum and capacity bounds are derived

Channels exhibit regions of non-indivisibility

Abstract

In $d=2j+1$ dimensions, the Landau-Streater quantum channel is defined on the basis of spin $j$ representation of the $su(2)$ algebra. Only for $j=1$, this channel is equivalent to the Werner-Holevo channel and enjoys covariance properties with respect to the group $SU(3)$. We extend this class of channels to higher dimensions in a way which is based on the Lie algebra $so(d)$ and $su(d)$. As a result it retains its equivalence to the Werner-Holevo channel in arbitrary dimensions. The resulting channel is covariant with respect to the unitary group $SU(d)$. We then modify this channel in a way which can act as a noisy channel on qudits. The resulting modified channel now interpolates between the identity channel and the Werner-Holevo channel and its covariance is reduced to the subgroup of orthogonal matrices $SO(d)$. We then investigate some of the propeties of the resulting two-parameter family of channels, including their spectrum, their regions of lack of indivisibility, their Holevo quantity, entanglement-assisted capacity and the closed form of their complement channel and a possible lower bound for their quantum capacity.