Asymptotic analysis for $O_N^+$-Temperley-Lieb quantum channels

TL;DR

This paper investigates a class of quantum channels with symmetries from free orthogonal quantum groups, approximates them with simpler channels, and explores their capacity properties in the large N limit.

Contribution

It introduces an approximation method for $O_N^+$-Temperley-Lieb channels and analyzes their capacity and additivity properties asymptotically.

Findings

Channels can be approximated by simpler ones in Bures distance

Strong additivity questions are addressed for large N

Capacities like classical, private, and quantum are characterized asymptotically

Abstract

In this paper, we focus on a class of quantum channels which are covariant for symmetries from free orthogonal quantum groups $O_N^+$. These quantum channels are called $O_N^+$-Temperley-Lieb channels, and their information-theoretic properties such as Holevo information and coherent information were analyzed in [BCLY20], but their additivity questions remained open. The main result of this paper is to approximate $O_N^+$-Temperley-Lieb quantum channels by much simpler ones in terms Bures distance. As applications, we study strong additivity questions for $O_N^+$-Temperley-Lieb quantum channels, and their classical capacity, private classical capacity and quantum capacity in the asymptotic regime $N\rightarrow \infty$.