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

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 $N\rightarrow \infty$.