  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 $N\rightarrow \infty$.
