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

Studies on conservation of quantum symmetries have been initiated by recent papers (Brannan et al. in Commun Math Phys 376(2):795–839, 2020; Lee Quantum channels with group symmetry, 2020). We, this paper, investigate how can be applied to study additivity questions for covariant channels, particularly the so-called \(O_N^+\)-Temperley–Lieb channels. Their information-theoretic properties were analyzed Brannan (Commun 2020), but associated remained open due highly nontrivial structures. We present a new approach analyze small perturbations terms Bures distance within asymptotic regime \(N\rightarrow \infty \) and apply continuity bounds classical capacity, private capacity strong questions.