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

Abstract

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