Mayank Bhatia

We study the information-theoretic properties of the full two-parameter family of quantum channels covariant under the orthogonal group O(d), which we call Brauer channels. This family contains the depolarizing and generalized Werner-Holevo channels as one-parameter subfamilies, and its Choi matrix admits a three-block decomposition via Schur-Weyl duality for O(d). We derive closed-form expressions for the maximum output p-norms of Brauer channels and identify a region where two-copy multiplicativity of these norms fails. We prove that the minimum output Renyi 2-entropy is additive for two copies across the entire CPTP region, extending prior partial results. Using orthogonal covariance, we simplify several classical and quantum capacity upper bounds, including SDP-based, approximate entanglement-breaking, approximate covariance, Rains information, and additive-extension bounds, and compare them across the family of Brauer channels. Finally, we derive a closed-form expression for the coherent information of qudit repetition codes through multiple copies of any Brauer channel. We find that repetition codes exhibit positive coherent information beyond the hashing bound in a broad region of channels that includes the qudit depolarizing channel, demonstrating superadditivity of coherent information for Brauer channels.