Fundamental limitations on distillation of quantum channel resources

Quantum channels underlie the dynamics of quantum systems, but in many practical settings it is themselves that require processing. We establish universal limitations on processing both states and channels, expressed form no-go theorems quantitative bounds for manipulation general channel resources under most transformation protocols. Focusing class distillation tasks -- which can be understood either as purification noisy into unitary ones, or extraction state-based from we develop fundamental restrictions error incurred such transformations comprehensive lower overhead any protocol. In asymptotic setting, our results yield broadly applicable rates distillation. demonstrate through applications to fault-tolerant computation, where obtain state-of-the-art cost magic state distillation, well communication, recover a number strong converse capacity.