Converse Bounds on Probabilistic Distillation of Quantum Channel Resources

Probabilistic protocols can enlarge the set of feasible resource transformations by conditioning on successful outcomes, but in many practical setting there are fundamental limitations on the success probability and the error incurred in such transformation. We derive complementary one-shot converse bounds and their regularized asymptotic rate bounds. Successful outcomes are represented by branches of free superinstruments. While projective robustness yields an accuracy constraint independent of the success probability, generalized robustness directly bounds the probability itself. In particular, we establish the explicit relationship between the success probability and the error of the protocol using robustness measure. For a flagged erasure channel, postselection recovers the identity channel exactly. In this case, generalized robustness remains finite although projective robustness is infinite. Restricting the framework to preparation channels recovers state distillation and gives explicit bounds for coherence distillation from noisy coherent states. Together, these examples distinguish channel-level behavior from the state-theoretic case obtained by restricting the framework to preparation channels.