This paper studies how well one can tell two quantum channels apart when one demands a fixed upper bound on the Type‑I error (the chance of wrongly rejecting the null channel). The main result is that three wide classes of testing procedures—parallel probes, adaptive (sequential) probes, and fully general testers that even allow indefinite causal order—all achieve the same asymptotic error rate. That rate is the regularized channel relative entropy, a quantity that measures how distinguishable the two channels are when many independent uses are allowed.

Concretely, the authors consider finite‑dimensional, memoryless channels used many times. For any fixed Type‑I error tolerance ε between 0 and 1, the best possible exponential decay rate of the Type‑II error (accepting the null when the alternative channel is present) equals the regularized channel relative entropy. If one tries to force a faster decay than that rate, the probability of correctly accepting the null instead must fall exponentially. In short, using adaptive strategies or exotic processes without a definite order does not improve the asymptotic asymmetric discrimination rate.

The proof combines several technical ideas about channel representations and divergences. Channels are handled through their Choi operators, which turn channel discrimination into operator inequalities. The authors express the testing score as a minimal normalized positive “Choi slack” and use a fixed‑marginal de Finetti reduction to replace that slack by a mixture of independent and identically distributed channel Choi operators with only polynomial overhead. A second key step is a continuity result for the regularized sandwiched Rényi channel divergence at order one. That continuity allows control over arbitrarily entangled inputs through a supported‑inverse factorization and a tensor moment estimate. Together these steps let the authors reduce general tests to parallel tests and close the remaining technical endpoint.