A preprint posted to arXiv — not yet peer-reviewed — addresses a foundational question in quantum hypothesis testing: does the order or adaptivity of measurements matter when trying to distinguish between two quantum channels asymptotically? The authors claim to show that for any two finite-dimensional memoryless quantum channels, parallel strategies, adaptive strategies, and fully general testers (including those exploiting indefinite causal order) all achieve the same Stein exponent, given by the regularized channel relative entropy.
The Stein exponent characterizes the optimal exponential decay rate of the type-II error (false acceptance of the null hypothesis) while holding the type-I error below a fixed tolerance. The paper's central assertion is that no testing strategy — however causally sophisticated — can improve upon this rate asymptotically. The technical core of the argument rests on a continuity result for the regularized sandwiched Rényi channel divergence in the limit as its order approaches one, which the authors use to connect one-shot and asymptotic regimes. The paper also derives what it calls the exact strong-converse exponent, characterizing how quickly correct acceptance must decay when one attempts to exceed the Stein rate.
If the results survive peer review, they would place a firm information-theoretic boundary on the practical utility of exotic causal structures — such as the quantum switch — for channel discrimination tasks. As an unreviewed preprint, however, the claims, particularly the generality of the indefinite causal order setting and the continuity argument at the heart of the proof, await independent scrutiny.