Parallelization of Adaptive Quantum Channel Discrimination in the Non-Asymptotic Regime

Abstract

We investigate the performance of parallel and adaptive quantum channel discrimination strategies for a finite number of channel uses. It has recently been shown that, in the asymmetric setting with asymptotically vanishing type I error probability, adaptive strategies are asymptotically not more powerful than parallel ones. We extend this result to the non-asymptotic regime with finitely many channel uses, by explicitly constructing a parallel strategy for any given adaptive strategy, and bounding the difference in their performances, measured in terms of the decay rate of the type II error probability per channel use. We further show that all parallel strategies can be optimized over in time polynomial in the number of channel uses, and hence our result can also be used to obtain a poly-time-computable asymptotically tight upper bound on the performance of general adaptive strategies.

v2: Accepted Version. Changes to v1: Added an entire section on computability of n-shot exponents, reworked the example section, and added many remarks and clarifications. 21 pages, 3 figures

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• An invitation to the sample complexity of quantum hypothesis testing
• Adversarial quantum channel discrimination
• Extendible quantum measurements and limitations on classical communication
• Attainability of quantum state discrimination bounds with collective measurements on finite copies