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

TL;DR

This paper compares parallel and adaptive quantum channel discrimination strategies for finite uses, showing parallel strategies can match adaptive ones in performance and are computationally efficient to optimize.

Contribution

It extends asymptotic equivalence results to the non-asymptotic regime, providing explicit bounds and polynomial-time optimization methods for quantum channel discrimination strategies.

Findings

Parallel strategies can be constructed to match adaptive performance.

All parallel strategies can be optimized in polynomial time.

Provides tight upper bounds on adaptive strategy performance.

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.