Parallelization of Adaptive Quantum Channel Discrimination in the
Non-Asymptotic Regime
- URL: http://arxiv.org/abs/2206.08350v2
- Date: Wed, 17 Jan 2024 03:17:47 GMT
- Title: Parallelization of Adaptive Quantum Channel Discrimination in the
Non-Asymptotic Regime
- Authors: Bjarne Bergh, Nilanjana Datta, Robert Salzmann, Mark M. Wilde
- Abstract summary: We investigate the performance of parallel and adaptive quantum channel discrimination strategies for a finite number of channel uses.
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.
- Score: 11.538345159297839
- License: http://creativecommons.org/licenses/by/4.0/
- 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.
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