Parallel and Adaptive Quantum Channel Discrimination with Simple and Composite Hypotheses

Parallel and Adaptive Quantum Channel Discrimination with Simple and Composite Hypotheses

Seminar author:Bjarne Bergh

Event date and time:12/15/2022 04:00:pm

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We intestigate the difference between adaptive and parallel quantum channel discrimination strategies in the asymmetric setting.

In the case of two simple channel hypotheses, it has been shown that adaptive strategies are not more powerful asymptotically than sequential ones (as long as the type I error probability also asymptotically vanishes), whereas for a finite number of channel uses the difference (measured in terms of the decay rate of the type II error probability per channel use) can be arbitrarily large. We provide an upper bound on this difference, and hence extend the asymptotic result to the finite regime, by explicitly constructing a parallel strategy for any given sequential strategy and bounding the difference in their performances, and hence showing how adaptive strategies can be replaced with parallel ones in a practical setting.

In the case of composite hypotheses (hypotheses given by two sets of channels), we find the asymptotic error exponent for parallel discrimination strategies, and show that already classically, adaptive strategies can lead to an asymptotical advantage.