Unitary channel discrimination beyond group structures: Advantages of sequential and indefinite-causal-order strategies

TL;DR

This paper investigates the advantages of sequential and indefinite-causal-order strategies over parallel strategies in unitary channel discrimination, revealing conditions where each approach is optimal and establishing a tight upper bound for success probability.

Contribution

It demonstrates that sequential and indefinite-causal-order strategies can outperform parallel ones in certain discrimination tasks and provides a tight upper bound for success probability across all strategies.

Findings

Sequential strategies can outperform parallel ones in minimum-error discrimination.

Indefinite causal order strategies are advantageous beyond group-structured channels.

A tight upper bound for success probability is derived and saturated by unitary k-designs.

Abstract

For minimum-error channel discrimination tasks that involve only unitary channels, we show that sequential strategies may outperform the parallel ones. Additionally, we show that general strategies that involve indefinite causal order are also advantageous for this task. However, for the task of discriminating a uniformly distributed set of unitary channels that forms a group, we show that parallel strategies are, indeed, optimal, even when compared to general strategies. We also show that strategies based on the quantum switch cannot outperform sequential strategies in the discrimination of unitary channels. Finally, we derive an absolute upper bound for the maximal probability of successfully discriminating any set of unitary channels with any number of copies for the most general strategies that are suitable for channel discrimination. Our bound is tight since it is saturated by sets of unitary channels forming a group k-design.