Strict hierarchy between parallel, sequential, and indefinite-causal-order strategies for channel discrimination

TL;DR

This paper demonstrates a strict hierarchy in quantum channel discrimination strategies, showing that sequential and indefinite causal order strategies can outperform parallel ones, with a systematic method to identify such channels.

Contribution

It introduces a hierarchy among quantum channel discrimination strategies, including indefinite causal order, and provides a systematic way to find channels exhibiting this hierarchy.

Findings

Sequential strategy outperforms parallel in certain cases

Indefinite causal order strategies can outperform both

Hierarchy among all strategies established

Abstract

We present an instance of a task of minimum-error discrimination of two qubit-qubit quantum channels for which a sequential strategy outperforms any parallel strategy. We then establish two new classes of strategies for channel discrimination that involve indefinite causal order and show that there exists a strict hierarchy among the performance of all four strategies. Our proof technique employs a general method of computer-assisted proofs. We also provide a systematic method for finding pairs of channels that showcase this phenomenon, demonstrating that the hierarchy between the strategies is not exclusive to our main example.