Higher-order incompatibility improves distinguishability of causal quantum networks

TL;DR

This paper demonstrates that higher-order quantum incompatibility enhances the ability to distinguish quantum networks, showing incompatible testers outperform compatible ones in specific quantum tasks, thus establishing incompatibility as a resource.

Contribution

It introduces the concept that incompatibility of quantum testers improves distinguishability of quantum processes and generalizes previous findings on resourcefulness in quantum state discrimination.

Findings

Incompatible quantum testers outperform compatible ones in a two-party distinguishing game.

Resource measures like convex weight quantify the resourcefulness of incompatibility.

Incompatibility acts as a genuine resource in quantum process discrimination tasks.

Abstract

Higher-order quantum theory deals with causal quantum processes, described by quantum combs, and test procedures, described by quantum testers, "measuring" these processes. In this work, we show that "jointly non-implementable" or incompatible quantum testers perform better in distinguishability tasks than their compatible counterparts. To demonstrate our finding, we consider a specific two-party game based on distinguishing quantum combs. We show that the player does better at winning the game when they have exclusive access to incompatible testers over compatible ones. Moreover, we show that, using the resource theoretic measure convex weight, any general quantum resource present in testers is resourceful in quantum comb exclusion tasks. These investigations generalise, respectively, an earlier finding that incompatibility of quantum observables to be a bona fide resource in quantum state distinguishability tasks and another finding that any resource present in observables result in improved performance in state exclusion or antidistinguishability tasks.