Operational Advantage of Quantum Resources in Subchannel Discrimination

TL;DR

This paper demonstrates that all convex quantum resource theories provide an operational advantage in subchannel discrimination tasks, with the generalized robustness measure quantifying this advantage across various resource types.

Contribution

It establishes that any resource state offers an advantage in channel discrimination, linking the generalized robustness to operational benefits in multiple quantum resource theories.

Findings

Resource states enable higher success probabilities in discrimination tasks.

Generalized robustness quantifies the maximum operational advantage.

The results apply to entanglement, coherence, and magic resource theories.

Abstract

One of the central problems in the study of quantum resource theories is to provide a given resource with an operational meaning, characterizing physical tasks in which the resource can give an explicit advantage over all resourceless states. We show that this can always be accomplished for all convex resource theories. We establish in particular that any resource state enables an advantage in a channel discrimination task, allowing for a strictly greater success probability than any state without the given resource. Furthermore, we find that the generalized robustness measure serves as an exact quantifier for the maximal advantage enabled by the given resource state in a class of subchannel discrimination problems, providing a universal operational interpretation to this fundamental resource quantifier. We also consider a wider range of subchannel discrimination tasks and show that the generalized robustness still serves as the operational advantage quantifier for several well-known theories such as entanglement, coherence, and magic.