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Every convex quantum resource is useful for channel discrimination

Banff International Research Station for Mathematical Innovation and Discovery

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.

Mathematics; Quantum theory; Operator theory; Mathematical physics

video/mp4

Author affiliation: University of Nottingham

2020-01-20

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/73348

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/