General resource theories in quantum mechanics and beyond: operational characterization via discrimination tasks



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19050015

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 relevant to information processing 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. 

Next, we significantly extend the above consideration beyond "quantum" resource theories of "states"; we establish an operational characterization of general convex resource theories --- describing the resource content of not only states, but also measurements and channels, both within quantum mechanics and in general probabilistic theories (GPTs) --- in the context of state and channel discrimination. We find that discrimination tasks provide a unified operational description for quantification and manipulation of resources by showing that the family of robustness measures can be understood as the maximum advantage provided by any physical resource in several different discrimination tasks, as well as establishing that such discrimination problems can fully characterize the allowed transformations within the given resource theory. Our results establish a fundamental connection between the operational tasks of discrimination and core concepts of resource theories --- the geometric quantification of resources and resource manipulation --- valid for all physical theories beyond quantum mechanics with no additional assumptions about the structure of the GPT required.

References: 

[1] Ryuji Takagi, Bartosz Regula, Kaifeng Bu, Zi-Wen Liu, and Gerardo Adesso, "Operational Advantage of Quantum Resources in Subchannel Discrimination", Phys. Rev. Lett. 122.140402 (2019)

[2] Ryuji Takagi and Bartosz Regula, "General resource theories in quantum mechanics and beyond: operational characterization via discrimination tasks", arXiv: 1901.08127