Abstract
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. Specifically, we introduce quantifiers of resourcefulness of states, measurements, and channels in any GPT based on the generalized robustness, and show that they exactly characterize the maximum advantage that a given resource provides over all free states, measurements, or channels in a class of state or channel discrimination tasks. In quantum mechanics, we show that the robustness of measurement can be alternatively understood as the maximal increase in one-shot accessible information when compared to free measurements. We furthermore endow the standard robustness of a state with an operational meaning as the quantifier of the maximum advantage in binary channel discrimination tasks. Finally, we show that several classes of channel and state discrimination tasks can form complete families of monotones fully characterizing the transformations of states and measurements under any chosen class of free operations. Our results establish a fundamental connection between operational tasks of discrimination and core concepts of resource theories, valid for all physical theories with no additional assumptions about the structure of the GPT required.
Highlights
The advantages provided by quantum phenomena in the transfer and processing of information allowed for the technological boom currently transforming areas such as communication, computation, cryptography, and sensing [1,2]
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
We introduce a quantifier of resourcefulness of a measurement in any general probabilistic theories (GPTs), the generalized robustness of measurement, and show that it admits an operational interpretation as the maximum advantage that a given measurement provides over resourceless measurements in all state discrimination tasks
Summary
The advantages provided by quantum phenomena in the transfer and processing of information allowed for the technological boom currently transforming areas such as communication, computation, cryptography, and sensing [1,2]. Quantum mechanics can be regarded precisely as resources in information processing tasks sparked an investigation of quantum information in the so-called resource-theoretic setting, aiming to establish the theoretical and practical methods to characterize both the advantages and the limitations associated with different physical properties of quantum systems, measurements, and transformations [3]. Similar results were subsequently found in several different resource theories of states [36,79,80,81,82] and measurements [25,48,83], and the work of Takagi et al [36] showed that this property is shared by any convex resource theory of quantum states It remains to understand how general this property truly is and whether all resources—both static and dynamic, both within quantum mechanics and beyond—can provide explicit advantages in such operational tasks. A comprehensive extension of this type of an operational characterization to more general settings which, together with quantification, would complete an operational characterization of general resource theories, has hitherto remained elusive
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