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Resource theories constitute a powerful theoretical framework and a tool thatcaptures, in an abstract structure, pragmatic aspects of the most variedtheories and processes. For physical theories, while this framework dealsdirectly with questions about the concrete possibilities of carrying out tasksand processes, resource theories also make it possible to recast these alreadyestablished theories on a new language, providing not only new perspectives onthe potential of physical phenomena as valuable resources for technologicaldevelopment, for example, but they also provide insights into the veryfoundations of these theories. In this work, we will investigate someproperties of a resource theory for quantum contextuality, an essentialcharacteristic of quantum phenomena that ensures the impossibility ofinterpreting the results of quantum measurements as revealing properties thatare independent of the set of measurements being made. We will present theresource theory to be studied and investigate certain global properties of thistheory using tools and methods that, although already developed and studied bythe community in other resource theories, had not yet been used to characterizeresource theories of contextuality. In particular, we will use the so calledcost and yield monotones, extending the results of reference Quantum 4, 280(2020) to general contextuality scenarios.

Investigating the Global Properties of a Resource Theory of Contextuality