Multiobject operational tasks for convex quantum resource theories of state-measurement pairs

Abstract

The prevalent modus operandi within the framework of quantum resource theories has been to characterize and harness the resources within single objects, in what we can call single-object quantum resource theories. One can wonder, however, whether the resources contained within multiple different types of objects, now in a multiobject quantum resource theory, can simultaneously be exploited for the benefit of an operational task. In this work, we introduce examples of such multiobject operational tasks in the form of subchannel discrimination and subchannel exclusion games, in which the player harnesses the resources contained within the composite object of a state-measurement pair. We prove that for any state-measurement pair in which either of them is resourceful, there exist discrimination and exclusion games for which such a pair outperforms any possible free state-measurement pair. These results hold for arbitrary convex resources of states, and arbitrary convex resources of measurements where the set of free measurements is closed under classical post-processing. Furthermore, we prove that the advantage in these multiobject operational tasks is determined, in a multiplicative manner, by the resource quantifiers of: Generalized robustness of resource of both state and measurement for discrimination games and weight of resource of both state and measurement for exclusion games.