Multi-object operational tasks for convex quantum resource theories

• URL: http://arxiv.org/abs/2004.12898v1
• Date: Mon, 27 Apr 2020 15:59:41 GMT
• Title: Multi-object operational tasks for convex quantum resource theories
• Authors: Andr\'es F. Ducuara and Patryk Lipka-Bartosik and Paul Skrzypczyk
• Abstract summary: We introduce examples of multi-object operational tasks in the form of subchannel discrimination and subchannel exclusion games. 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The prevalent modus operandi within the framework of quantum resource theories has been to characterise and harness the resources within single objects, in what we can call \emph{single-object} quantum resource theories. One can wonder however, whether the resources contained within multiple different types of objects, now in a \emph{multi-object} quantum resource theory, can simultaneously be exploited for the benefit of an operational task. In this work, we introduce examples of such multi-object operational tasks in the form of subchannel discrimination and subchannel exclusion games, in which the player harnesses the resources contained within 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 for which classical post-processing is a free operation. Furthermore, we prove that the advantage in these multi-object operational tasks is determined, in a multiplicative manner, by the resource quantifiers of: \emph{generalised robustness of resource} of both state and measurement for discrimination games and \emph{weight of resource} of both state and measurement for exclusion games.

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