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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