A comonadic view of simulation and quantum resources
arXiv:1904.10035 · doi:10.1109/LICS.2019.8785677
Abstract
We study simulation and quantum resources in the setting of the sheaf-theoretic approach to contextuality and non-locality. Resources are viewed behaviourally, as empirical models. In earlier work, a notion of morphism for these empirical models was proposed and studied. We generalize and simplify the earlier approach, by starting with a very simple notion of morphism, and then extending it to a more useful one by passing to a co-Kleisli category with respect to a comonad of measurement protocols. We show that these morphisms capture notions of simulation between empirical models obtained via `free' operations in a resource theory of contextuality, including the type of classical control used in measurement-based quantum computation schemes.
arXiv commentTo appear in Proceedings of LiCS 2019
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Cited by in corpus (10)
- Kochen-Specker Contextuality
- Neither Contextuality nor Nonlocality Admits Catalysts
- Simplicial quantum contextuality
- The Sheaf-Theoretic Structure of Definite Causality
- Categorical composable cryptography
- Closing Bell: Boxing black box simulations in the resource theory of contextuality
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