Closing Bell: Boxing black box simulations in the resource theory of contextuality
arXiv:2104.11241 · doi:10.1007/978-3-031-24117-8_13
Abstract
This chapter contains an exposition of the sheaf-theoretic framework for contextuality emphasising resource-theoretic aspects, as well as some original results on this topic. In particular, we consider functions that transform empirical models on a scenario S to empirical models on another scenario T, and characterise those that are induced by classical procedures between S and T corresponding to 'free' operations in the (non-adaptive) resource theory of contextuality. We construct a new 'hom' scenario built from S and T, whose empirical models induce such functions. Our characterisation then boils down to being induced by a non-contextual model. We also show that this construction on scenarios provides a closed structure on the category of measurement scenarios.
arXiv commentCorrected a mistake in Theorem 44 and other fixes stemming from it. This supersedes the published version and should be considered the version of reference
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