Closing Bell: Boxing black box simulations in the resource theory of contextuality

TL;DR

This paper explores the sheaf-theoretic framework for contextuality, focusing on resource-theoretic aspects, and introduces a new categorical construction to characterize classical transformations between empirical models.

Contribution

It introduces a novel 'hom' scenario construction that characterizes classical transformations in the resource theory of contextuality using non-contextual models.

Findings

Constructed a new 'hom' scenario for empirical models

Characterized classical transformations as induced by non-contextual models

Provided a closed structure on the category of measurement scenarios

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.