Generalized Bell scenarios: disturbing consequences on local-hidden-variable models

TL;DR

This paper reviews and extends a unified framework for Bell nonlocality and Kochen-Specker contextuality, exploring local models, their relations to quantum correlations, and identifying post-quantum behaviors and complex local sets.

Contribution

It introduces new results on local models with contextual features, analyzes their relation to quantum correlations, and extends foundational theorems in quantum theory.

Findings

Discovery of post-quantum local behaviors

Identification of correlations that are local and non-contextual but incompatible in hidden variable models

Extension of the Fine-Abramsky-Brandenburger theorem

Abstract

Bell nonlocality and Kochen-Specker contextuality are among the main topics of foundations of quantum theory. Both of them are related to stronger-than-classical correlations, with the former usually referring to spatially separated systems while the latter considering a single system. In recent works, a unified framework for these phenomena was presented. This article reviews, expands and obtains new results regarding this framework. Contextual and disturbing features inside the local models are explored, which allows for the definition of different local sets with a non-trivial relation among them. The relations between the set of quantum correlations and these local sets are also considered, and post-quantum local behaviours are found. Moreover, examples of correlations that are both local and non-contextual but such that these two classical features cannot be expressed by the same hidden variable model are shown. Extensions of the Fine-Abramsky-Brandenburger theorem are also discussed.