Contextuality and Expressivity of Non-locality

TL;DR

This paper explores the relationship between contextuality and non-locality using hypergraph methods, demonstrating how to embed any contextual scenario into a bipartite non-local game and analyzing their equivalences.

Contribution

It introduces a method to associate contextual scenarios with non-local games and shows how to embed any contextual scenario into a bipartite non-local game.

Findings

Any contextual scenario can be embedded into a two-player non-local game.

The construction for embedding is not always optimal, especially for graph-based scenarios.

Different equivalences of contextuality scenarios are discussed and compared.

Abstract

Contextuality is often referred to as a generalization of non-locality. In this work, using the hypergraph approach for contextuality we show how to associate a contextual scenario to a general k-partite non local game, and consider the reverse direction: how and when is it possible to represent a general contextuality scenario as a non local game. Using the notion of conditional contextuality, we show that it is possible to embed any contextual scenario in a two players non local game. We also discuss different equivalences of contextuality scenarios and show that the construction used in the proof is not optimal by giving a simpler bipartite non local game when the contextual scenario is a graph instead of a general hypergraph.