Warring Contextualities -- Provably Classical vs Provably Nonclassical

TL;DR

This paper compares two definitions of contextuality, showing how Kochen-Specker's and Spekkens' notions relate within a hierarchy of classicality and nonclassicality.

Contribution

It reconciles two different contextuality definitions, framing them as stages in a hierarchy of classical and nonclassical systems.

Findings

Kochen-Specker contextuality generalizes nonclassicality.

Spekkens' noncontextuality generalizes classicality.

The two notions are connected within a hierarchical framework.

Abstract

In the literature, there are two differing definitions of contextuality: Kochen and Specker's, and Spekkens' (or ``generalised''). However, researchers using one of these definitions rarely consider the other, meaning comparative analysis of these two notions is rare. In this paper, we advance the idea that Kochen-Specker contextuality provides a generalisation of the idea of system being fundamentally nonclassical, while Spekkens' noncontextuality provides a generalisation of the idea of a system being classical. This allows us to reconcile the two approaches, as different stages in a hierarchy of classicality/nonclassicality.