Warring Contextualities - Provably Classical vs Provably Nonclassical

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 \emph{nonclassical}, while Spekkens' noncontextuality provides a generalisation of the idea of a system being \emph{classical}. This allows us to reconcile the two approaches, as different stages in a hierarchy of classicality/nonclassicality.

16+13 pages, 2+1 figures. v2. Fig 1a fixed, added brief discussion of related results for (un)steerability