Warring Contextualities - Provably Classical vs Provably Nonclassical

Quantum Physics [Submitted on 15 Apr 2026] Warring Contextualities - Provably Classical vs Provably Nonclassical Enrico Bozzetto, Jonte R. Hance 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. Comments: 16+14 pages, 2+1 figures Subjects: Quantum Physics (quant-ph); History and Philosophy of Physics (physics.hist-ph) Cite as: arXiv:2604.14319 [quant-ph]   (or arXiv:2604.14319v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.14319 Focus to learn more Submission history From: Jonte Hance [view email] [v1] Wed, 15 Apr 2026 18:22:06 UTC (588 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 Change to browse by: physics physics.hist-ph References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)