On Measures and Measurements: a Fibre Bundle approach to Contextuality

Abstract

Contextuality is the failure of "local" probabilistic models to become global ones. In this paper we introduce the notions of \emph{measurable fibre bundles}, \emph{probability fibre bundles}, and \emph{sample fibre bundle} which capture and make precise the former statement. The central notions of contextuality are discussed under this formalism, examples worked out, and some new aspects pointed out.

arXiv comment14 pages; no figures; Purdue-Winer Memorial Lectures 2018; submitted to Phil. Trans. Roy. Soc. A. Comments are very welcome

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• Simplicial quantum contextuality
• Continuous-variable nonlocality and contextuality
• Wigner and friends, a map is not the territory! Contextuality in multi-agent paradoxes
• The Interplay between Quantum Contextuality and Wigner Negativity