On Measures and Measurements: a Fibre Bundle approach to Contextuality

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.Comment: 14 pages; no figures; Purdue-Winer Memorial Lectures 2018; submitted to Phil. Trans. Roy. Soc. A. Comments are very welcom

How to Extract Entanglement from a Piece of Solid or a Bunch of Neutrons

We review how to obtain spin entangled pairs of fermions from a Fermi gas. An experiment with neutrons is proposed in order to get such pairs.Comment: Prepared for the Proceedings of Central European Workshop on Quantum Optics, Vienna - 200

The exclusivity principle forbids sets of correlations larger than the quantum set

We show that the exclusivity (E) principle singles out the set of quantum correlations associated to any exclusivity graph assuming the set of quantum correlations for the complementary graph. Moreover, we prove that, for self-complementary graphs, the E principle, by itself (i.e., without further assumptions), excludes any set of correlations strictly larger than the quantum set. Finally, we prove that, for vertex-transitive graphs, the E principle singles out the maximum value for the quantum correlations assuming only the quantum maximum for the complementary graph. This opens the door for testing the impossibility of higher-than-quantum correlations in experiments.Comment: REVTeX4, 4 pages, one new result (Result 2) and two new authors, title changed accordingl