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The sheaf-theoretic structure of non-locality and contextuality

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This paper presents a highly novel and ground-breaking approach to fundamental notions of quantum mechanics, which play a key role in quantum information, namely non-locality (as in Bell’s theorem) and contextuality (as in the Kochen-Specker theorem). It unifies and generalizes these notions in terms of obstructions to the existence of global sections. It gives algorithmic methods for computing obstructions. It gives a novel hierarchy of levels of contextuality, bringing the key notion of strong contextuality to the fore. A striking result on negative probabilities shows that these allow local hidden-variable realizations of all no-signalling models.