We introduce a new framework for contextuality based on simplicial sets, combinatorial models of topological spaces that play prominent role in modern homotopy theory. Our approach extends measurement scenarios to consist (rather than sets) measurements and outcomes, thereby generalizes nonsignaling distributions distributions, which are modeled by sets. Using this formalism we present topologi...

A notion of morphism that is suitable for the sheaf-theoretic approach to contextuality is developed, resulting in a resource theory for contextuality. The key features involve using an underlying relation rather than a function between measurement scenarios, and allowing for stochastic mappings of outcomes to outcomes. This formalizes an intuitive idea of using one empirical model to simulate ...

It has been argued that any test of quantum contextuality is nullified by the fact that perfect orthogonality and perfect compatibility cannot be achieved in finite precision experiments. We introduce experimentally testable two-qutrit violations of inequalities for noncontextual theories in which compatibility is guaranteed by the fact that measurements are performed on separated qutrits. The ...

We discuss quantum non-locality and contextuality, emphasising logical and structural aspects. We also show how the same mathematical structures arise in various areas of classical computation.

In quantum physics, the notion of contextuality has a variety interpretations, which are typically associated with names their inventors, say, Bohr, Bell, Kochen, Specker, and recently Dzhafarov. fact, Bohr was first who pointed to measurements as part formulation his principle complementarity. (Instead “contextuality,” he considered dependence on “experimental conditions.”) Unfortunately, coun...

We present a proof for a conjecture previously formulated by Dzhafarov, Kujala, and Larsson (Foundations of Physics, in press, arXiv:1411.2244). The conjecture specifies a measure for the degree of contextuality and a criterion (necessary and sufficient condition) for contextuality in a broad class of quantum systems. This class includes Leggett-Garg, EPR/Bell, and Klyachko-Can-Binicioglu-Shumo...

We present a simple proof of quantum contextuality for a spinless particle with a one dimensional configuration space. We then discuss how the maximally realistic deterministic quantum mechanics recently constructed by this author and V. Singh can be applied to different contexts.