In a previous paper with Adam Brandenburger, we used sheaf theory to analyze the structure of non-locality and contextuality. Moreover, on the basis of this formulation, we showed that the phenomena of non-locality and contextuality can be characterized precisely in terms of obstructions to the existence of global sections. Our aim in the present work is to build on these results, and to use th...

It is well known that in quantum mechanics we cannot always define consistently properties that are context independent. Many approaches exist to describe contextual properties, such as Contextuality by Default (CbD), sheaf theory, topos theory, and non-standard or signed probabilities. In this paper, we propose a treatment of contextual properties that is specific to quantum mechanics, as it r...

We present a formal theory of contextuality for a set of random variables grouped into different subsets (contexts) corresponding to different, mutually incompatible conditions. Within each context the random variables are jointly distributed, but across different contexts they are stochastically unrelated. The theory of contextuality is based on the analysis of the extent to which some of thes...

Two entangled particles in threedimensional Hilbert space (per particle) are considered in an EPR-type arrangement. On each side the Kochen-Specker observables {J 1 , J 2 2 , J 2 3 } and {J̄ 2 1 , J̄ 2 2 , J 2 3 } with [J 2 1 , J̄ 2 1 ] 6= 0 are measured. The outcomes of measurements of J 3 (via J 2 1 , J 2 2 ) and J 2 3 (via J̄ 1 , J̄ 2 2 ) are compared. We investigate the possibility that, althoug...

It is explained on a physical basis how absence of contextuality allows Bell inequalities to be violated, without bringing an implication on locality or realism. Hereto we connect first to the local realistic theory Stochastic Electrodynamics, and then put the argument more broadly. Thus even if Bell Inequality Violation is demonstrated beyond reasonable doubt, it will have no say on local real...

Contextuality is a foundational phenomenon underlying key differences between quantum theory and classical realistic descriptions of the world. Here we propose an experimental test which is capable of revealing contextuality in all qutrit systems, except the completely mixed state, provided we choose the measurement basis appropriately. The 3-level system is furnished by the polarization and sp...

Contextuality is a natural generalization of nonlocality which does not need composite systems or spacelike separation and offers a wider spectrum of interesting phenomena. Most notably, in quantum mechanics there exist scenarios where the contextual behavior is independent of the quantum state. We show that the quest for an optimal inequality separating quantum from classical noncontextual cor...

Using a single trapped ion, we have experimentally demonstrated state-independent violation of a recent version of the Kochen-Specker inequality in a three-level system (qutrit) that is intrinsically indivisible. Three ground states of the (171)Yb(+) ion representing a qutrit are manipulated with high fidelity through microwaves and detected with high efficiency through a two-step quantum jump ...