We discuss three measures of the degree of contextuality in contextual systems of dichotomous random variables. These measures are developed within the framework of the Contextuality-by-Default (CbD) theory, and apply to inconsistently connected systems (those with 'disturbance' allowed). For one of these measures of contextuality, presented here for the first time, we construct a corresponding measure of the degree of non-contextuality in non-contextual systems. The other two CbD-based measures do not suggest ways in which degree of non-contextuality of a non-contextual system can be quantified. We find the same to be true for the contextual fraction measure developed by Abramsky, Barbosa and Mansfield. This measure of contextuality is confined to consistently connected systems, but CbD allows one to generalize it to arbitrary systems. This article is part of the theme issue 'Contextuality and probability in quantum mechanics and beyond'.
Contextuality is a fundamental property of quantum mechanics. Contrary to entanglement, which can only exist in composite systems, contextuality is also present for single entities. The case of a three-level system is of particular interest because--in agreement with the Bell-Kochen-Specker theorem--it is the simplest in which quantum contextuality is necessarily present. We verify that the polarizations of spin-1 massive particles produced at collider experiments indeed exhibit contextuality. To this purpose we consider
W gauge bosons produced in top-quark decays,
J/ψ and
K∗(892)0 mesons created in
B-meson decays and
ϕ mesons resulting from
χc0 charmonium decays, making use of the data collected and analyzed by the ATLAS, LHCb and BESIII collaborations, respectively. The polarizations of all these four particles show contextuality with a significance of more than
5σ.