Probabilistic foundations of contextuality
Dzhafarov, E. N., & Kujala, J. (2017). Probabilistic foundations of contextuality. Fortschritte der Physik - Progress of Physics, 65 (6-8), 1600040. doi:10.1002/prop.201600040
Published inFortschritte der Physik - Progress of Physics
© 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. This is a final draft version of an article whose final and definitive form has been published by Wiley. Published in this repository with the kind permission of the publisher.
Contextuality is usually defined as absence of a joint distribution for a set of measurements (random variables) with known joint distributions of some of its subsets. However, if these subsets of measurements are not disjoint, contextuality is mathematically impossible even if one generally allows (as one must) for random variables not to be jointly distributed. To avoid contradictions one has to adopt the Contextuality-by-Default approach: measurements made in different contexts are always distinct and stochastically unrelated to each other. Contextuality is reformulated then in terms of the (im)possibility of imposing on all the measurements in a system a joint distribution of a particular kind: such that any measurements of one and the same property made in different contexts satisfy a specified property, C. In the traditional analysis of contextuality C means “are equal to each other with probability 1”. However, if the system of measurements violates the “nodisturbance principle”, due to signaling or experimental biases, then the meaning of C has to be generalized, and the proposed generalization is “are equal to each other with maximal possible probability” (applied to any set of measurements of one and the same property). This approach is illustrated on arbitrary systems of binary measurements, including most of quantum systems of traditional interest in contextuality studies (irrespective of whether the “no-disturbance” principle holds in them). ...