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Probabilistic foundations of contextuality

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Dzhafarov, E. N., & Kujala, J. (2017). Probabilistic foundations of contextuality. Fortschritte der Physik - Progress of Physics, 65(6-8), Article 1600040. https://doi.org/10.1002/prop.201600040
Published in
Fortschritte der Physik - Progress of Physics
Authors
Dzhafarov, Ehtibar N. |
Kujala, Janne
Date
2017
Discipline
TietotekniikkaMathematical Information Technology
Copyright
© 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). ...
Publisher
Wiley - VCH Verlag GmbH & Co. KGaA
ISSN Search the Publication Forum
0015-8208
Keywords
cyclic system (in)consistent connectedness multimaximal coupling kontekstuaalisuus kytkentä
DOI
https://doi.org/10.1002/prop.201600040
URI

http://urn.fi/URN:NBN:fi:jyu-201706273070

Publication in research information system

https://converis.jyu.fi/converis/portal/detail/Publication/26201107

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