A1 Refereed original research article in a scientific journal
Measures of contextuality and non-contextuality
Authors: Kujala JV, Dzhafarov EN
Publisher: ROYAL SOCIETY PUBLISHING
Publication year: 2019
Journal: Philosophical Transactions A: Mathematical, Physical and Engineering Sciences
Journal name in source: PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
Journal acronym: PHILOS T R SOC A
Article number: ARTN 20190149
Volume: 377
Issue: 2157
Number of pages: 16
ISSN: 1364-503X
eISSN: 1471-2962
DOI: https://doi.org/10.1098/rsta.2019.0149
Abstract
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'.
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'.
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