Affiliation:
1. Instituto de Física, Universidade de São Paulo, Brasil
2. Department of Psychology, University of Illinois Urbana, Champaign, IL, USA
Abstract
Several principled measures of contextuality have been proposed for general systems of random variables (i.e. inconsistently connected systems). One such measure is based on quasi-couplings using negative probabilities (here denoted by
CNT
3
, Dzhafarov & Kujala, 2016
Quantum interaction
). Dzhafarov & Kujala (Dzhafarov & Kujala 2019
Phil. Trans. R. Soc. A
377
, 20190149. (
doi:10.1098/rsta.2019.0149
)) introduced a measure of contextuality,
CNT
2
, that naturally generalizes to a measure of non-contextuality. Dzhafarov & Kujala (Dzhafarov & Kujala 2019
Phil. Trans. R. Soc. A
377
, 20190149. (
doi:10.1098/rsta.2019.0149
)) additionally conjectured that in the class of cyclic systems these two measures are proportional. Here we prove that conjecture is correct. Recently, Cervantes (Cervantes 2023
J. Math. Psychol
.
112
, 102726. (
doi:10.1016/j.jmp.2022.102726
)) showed the proportionality of
CNT
2
and the Contextual Fraction measure introduced by Abramsky & Brandenburger (Abramsky & Brandenburger 2011
New J. Phys
.
13
, 113036. (
doi:10.1088/1367-2630/13/11/113036
)). The present proof completes the description of the interrelations of all contextuality measures proposed within or translated into the Contextuality-by-Default framework so far as they pertain to cyclic systems.
This article is part of the theme issue ‘Quantum contextuality, causality and freedom of choice’.
Subject
General Physics and Astronomy,General Engineering,General Mathematics
Cited by
1 articles.
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