Related Experiment Video
Updated: Feb 21, 2026

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments
Published on: March 1, 2022
Contextuality in canonical systems of random variables
Ehtibar N Dzhafarov1, Víctor H Cervantes2, Janne V Kujala3
1Psychological Sciences, Purdue University, West Lafayette, IN, USA ehtibar@purdue.edu.
Abstract:
Random variables representing measurements, broadly understood to include any responses to any inputs, form a system in which each of them is uniquely identified by its content (that which it measures) and its context (the conditions under which it is recorded). Two random variables are jointly distributed if and only if they share a context. In a canonical representation of a system, all random variables are binary, and every content-sharing pair of random variables has a unique maximal coupling (the joint distribution imposed on them so that they coincide with maximal possible probability). The system is contextual if these maximal couplings are incompatible with the joint distributions of the context-sharing random variables. We propose to represent any system of measurements in a canonical form and to consider the system contextual if and only if its canonical representation is contextual. As an illustration, we establish a criterion for contextuality of the canonical system consisting of all dichotomizations of a single pair of content-sharing categorical random variables.This article is part of the themed issue 'Second quantum revolution: foundational questions'.
Related Concept Videos
Random Variables
Uppercase letters such as X or Y denote a random variable. Lowercase letters like x or y denote the value of a random variable. If X is a random variable, then X is written in words, and x is given as a number.
For example, let X = the...
Propagation of Uncertainty from Random Error
Propagation of Uncertainty from Systematic Error
Classification of Systems-I
Homogeneity dictates that if an input x(t) is multiplied by a constant c, the output y(t) is multiplied by the same constant. Mathematically, this is expressed as:
Classification of Systems-II
Entropy Change in Reversible Processes
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.

