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Embedding Quantum into Classical: Contextualization vs Conditionalization

We compare two approaches to embedding joint distributions of random variables recorded under different conditions (such as spins of entangled particles for different settings) into the framework of classical, Kolmogorovian probability theory. In the contextualization approach each random variable i...

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Detalles Bibliográficos
Autores principales: Dzhafarov, Ehtibar N., Kujala, Janne V.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Public Library of Science 2014
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3969371/
https://www.ncbi.nlm.nih.gov/pubmed/24681665
http://dx.doi.org/10.1371/journal.pone.0092818
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author Dzhafarov, Ehtibar N.
Kujala, Janne V.
author_facet Dzhafarov, Ehtibar N.
Kujala, Janne V.
author_sort Dzhafarov, Ehtibar N.
collection PubMed
description We compare two approaches to embedding joint distributions of random variables recorded under different conditions (such as spins of entangled particles for different settings) into the framework of classical, Kolmogorovian probability theory. In the contextualization approach each random variable is “automatically” labeled by all conditions under which it is recorded, and the random variables across a set of mutually exclusive conditions are probabilistically coupled (imposed a joint distribution upon). Analysis of all possible probabilistic couplings for a given set of random variables allows one to characterize various relations between their separate distributions (such as Bell-type inequalities or quantum-mechanical constraints). In the conditionalization approach one considers the conditions under which the random variables are recorded as if they were values of another random variable, so that the observed distributions are interpreted as conditional ones. This approach is uninformative with respect to relations between the distributions observed under different conditions because any set of such distributions is compatible with any distribution assigned to the conditions.
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spelling pubmed-39693712014-04-01 Embedding Quantum into Classical: Contextualization vs Conditionalization Dzhafarov, Ehtibar N. Kujala, Janne V. PLoS One Research Article We compare two approaches to embedding joint distributions of random variables recorded under different conditions (such as spins of entangled particles for different settings) into the framework of classical, Kolmogorovian probability theory. In the contextualization approach each random variable is “automatically” labeled by all conditions under which it is recorded, and the random variables across a set of mutually exclusive conditions are probabilistically coupled (imposed a joint distribution upon). Analysis of all possible probabilistic couplings for a given set of random variables allows one to characterize various relations between their separate distributions (such as Bell-type inequalities or quantum-mechanical constraints). In the conditionalization approach one considers the conditions under which the random variables are recorded as if they were values of another random variable, so that the observed distributions are interpreted as conditional ones. This approach is uninformative with respect to relations between the distributions observed under different conditions because any set of such distributions is compatible with any distribution assigned to the conditions. Public Library of Science 2014-03-28 /pmc/articles/PMC3969371/ /pubmed/24681665 http://dx.doi.org/10.1371/journal.pone.0092818 Text en © 2014 Dzhafarov, Kujala http://creativecommons.org/licenses/by/4.0/ This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are properly credited.
spellingShingle Research Article
Dzhafarov, Ehtibar N.
Kujala, Janne V.
Embedding Quantum into Classical: Contextualization vs Conditionalization
title Embedding Quantum into Classical: Contextualization vs Conditionalization
title_full Embedding Quantum into Classical: Contextualization vs Conditionalization
title_fullStr Embedding Quantum into Classical: Contextualization vs Conditionalization
title_full_unstemmed Embedding Quantum into Classical: Contextualization vs Conditionalization
title_short Embedding Quantum into Classical: Contextualization vs Conditionalization
title_sort embedding quantum into classical: contextualization vs conditionalization
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3969371/
https://www.ncbi.nlm.nih.gov/pubmed/24681665
http://dx.doi.org/10.1371/journal.pone.0092818
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