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Embedding quantum into classical: contextualization vs conditionalization.

Ehtibar N Dzhafarov1, Janne V Kujala2

  • 1Department of Psychological Sciences, Purdue University, West Lafayette, Indiana, United States of America.

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Summary
This summary is machine-generated.

We compare contextualization and conditionalization approaches for embedding joint probability distributions. Contextualization reveals relationships between distributions under different conditions, unlike conditionalization which is uninformative.

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Area of Science:

  • Foundations of Probability Theory
  • Quantum Mechanics Foundations

Background:

  • Classical probability theory struggles to embed joint distributions of variables recorded under varying conditions.
  • Understanding relationships between these distributions is crucial for foundational physics and probability.

Purpose of the Study:

  • To compare two distinct approaches for embedding joint distributions within classical probability.
  • To evaluate the informativeness of each approach regarding relationships between distributions under different conditions.

Main Methods:

  • The contextualization approach labels variables with recording conditions and imposes joint distributions.
  • The conditionalization approach treats conditions as values of another random variable, yielding conditional distributions.

Main Results:

  • Contextualization enables characterization of relationships between distributions, including Bell-type inequalities and quantum constraints.
  • Conditionalization proves uninformative about relationships between distributions across different conditions.

Conclusions:

  • The contextualization approach is superior for analyzing inter-distributional relationships in classical probability.
  • Conditionalization fails to provide insights into how distributions vary across different experimental settings.