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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.
Summary
This study introduces a canonical representation for systems of random variables, defining contextuality based on the compatibility of maximal couplings. It proposes a criterion to identify contextuality in measurement systems.
Area of Science:
- Foundational physics
- Quantum information theory
- Probability theory
Background:
- Measurements are represented by random variables, uniquely identified by content and context.
- Joint distributions arise when random variables share a context.
- Canonical representation simplifies systems by using binary random variables and maximal couplings.
Purpose of the Study:
- To propose a canonical representation for systems of measurements.
- To define contextuality based on the compatibility of maximal couplings within this canonical form.
- To establish a criterion for contextuality in specific measurement systems.
Main Methods:
- Representing measurement systems in a canonical form.
- Defining contextuality based on the incompatibility of maximal couplings with observed joint distributions.
- Analyzing dichotomizations of content-sharing categorical random variables.
Main Results:
- A system is defined as contextual if its canonical representation is contextual.
- Maximal couplings are introduced for content-sharing random variables.
- A criterion for contextuality is established for a specific canonical system.
Conclusions:
- The proposed canonical representation provides a framework for understanding contextuality in measurement systems.
- The criterion for contextuality offers a method for identifying context-dependent behaviors.
- This work contributes to foundational questions in quantum mechanics and information theory.
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