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Degrees, Levels, and Profiles of Contextuality
Ehtibar N Dzhafarov1, Víctor H Cervantes2
1Department of Psychological Sciences, Purdue University, West Lafayette, IN 47907, USA.
Entropy (Basel, Switzerland)
|May 26, 2026
Summary
We introduce contextuality profiles to better understand systems of random variables. This new approach characterizes contextuality using a curve, offering a more nuanced view than a single degree value.
Area of Science:
- Quantum Information Theory
- Foundations of Physics
- Probability Theory
Background:
- Traditional measures of contextuality provide a single value for a system.
- This single value may not fully capture the complex nature of contextuality.
- Nonlocality is a specific instance of contextuality.
Purpose of the Study:
- Introduce the concept of a contextuality profile for systems of random variables.
- Develop a method to characterize contextuality using a curve based on system representation level.
- Enable a level-wise analysis of contextuality applicable to various measures.
Main Methods:
- Define contextuality profile based on a system's representation level (n).
- Relate the degree of contextuality to the level of joint distributions considered (k≤n).
- Utilize a method of concatenated systems for systematic exploration of profiles.
Main Results:
- Contextuality can be represented by a curve (profile) instead of a single number.
- The level-wise analysis is compatible with diverse contextuality measures.
- Applied the method to analyze profiles for three prominent contextuality measures.
Conclusions:
- Contextuality profiles offer a richer characterization of systems than single-value measures.
- The level-wise approach provides a flexible framework for analyzing contextuality.
- This work advances the understanding of contextuality and nonlocality in complex systems.
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