Degrees, Levels, and Profiles of Contextuality

• URL: http://arxiv.org/abs/2603.26692v2
• Date: Wed, 01 Apr 2026 09:34:45 GMT
• Title: Degrees, Levels, and Profiles of Contextuality
• Abstract summary: We introduce a new notion of a contextuality profile of a system of random variables.<n>We show how it can be characterized by a curve relating degree of contextuality to level at which the system is considered.<n>We show that the level-wise contextuality analysis can be used in conjunction with any well-constructed measure of contextuality.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We introduce a new notion, that of a contextuality profile of a system of random variables. Rather than characterizing a system's contextuality by a single number, its overall degree of contextuality, we show how it can be characterized by a curve relating degree of contextuality to level at which the system is considered. A system is represented at level n if one only considers the joint distributions with no more than n variables, ignoring higher-order joint distributions. We show that the level-wise contextuality analysis can be used in conjunction with any well-constructed measure of contextuality. We present a method of concatenated systems to explore contextuality profiles systematically, and we apply it to the contextuality profiles for three major measures of contextuality proposed in the literature.

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