Measures of contextuality and non-contextuality

Area of Science:

• Quantum mechanics
• Probability theory
• Information theory

Background:

• Contextuality is a key concept in quantum mechanics, influencing interpretations of quantum theory.
• Existing measures of contextuality often apply only to specific types of systems.
• The Contextuality-by-Default (CbD) framework offers a generalized approach to studying contextuality.

Purpose of the Study:

• To introduce and analyze three measures for quantifying contextuality in systems of dichotomous random variables.
• To develop a measure for the degree of non-contextuality in non-contextual systems.
• To generalize existing contextuality measures to broader classes of systems.

Main Methods:

• Development of three contextuality measures within the Contextuality-by-Default (CbD) framework.
• Application of these measures to inconsistently connected systems.
• Construction of a non-contextuality measure corresponding to one of the CbD measures.

Main Results:

• Three CbD-based measures of contextuality are presented for dichotomous random variables.
• A novel measure for the degree of non-contextuality in non-contextual systems is introduced.
• Two CbD measures and the contextual fraction measure do not provide a way to quantify non-contextuality.

Conclusions:

• The CbD framework provides a versatile tool for analyzing contextuality in various systems.
• The newly developed non-contextuality measure offers a quantitative approach for non-contextual systems.
• CbD allows for the generalization of existing contextuality measures, such as the contextual fraction, to arbitrary systems.