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Measures of contextuality

Andrzej Grudka, Karol Horodecki, Michał Horodecki, Paweł Horodecki, Ryszard Horodecki, Pankaj S. Joshi, Waldemar Kłobus, Antoni Wójcik

Published Sep 17, 2012• 0 citations
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Measures of the Degree of Contextuality

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Cambridge University Press eBooks•Feb 28, 2026•0 citations

Degrees, Levels, and Profiles of Contextuality

Ehtibar N. Dzhafarov, Victor H. Cervantes

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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Measures of contextuality and non-contextuality

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We discuss three measures of the degree of contextuality in contextual systems of dichotomous random variables. These measures are developed within the framework of the Contextuality-by-Default (CbD) theory, and apply to inconsistently connected systems (those with 'disturbance' allowed). For one of these measures of contextuality, presented here for the first time, we construct a corresponding measure of the degree of non-contextuality in non-contextual systems. The other two CbD-based measures do not suggest ways in which degree of non-contextuality of a non-contextual system can be quantified. We find the same to be true for the contextual fraction measure developed by Abramsky, Barbosa and Mansfield. This measure of contextuality is confined to consistently connected systems, but CbD allows one to generalize it to arbitrary systems. This article is part of the theme issue 'Contextuality and probability in quantum mechanics and beyond'.

arXiv:1903.07170•Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences•Sep 16, 2019•36 citations

Context-Dependence and Contextuality

Ehtibar N. Dzhafarov, Janne V. Kujala, Victor Hernando Cervantes

Cambridge University Press eBooks•Feb 28, 2026•0 citations

Revealing quantum contextuality using a single measurement device by generalizing measurement non-contextuality

Jaskaran Singh, Arvind Arvind

In this letter we generalize Spekkens' notion of measurement non-contextuality (NC). We show that any non-contextual ontological model based on this notion of contextuality fails to explain the statistics of outcomes of a single carefully constructed POVM executed sequentially on a quantum system. The POVM essentially forms a single measurement device. The context of measurement arises from the different configurations in which the device can be used. We develop an inequality from the non-contextual ontic model, and construct corresponding quantum situations where the measurement outcomes from the device violate this NC inequality. Our work brings out the hitherto unexplored implications of contextuality for a single measurement device, and paves the way for further study of consequences of contextuality for sequential measurements.

•Jan 31, 2021•1 citation

Contextuality

WORLD SCIENTIFIC eBooks•Mar 1, 2025•0 citations
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.
We discuss three measures of the degree of contextuality in contextual systems of dichotomous random variables. These measures are developed within the framework of the Contextuality-by-Default (CbD) theory, and apply to inconsistently connected systems (those with 'disturbance' allowed). For one of these measures of contextuality, presented here for the first time, we construct a corresponding measure of the degree of non-contextuality in non-contextual systems. The other two CbD-based measures do not suggest ways in which degree of non-contextuality of a non-contextual system can be quantified. We find the same to be true for the contextual fraction measure developed by Abramsky, Barbosa and Mansfield. This measure of contextuality is confined to consistently connected systems, but CbD allows one to generalize it to arbitrary systems. This article is part of the theme issue 'Contextuality and probability in quantum mechanics and beyond'.
In this letter we generalize Spekkens' notion of measurement non-contextuality (NC). We show that any non-contextual ontological model based on this notion of contextuality fails to explain the statistics of outcomes of a single carefully constructed POVM executed sequentially on a quantum system. The POVM essentially forms a single measurement device. The context of measurement arises from the different configurations in which the device can be used. We develop an inequality from the non-contextual ontic model, and construct corresponding quantum situations where the measurement outcomes from the device violate this NC inequality. Our work brings out the hitherto unexplored implications of contextuality for a single measurement device, and paves the way for further study of consequences of contextuality for sequential measurements.