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Contextuality-by-Default 2.0: Systems with Binary Random Variables

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Quantum Interaction (QI 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10106))

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Abstract

The paper outlines a new development in the Contextuality-by-Default theory as applied to finite systems of binary random variables. The logic and principles of the original theory remain unchanged, but the definition of contextuality of a system of random variables is now based on multimaximal rather than maximal couplings of the variables that measure the same property in different contexts: a system is considered noncontextual if these multimaximal couplings are compatible with the distributions of the random variables sharing contexts. A multimaximal coupling is one that is a maximal coupling of any subset (equivalently, of any pair) of the random variables being coupled. Arguments are presented for why this modified theory is a superior generalization of the traditional understanding of contextuality in quantum mechanics. The modified theory coincides with the previous version in the important case of cyclic systems, which include the systems whose contextuality was most intensively studied in quantum physics and behavioral sciences.

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Acknowledgments

This research has been supported by NSF grant SES-1155956 and AFOSR grant FA9550-14-1-0318. We are grateful to Victor H. Cervantes for his critical comments on the manuscript.

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Authors and Affiliations

  1. Purdue University, West Lafayette, USA

    Ehtibar N. Dzhafarov

  2. University of Jyväskylä, Jyväskylä, Finland

    Janne V. Kujala

Authors
  1. Ehtibar N. Dzhafarov
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  2. Janne V. Kujala
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Correspondence to Ehtibar N. Dzhafarov .

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Editors and Affiliations

  1. San Francisco State University, San Francisco, California, USA

    Jose Acacio de Barros

  2. University of Oxford, Oxford, United Kingdom

    Bob Coecke

  3. City University of London, London, United Kingdom

    Emmanuel Pothos

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Dzhafarov, E.N., Kujala, J.V. (2017). Contextuality-by-Default 2.0: Systems with Binary Random Variables. In: de Barros, J., Coecke, B., Pothos, E. (eds) Quantum Interaction. QI 2016. Lecture Notes in Computer Science(), vol 10106. Springer, Cham. https://doi.org/10.1007/978-3-319-52289-0_2

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  • DOI: https://doi.org/10.1007/978-3-319-52289-0_2

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