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Contextuality in Three Types of Quantum-Mechanical Systems
Purdue University, IN 47907 USA.
University of Jyvaskyla, Finland.
Linköping University, Department of Electrical Engineering, Information Coding. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0002-1082-8325
2015 (English)In: Foundations of physics, ISSN 0015-9018, E-ISSN 1572-9516, Vol. 45, no 7, 762-782 p.Article in journal (Refereed) Published
Abstract [en]

We present a formal theory of contextuality for a set of random variables grouped into different subsets (contexts) corresponding to different, mutually incompatible conditions. Within each context the random variables are jointly distributed, but across different contexts they are stochastically unrelated. The theory of contextuality is based on the analysis of the extent to which some of these random variables can be viewed as preserving their identity across different contexts when one considers all possible joint distributions imposed on the entire set of the random variables. We illustrate the theory on three systems of traditional interest in quantum physics (and also in non-physical, e.g., behavioral studies). These are systems of the Klyachko-Can-Binicioglu-Shumovsky-type, Einstein-Podolsky-Rosen-Bell-type, and Suppes-Zanotti-Leggett-Garg-type. Listed in this order, each of them is formally a special case of the previous one. For each of them we derive necessary and sufficient conditions for contextuality while allowing for experimental errors and contextual biases or signaling. Based on the same principles that underly these derivations we also propose a measure for the degree of contextuality and compute it for the three systems in question.

Place, publisher, year, edition, pages
Springer Verlag (Germany) , 2015. Vol. 45, no 7, 762-782 p.
Keyword [en]
CHSH inequalities; Contextuality; Klyachko inequalities; Leggett-Garg inequalities; Probabilistic couplings; Signaling
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
URN: urn:nbn:se:liu:diva-120035DOI: 10.1007/s10701-015-9882-9ISI: 000356263600006OAI: oai:DiVA.org:liu-120035DiVA: diva2:840025
Note

Funding Agencies|NSF [SES-1155956]; AFOSR [FA9550-14-1-0318]

Available from: 2015-07-06 Created: 2015-07-06 Last updated: 2016-08-31

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Larsson, Jan-Åke
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