The discussion on noncontextual hidden variable models as an underlying description for the quantum-mechanical predictions started in ernest with 1967 paper by Kochen and Specker. There, it was shown that no noncontextual hidden-variable model can give these predictions. The proof used in that paper is complicated, but recently, a paper by Yu and Oh [PRL, 2012] proposes a simpler statistical proof that can also be the basis of an experimental test. Here we report on a sharper version of that statistical proof, and also explain why the algebraic upper bound to the expressions used are not reachable, even with a reasonable contextual hidden variable model. Specifically, we show that the quantum mechanical predictions reach the maximal possible value for a contextual model that keeps the expectation value of the measurement outcomes constant.
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18 December 2012
QUANTUM THEORY: RECONSIDERATION OF FOUNDATIONS 6
11–14 June 2012
Vaxjo, Sweden
Research Article|
December 18 2012
Maximal violation of state-independent contextuality inequalities
Jan-Åke Larsson;
Jan-Åke Larsson
Institutionen för Systemteknik, Linköpings Universitet, SE-581 83 Linköping,
Sweden
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Matthias Kleinmann;
Matthias Kleinmann
Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Str. 3, D-57068 Siegen,
Germany
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Constantino Budroni;
Constantino Budroni
Departamento de Física Aplicada II, Universidad de Sevilla, E-41012 Sevilla, Spain and Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Str. 3, D-57068,
Germany
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Otfried Gühne;
Otfried Gühne
Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Str. 3, D-57068 Siegen,
Germany
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Adán Cabello
Adán Cabello
Departamento de Física Aplicada II, Universidad de Sevilla, E-41012 Sevilla,
Spain
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AIP Conf. Proc. 1508, 265–274 (2012)
Citation
Jan-Åke Larsson, Matthias Kleinmann, Constantino Budroni, Otfried Gühne, Adán Cabello; Maximal violation of state-independent contextuality inequalities. AIP Conf. Proc. 18 December 2012; 1508 (1): 265–274. https://doi.org/10.1063/1.4773138
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