In this paper, we explore the graph approach to contextuality to restate the extended definition of noncontextuality as given by Kujala et al. [Phys. Rev. Lett. 115, 150401 (2015)] using graph-theoretical terms. This extended definition avoids the assumption of the pre-sheaf or non-disturbance condition, which states that if two contexts overlap, then the marginal distribution obtained for the intersection must be the same, a restriction that will never be perfectly satisfied in real experiments. With this, we are able to derive necessary conditions for extended noncontextuality for any set of random variables based on the geometrical aspects of the graph approach, which can be tested directly with experimental data in any contextuality experiment and which reduce to traditional necessary conditions for noncontextuality if the non-disturbance condition is satisfied.
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July 2018
Research Article|
July 13 2018
Necessary conditions for extended noncontextuality in general sets of random variables
Barbara Amaral
;
Barbara Amaral
1
Departamento de Física e Matemática, CAP–Universidade Federal de São João del-Rei
, 36.420-000 Ouro Branco, MG, Brazil
2
International Institute of Physics, Federal University of Rio Grande do Norte
, P.O. Box 1613, 59078-970 Natal, Brazil
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Cristhiano Duarte;
Cristhiano Duarte
2
International Institute of Physics, Federal University of Rio Grande do Norte
, P.O. Box 1613, 59078-970 Natal, Brazil
3
Departamento de Matemática, Instituto de Ciências Exatas, Universidade Federal de Minas Gerais
, CP 702, CEP, 30123-970 Belo Horizonte, Minas Gerais, Brazil
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Roberto I. Oliveira
Roberto I. Oliveira
4
Instituto de Matemática Pura e Aplicada (IMPA)
, Rio de Janeiro, RJ, Brazil
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J. Math. Phys. 59, 072202 (2018)
Article history
Received:
February 05 2018
Accepted:
June 24 2018
Citation
Barbara Amaral, Cristhiano Duarte, Roberto I. Oliveira; Necessary conditions for extended noncontextuality in general sets of random variables. J. Math. Phys. 1 July 2018; 59 (7): 072202. https://doi.org/10.1063/1.5024885
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