Contextuality-by-default for behaviours in compatibility scenarios

• URL: http://arxiv.org/abs/2008.02273v1
• Date: Wed, 5 Aug 2020 17:54:14 GMT
• Title: Contextuality-by-default for behaviours in compatibility scenarios
• Authors: Alisson Tezzin, Rafael Wagner, Barbara Amaral
• Abstract summary: We show that the assumption that a physical measurement has to be understood as a contextual collection of random variables is implicit in the compatibility-hypergraph approach to contextuality (CA) We introduce in CA the non-degeneracy condition, which is the analogous of consistent connectedness, and prove that this condition is, in general, weaker than non-disturbance condition. We introduce the idea of extended contextuality for behaviours and prove that a behaviour is non-contextual in the standard sense iff it is non-degenerate and non-contextual in the extended sense.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We show that the main idea behind contextuality-by-default (CbD), i.e., the assumption that a physical measurement has to be understood as a contextual collection of random variables, is implicit in the compatibility-hypergraph approach to contextuality (CA) and use this result to develop in the latter important concepts which were introduced in the former. We introduce in CA the non-degeneracy condition, which is the analogous of consistent connectedness, and prove that this condition is, in general, weaker than non-disturbance condition. The set of non-degenerate behaviours defines a polytope, implying that one can characterize consistent connectedness using linear inequalities. We introduce the idea of extended contextuality for behaviours and prove that a behaviour is non-contextual in the standard sense iff it is non-degenerate and non-contextual in the extended sense. Finally, we use extended scenarios and behaviours to shed new light on our results.

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