Contextuality-by-default for behaviours in compatibility scenarios


Alves Tezzin, A.C. (2020). Contextuality-by-default for behaviours in compatibility scenarios . Perimeter Institute. https://pirsa.org/20100067


Alves Tezzin, Alisson Cordeiro. Contextuality-by-default for behaviours in compatibility scenarios . Perimeter Institute, Oct. 30, 2020, https://pirsa.org/20100067


          @misc{ pirsa_20100067,
            doi = {10.48660/20100067},
            url = {https://pirsa.org/20100067},
            author = {Alves Tezzin, Alisson Cordeiro},
            keywords = {Quantum Foundations},
            language = {en},
            title = {Contextuality-by-default for behaviours in compatibility scenarios },
            publisher = {Perimeter Institute},
            year = {2020},
            month = {oct},
            note = {PIRSA:20100067 see, \url{https://pirsa.org}}

Alisson Cordeiro Alves Tezzin State University of Sao Paulo (UNESP)


The compatibility-hypergraph approach to contextuality (CA) and the contextuality-by-default approach (CbD) are usually presented as products of entirely different views on how physical measurements and measurement contexts should be understood: the latter is based on the idea that a physical measurement has to be seen by a collection of random variables, one for each context containing that measurement, while the imposition of the non-disturbance condition as a physical requirement in the former precludes such interpretation of measurements. The aim of our work is to present both approaches as entirely compatible ones and to introduce in the compatibility-hypergraph approach ideas which arises from contextuality-by-default. We

introduce in CA the non-degeneracy condition, which is the analogous of consistent connectedness (an important concept from CbD), and prove that this condition is, in general, weaker than non-disturbance. The set of non-degenerate behaviours defines a polytope, therefore one can characterize non-degeneracy using a finite set of linear inequalities. We introduce extended contextuality for behaviours and prove that a behaviour is non-contextual in the standard sense if and only if 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.