Unicamp, Brazil, tcunha@unicamp.br
(joint work with Anna Lina Vandré)
The graph approach to contextuality [1] is a major contribution to the understanding of Kochen-Specker contextuality [2]. The first worked example is Clauser-Horne-Shimony-Holt scenario and inequality [3]. As any Bell inequality, CHSH is also a Non-Contextuality inequality. When written as a sum of eight probabilities, its quantum bound is the same in both cases: with or without Bell restriction. What about behaviours? Is it true that any behaviour obtained by the Born rule under the restriction of CHSH NC-inequality can also be obtained in the CHSH Bell scenario? The Coloured Graph Approach [4], originally proposed for Nonlocality, is much more general: it applies to Contextuality with Parts, which includes the so called Generalised Bell Scenarios [5], when each part is also allowed to make locally compatible measurements. With this apparatus, we answer negatively the question posed above, by exhibiting families of coloured graphs with different nested quantum sets, the outer most being CHSH NC-inequality one, the inner most the CHSH Bell-inequality one [6,7].
[1] Adán Cabello, Simone Severini, and Andreas Winter, Phys. Rev. Lett. 112, 040401 (2014).
[2] Simon Kochen and Ernest Specker, J. Math. Mech. 17, 59 (1967).
[3] John F. Clauser, Michael A. Horne, Abner Shimony, and Richard A. Holt Phys. Rev. Lett. 23, 880 (1969).
[4] Rafael Rabelo et. al, J. Phys. A: Math. Theor. 47 424021 (2014).
[5] Tassius Temistocles, Rafael Rabelo, and Marcelo Terra Cunha, Phys. Rev. A 99 042120 (2019).
[6] Anna Lina Vandré and Marcelo Terra Cunha, in preparation.
[7] Anna Lina Vandré, Masters Thesis, University of Innsbruck.