Bilkent University, Turkey, cihan.okay@bilkent.edu.tr
(joint work with Selman Ipek and Aziz Kharoof)
In this talk, I will introduce a new framework for contextuality based on simplicial sets, combinatorial models of topological spaces that play a prominent role in modern homotopy theory. Our approach extends measurement scenarios to consist of spaces (rather than sets) of measurements and outcomes and thereby generalizes nonsignaling distributions, formulated using sheaf theory, to simplicial distributions that describe distributions on spaces. Strong contextuality can be generalized suitably for simplicial distributions, allowing us to define cohomological witnesses that extend the earlier topological constructions restricted to algebraic relations among quantum observables to the level of probability distributions. This also extends an earlier approach to quantum contextuality based on group cohomology.
[1] arXiv:2204.06648