Twisted simplicial distributions

C Okay, WH Stern - arxiv preprint arxiv:2403.19808, 2024‏ - arxiv.org
We introduce a theory of twisted simplicial distributions on simplicial principal bundles,
which allow us to capture Bell's non-locality, and the more general notion of quantum …

A bundle perspective on contextuality: Empirical models and simplicial distributions on bundle scenarios

RS Barbosa, A Kharoof, C Okay - arxiv preprint arxiv:2308.06336, 2023‏ - arxiv.org
This paper provides a bundle perspective to contextuality by introducing new categories of
contextuality scenarios based on bundles of simplicial complexes and simplicial sets. The …

Homotopical characterization of strongly contextual simplicial distributions on cone spaces

A Kharoof, C Okay - Topology and its Applications, 2024‏ - Elsevier
This paper offers a novel homotopical characterization of strongly contextual simplicial
distributions with binary outcomes, specifically those defined on the cone of a 1-dimensional …

Extremal simplicial distributions on cycle scenarios with arbitrary outcomes

A Kharoof, C Okay, S Ipek - arxiv preprint arxiv:2406.19961, 2024‏ - arxiv.org
Cycle scenarios are a significant class of contextuality scenarios, with the Clauser-Horne-
Shimony-Holt (CHSH) scenario being a notable example. While binary outcome …

Equivariant simplicial distributions and quantum contextuality

C Okay, I Sikora - arxiv preprint arxiv:2310.18135, 2023‏ - arxiv.org
We introduce an equivariant version of contextuality with respect to a symmetry group, which
comes with natural applications to quantum theory. In the equivariant setting, we construct …

[PDF][PDF] On the rank of two-dimensional simplicial distributions

C Okay - Hacettepe Journal of Mathematics and Statistics, 2023‏ - dergipark.org.tr
Simplicial distributions provide a framework for studying quantum contextuality, a
generalization ofBell's non-locality. Understanding extremal simplicial distributions is of …

The geometry of simplicial distributions on suspension scenarios

A Kharoof - arxiv preprint arxiv:2412.10963, 2024‏ - arxiv.org
Quantum measurements often exhibit non-classical features, such as contextuality, which
generalizes Bell's non-locality and serves as a resource in various quantum computation …

Simplicial effects and weakly associative partial groups

C Okay, V Castillo, WH Stern - arxiv preprint arxiv:2502.05958, 2025‏ - arxiv.org
In this paper, we introduce a new category of simplicial effects that extends the categories of
effect algebras and their multi-object counterpart, effect algebroids. Our approach is based …

[PDF][PDF] Categorical methods for a homotopical characterization of contextuality

A Kharoof, C Okay‏ - oxford24.github.io
Bell's notion of non-locality and its generalization quantum contextuality are fundamental
features of quantum theory [1, 2]. These inherently non-classical phenomena have attracted …