10 citations · 17 across the 11 of their papers we have counts for
12 papers
Possibilistic collapse and extremality of simplicial distributions
Aziz Kharoof, Cihan Okay
Consistent families of locally defined probability distributions that do not admit a joint global distribution are known as contextual, with primary examples arising in quantum the…
Vertex structure of fiber products of probability polytopes
Aziz Kharoof, Cihan Okay
We develop tools for characterizing vertices of fiber products of polytopes and apply them to simplicial distribution polytopes, a class of probability polytopes arising in quantum…
Simplicial methods in the resource theory of contextuality
Aziz Kharoof, Cihan Okay
We develop a resource theory of contextuality within the framework of symmetric monoidal categories, extending recent simplicial approaches to quantum contextuality. Building on th…
The geometry of simplicial distributions on suspension scenarios
Aziz Kharoof
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 mode…
Extremal simplicial distributions on cycle scenarios with arbitrary outcomes
Aziz Kharoof, Cihan Okay, Selman Ipek
Cycle scenarios are a significant class of contextuality scenarios, with the Clauser-Horne-Shimony-Holt (CHSH) scenario being a notable example. While binary outcome measurements i…
Homotopy types of diagrams of chain complexes
David Blanc, Surojit Ghosh, Aziz Kharoof
We study the homotopy theory of diagrams of chain complexes over a field indexed by a finite poset, and show that it can be completely described in terms of appropriate diagrams of…
Homotopical characterization of strongly contextual simplicial distributions on cone spaces
Aziz Kharoof, Cihan Okay
This paper offers a novel homotopical characterization of strongly contextual simplicial distributions with binary outcomes, specifically those defined on the cone of a 1-dimension…
A bundle perspective on contextuality: Empirical models and simplicial distributions on bundle scenarios
Rui Soares Barbosa, Aziz Kharoof, Cihan Okay
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…
Topological methods for studying contextuality: -cycle scenarios and beyond
Aziz Kharoof, Selman Ipek, Cihan Okay
Simplicial distributions are combinatorial models describing distributions on spaces of measurements and outcomes that generalize non-signaling distributions on contextuality scena…
Simplicial distributions, convex categories and contextuality
Aziz Kharoof, Cihan Okay
The data of a physical experiment can be represented as a presheaf of probability distributions. A striking feature of quantum theory is that those probability distributions obtain…
Simplicial quantum contextuality
Cihan Okay, Aziz Kharoof, Selman Ipek
We 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 approa…
Higher order Toda brackets
Aziz Kharoof
We describe two ways to define higher order Toda brackets in a pointed simplicial model category : one is a recursive definition using model categorical constructions,…