Related papers: Twisted simplicial distributions
Simplicial distributions provide a framework for studying quantum contextuality, a generalization of Bell's non-locality. Understanding extremal simplicial distributions is of fundamental importance with applications to quantum computing.…
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 models. Existing frameworks have rigorously captured these…
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 obtained in quantum mechanical experiments do not always admit a…
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 approach extends measurement scenarios to consist of spaces…
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 cohomology classes that can detect contextuality. This…
Twisting and classical background fields are two foundational techniques in supersymmetric quantum field theory, central to developments ranging from the Higgs mechanism to topological twisting and supersymmetric localisation. While…
We develop a resource theory of contextuality within the framework of symmetric monoidal categories, extending recent simplicial approaches to quantum contextuality. Building on the theory of simplicial distributions, which integrates…
Distributions, i.e., subsets of tangent bundles formed by piecing together subspaces of tangent spaces, are commonly encountered in the theory and application of differential geometry. Indeed, the theory of distributions is a fundamental…
A generalization of classical gauge theory is presented, in the framework of a noncommutative-geometric formalism of quantum principal bundles over smooth manifolds. Quantum counterparts of classical gauge bundles, and classical gauge…
Categorical bundles provide a natural framework for gauge theories involving multiple gauge groups. Unlike the case of traditional bundles there are distinct notions of triviality, and hence also of local triviality, for categorical…
A theory of principal bundles possessing quantum structure groups and classical base manifolds is presented. Structural analysis of such quantum principal bundles is performed. A differential calculus is constructed, combining differential…
The existence of the theory of `twisted cotangent bundles' (symplectic groupoids) allows to study classical mechanical systems which are generalized in the sense that their configurations form a Poisson manifold. It is natural to study from…
A noncommutative-geometric formalism of framed principal bundles is sketched, in a special case of quantum bundles (over quantum spaces) possessing classical structure groups. Quantum counterparts of torsion operators and Levi-Civita type…
We extend topological T-duality to the case of general circle bundles. In this setting we prove existence and uniqueness of T-duals. We then show that T-dual spaces have isomorphic twisted cohomology, twisted $K$-theory and Courant…
Quantum theory is known to be nonlocal in the sense that separated parties can perform measurements on a shared quantum state to obtain correlated probability distributions, which cannot be achieved if the parties share only classical…
Using tangent bundle geometry we construct an equivalent reformulation of classical field theory on flat spacetimes which simultaneously encodes the perspectives of multiple observers. Its generalization to curved spacetimes realizes a new…
In this paper, we introduce the concept of principal bundles on statistical manifolds. After necessary preliminaries on information geometry and principal bundles on manifolds, we study the $\alpha$-structure of frame bundles over…
A general noncommutative-geometric theory of principal bundles is presented. Quantum groups play the role of structure groups. General quantum spaces play the role of base manifolds. A differential calculus on quantum principal bundles is…
In recent years, the study of Bell nonlocality has been generalized to quantum networks, where multiple independent sources distribute physical systems to distant parties who perform local measurements. In this context, a central open…
We offer here a more direct approach to twisted K-theory, based on the notion of twisted vector bundles (of finite or infinite dimension) and of twisted principal bundles. This is closeely related to the classical notion ot torsors and…