Related papers: Geometric contextuality from the Maclachlan-Martin…
Contextuality is a central property in comparative analysis of classical, quantum, and supercorrelated systems. We examine and compare two well-motivated approaches to contextuality. One approach ("contextuality-by-default") is based on the…
We present a study of quantum contextuality of three-dimensional mixed states for the Klyachko-Can-Binicio\u{g}lu-Shumovsky (KCBS) and the Kurzy\'{n}ski-Kaszlikowski (KK) noncontextuality inequalities. For any class of states whose…
We prove rigidity results describing contextually-constrained maps defined on Grassmannians and manifolds of ordered independent line tuples in finite-dimensional vector or Hilbert spaces. One statement in the spirit of the Fundamental…
We present a formal theory of contextuality for a set of random variables grouped into different subsets (contexts) corresponding to different, mutually incompatible conditions. Within each context the random variables are jointly…
Quantum groups and quantum homogeneous spaces - developed by several authors since the 80's - provide a large class of examples of algebras which for many reasons we interpret as `coordinate algebras' over noncommutative spaces. This…
Group lattices (Cayley digraphs) of a discrete group are in natural correspondence with differential calculi on the group. On such a differential calculus geometric structures can be introduced following general recipes of noncommutative…
Every finite simple group P can be generated by two of its elements. Pairs of generators for P are available in the Atlas of finite group representations as (not neccessarily minimal) permutation representations P. It is unusual but…
Contextuality has been conjectured to be a super-classical resource for quantum computation, analogous to the role of non-locality as a super-classical resource for communication. We show that the presence of contextuality places a lower…
Quantum contextuality plays a significant role in supporting quantum computation and quantum information theory. The key tools for this are the Kochen--Specker and non-Kochen--Specker contextual sets. Traditionally, their representation has…
Quantum contextuality, a fundamental feature distinguishing quantum theory from classical models, is investigated via algebraic and topological structures inherent in modular tensor categories. This work rigorously demonstrates that braid…
The goal of the paper is to check whether the real eigenstates of the observables in the single qudit Pauli group may lead to quantum contextuality, the property that mutually compatible and independent experiments depend on each other. We…
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…
Generalized contextuality is a possible indicator of non-classical behaviour in quantum information theory. In finite-dimensional systems, this is justified by the fact that noncontextual theories can be embedded into some simplex, i.e.…
Let $G$ be a finitely generated group, $A$ a finite set of generators and $K$ a subgroup of $G$. We call the pair $(G,K)$ context-free if the set of all words over $A$ that reduce in $G$ to an element of $K$ is a context-free language. When…
The quantum predictions for a single nonrelativistic spin-1/2 particle can be reproduced by noncontextual hidden variables. Here we show that quantum contextuality for a relativistic electron moving in a Coulomb potential naturally emerges…
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…
Symmetry is at the heart of much of mathematics, physics, and art. Traditional geometric symmetry groups are defined in terms of isometries of the ambient space of a shape or pattern. If we slightly generalize this notion to allow the…
We provide a cohomological framework for contextuality of quantum mechanics that is suited to describing contextuality as a resource in measurement-based quantum computation. This framework applies to the parity proofs first discussed by…
We study a generalization of the Fuchsian triangle groups to the hyperbolic 3-space, namely, the groups generated by half-turns in three hyperbolic lines. The role of the hyperbolic triangles is now played by the right-angled hexagons. This…
Non-linear realizations of spacetime symmetries can be obtained by a generalization of the coset construction valid for internal ones. The physical equivalence of different representations for spacetime symmetries is not obvious, since…