Related papers: On Measures and Measurements: a Fibre Bundle appro…
Contextuality describes the nontrivial dependence of measurement outcomes on particular choices of jointly measurable observables. In this work we review and generalize the bundle diagram representation introduced in [S. Abramsky et al.,…
Contextuality can be understood as the impossibility to construct a globally consistent description of a model even if there is local agreement. In particular, quantum models present this property. We can describe contextuality with the…
Contextuality is usually defined as absence of a joint distribution for a set of measurements (random variables) with known joint distributions of some of its subsets. However, if these subsets of measurements are not disjoint,…
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 former approach generalizes earlier work on the…
We study finite probability theory through a category of finite probability schemes and probability-preserving maps, called \emph{bundles}. A bundle simultaneously records a quotient of a sample space, an algebra of random variables, and…
In quantum mechanics, not everything that can be observed can be observed simultaneously. Observational data exhibits \emph{contextuality} -- a generalisation of nonlocality -- if the result of an observation is necessarily dependent on…
Models of a phenomenon are often developed by examining it under different experimental conditions, or measurement contexts. The resultant probabilistic models assume that the underlying random variables, which define a measurable set of…
The object of contextuality analysis is a set of random variables each of which is uniquely labeled by a content and a context. In the measurement terminology, the content is that which the random variable measures, whereas the context…
This paper is a brief overview of the concepts involved in measuring the degree of contextuality and detecting contextuality in systems of binary measurements of a finite number of objects. We discuss and clarify the main concepts and…
An empirical model is a generalization of a probability space. It consists of a simplicial complex of subsets of a class X of random variables such that each simplex has an associated probability distribution. The ensuing marginalizations…
This paper has two purposes. One is to demonstrate contextuality analysis of systems of epistemic random variables. The other is to evaluate the performance of a new, hierarchical version of the measure of (non)contextuality introduced in…
Abstract Contextuality is a property of systems of random variables. The identity of a random variable in a system is determined by its joint distribution with all other random variables in the same context. When context changes, a variable…
In quantum physics the term `contextual' can be used in more than one way. One usage, here called `Bell contextual' since the idea goes back to Bell, is that if $A$, $B$ and $C$ are three quantum observables, with $A$ compatible (i.e.,…
In these lecture notes we will try to give an introduction to the use of the mathematics of fibre bundles in the understanding of some global aspects of gauge theories, such as monopoles and instantons. They are primarily aimed at beginning…
This paper provides a systematic yet accessible presentation of the Contextuality-by-Default theory. The consideration is confined to finite systems of categorical random variables, which allows us to focus on the basics of the theory…
We introduce a contextual quantum system comprising mutually complementary observables organized into two or more collections of pseudocontexts with the same probability sums of outcomes. These pseudocontexts constitute non-orthogonal bases…
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…
Contextuality is a feature of quantum correlations. It is crucial from a foundational perspective as a nonclassical phenomenon, and from an applied perspective as a resource for quantum advantage. It is commonly defined in terms of hidden…
We introduce a framework to describe probabilistic models in Bell experiments, and more generally in contextuality scenarios. Such a scenario is a hypergraph whose vertices represent elementary events and hyperedges correspond to…
Contextual situations are those in which seemingly "the same" random variable changes its identity depending on the conditions under which it is recorded. Such a change of identity is observed whenever the assumption that the variable is…