Related papers: Contextuality, Cohomology and Paradox
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,…
One can often encounter claims that classical (Kolmogorovian) probability theory cannot handle, or even is contradicted by, certain empirical findings or substantive theories. This note joins several previous attempts to explain that these…
Quantum theory departs from classical probabilistic theories in foundational ways. These departures--termed quantumness here--power quantum information and computation. This thesis charts the role of discrete structures in assessing…
Dzhafarov, Zhang, and Kujala (Phil. Trans. Roy. Soc. A 374, 20150099) reviewed several behavioral data sets imitating the formal design of the quantum-mechanical contextuality experiments. The conclusion was that none of these data sets…
We study simulation and quantum resources in the setting of the sheaf-theoretic approach to contextuality and non-locality. Resources are viewed behaviourally, as empirical models. In earlier work, a notion of morphism for these empirical…
Contextuality is a fundamental manifestation of nonclassicality, indicating that for certain quantum correlations, sets of jointly measurable variables cannot be pre-assigned values independently of the measurement context. In this work, we…
The use of quantum information in technology promises to supersede the so-called classical devices used nowadays. Understanding what features are inherently non-classical is crucial for reaching better-than-classical performance. This…
Contextuality is well known as a vital resource for locating the boundary between classical and quantum theories, as well as identifying tasks showing quantum advantage. In a surge of recent works [Schmid and Spekkens, Phys.Rev.X 8, 011015…
Contextuality is a signature of operational nonclassicality in the outcome statistics of an experiment. This notion of nonclassicality applies to a breadth of physical phenomena. Here, we establish its relation to two fundamental…
What if the paradoxical nature of quantum theory could find its source in some undecidability analog to that of G\"odel's incompleteness theorem ? This essay aims at arguing for such G\"odelian hunch via two case studies. Firstly, using a…
The predictions of quantum theory resist generalised noncontextual explanations. In addition to the foundational relevance of this fact, the particular extent to which quantum theory violates noncontextuality limits available quantum…
Realist interpretations of quantum mechanics presuppose the existence of elements of reality that are independent of the actions used to reveal them. Such a view is challenged by several no-go theorems that show quantum correlations cannot…
Within the framework of quantum contextuality, we discuss the ideas of extracontextuality and extravalence, that allow one to relate Kochen-Specker's and Gleason's theorems. We emphasize that whereas Kochen-Specker's is essentially a no-go…
Quantum contextuality is a concept used to describe the property of hidden-variable theory that measurement outcomes predetermined by the hidden variables depend on the measurement context. The term measurement context can have different…
We describe a scheme of quantum computation with magic states on qubits for which contextuality is a necessary resource possessed by the magic states. More generally, we establish contextuality as a necessary resource for all schemes of…
Generalized contextuality is a hallmark of nonclassical theories like quantum mechanics. Yet, three fundamental computational problems concerning its decidability and complexity remain open. First, determining the complexity of deciding if…
The generalized notion of noncontextuality provides an avenue to explore the fundamental departure of quantum theory from a classical explanation. Recently, extracting a different form of quantum advantage in various information processing…
There are two different and logically independent concepts of noncontextuality in quantum mechanics. First, an ontological (hidden variable) model for quantum mechanics is called noncontextual if every ontic (hidden) state determines the…
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…
Violation of a noncontextuality inequality or the phenomenon referred to `quantum contextuality' is a fundamental feature of quantum theory. In this article, we derive a novel family of noncontextuality inequalities along with their…