Related papers: Contextuality and the fundamental theorem of nonco…
Certain concrete "ontological models" for quantum mechanics (models in which measurement outcomes are deterministic and quantum states are equivalent to classical probability distributions over some space of `hidden variables') are…
In a recent article entitled "A simple explanation of the quantum violation of a fundamental inequality," Cabello proposes a condition on a class of probabilistic models that, he claims, gives the same bound on contextuality for the KCBS…
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.…
Our main theorem is in the generality of the axioms of Hilbert space, and the theory of unbounded operators. Consider two Hilbert spaces such that their intersection contains a fixed vector space D. It is of interest to make a precise…
We analyze the validity of Bell and Kochen-Specker theorems under local (or noncontextual) realism but avoiding an assumption of the existence of a joint probability distribution for incompatible observables. We formulate a realist model…
In this essay, I develop order-theoretic notions of determinism and contextuality on domains and topoi. In the process, I develop a method for quantifying contextuality and show that the order-theoretic sense of contextuality is analogous…
Contextuality is a central feature of quantum theory, traditionally understood as the impossibility of reproducing quantum measurement statistics using noncontextual ontological models. We study classical ontological descriptions in which a…
Contextuality provides a unifying paradigm for nonclassical aspects of quantum probabilities and resources of quantum information. Unfortunately, most forms of quantum contextuality remain experimentally unexplored due to the difficulty of…
In this letter I stress the role of causal reversibility (time-symmetry), together with causality and locality, in the justification of the quantum formalism. Firstly, in the algebraic quantum formalism, I show that the assumption of…
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…
We introduce an operator system, universal for the probabilistic models of a contextuality scenario, and identify its maximal C*-cover via the right C*-algebra of a canonical ternary ring of operators, arising from a hypergraph version of…
A set of quantum data can look classical in every local test and still fail to admit a single classical explanation of the whole composite system. We formulate this failure as global contextuality. Here global means global in the physical…
Standard quantum mechanics undeniably violates the notion of separability that classical physics accustomed us to consider as valid. By relating the phenomenon of quantum nonseparability to the all-important concept of potentiality, we…
This paper introduces an extension of the de Broglie-Bohm-Bell formulation of quantum mechanics, which includes intrinsic particle degrees of freedom, such as spin, as elements of reality. To evade constraints from the Kochen-Specker…
Contextuality - the obstruction to describing quantum mechanics in a classical statistical way - has been proposed as a resource that powers quantum computing. The measurement-based model provides a concrete manifestation of contextuality…
The resource theory of contextuality considers resourceful objects to be probabilistic data-tables, known as correlations or behaviors, that fail to have an explanation in terms of Kochen-Specker noncontextual models. In this work, we…
Applying the classical Serre-Swan theorem, as this is extended to topological (non-normed) algebras, one attains a classification of elementary particles via their spin-structure. In this context, our argument is virtually based on a…
Bivariant (equivariant) K-theory is the standard setting for non-commutative topology. We may carry over various techniques from homotopy theory and homological algebra to this setting. Here we do this for some basic notions from…
Contextuality is a natural generalization of nonlocality which does not need composite systems or spacelike separation and offers a wider spectrum of interesting phenomena. Most notably, in quantum mechanics there exist scenarios where the…
Using a quantum like algebraic formulation we give proof of Kochen-Specker theorem. We introduce new criteria in order to account for the contextual nature of measurements in quantum mechanics.