Related papers: Negative Probabilities and Contextuality
In this work, we elaborate on a measure-theoretic approach to negative probabilities. We study a natural notion of contextuality measure and characterize its main properties. Then, we apply this measure to relevant examples of quantum…
Negative probability has found diverse applications in theoretical physics. Thus, construction of sound and rigorous mathematical foundations for negative probability is important for physics. There are different axiomatizations of…
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,…
Several principled measures of contextuality have been proposed for general systems of random variables (i.e. inconsistentlly connected systems). The first of such measures was based on quasi-couplings using negative probabilities (here…
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…
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…
Identifying when observed statistics cannot be explained by any reasonable classical model is a central problem in quantum foundations. A principled and universally applicable approach to defining and identifying nonclassicality is given by…
Most behavioral and social experiments aimed at revealing contextuality are confined to cyclic systems with binary outcomes. In quantum physics, this broad class of systems includes as special cases Klyachko-Can-Binicioglu-Shumovsky-type,…
Negative probabilities arise primarily in physics, statistical quantum mechanics and quantum computing. Negative probabilities arise as mixing distributions of unobserved latent variables in Bayesian modeling. Our goal is to provide a link…
Here we briefly discuss how negative numbers, or "negative probabilities", can naturally arise in probabilistic expressions and be given an operational interpretation. Like the use of negative numbers in arithmetical expressions, the use of…
In this chapter, we review a principled way of defining and measuring contextuality in systems with deterministic inputs and random outputs, recently proposed and developed in \citep{KujalaDzhafarovLarsson2015,DKL2015FooP}.
In his constructive and well-informed commentary, Andrei Khrennikov acknowledges a privileged status of classical probability theory with respect to statistical analysis. He also sees advantages offered by the Contextuality-by-Default…
The paper outlines a new development in the Contextuality-by-Default theory as applied to finite systems of binary random variables. The logic and principles of the original theory remain unchanged, but the definition of contextuality of 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…
We show that the main idea behind contextuality-by-default (CbD), i.e., the assumption that a physical measurement has to be understood as a contextual collection of random variables, is implicit in the compatibility-hypergraph approach to…
Beginning with the Bell theorem, cyclic systems of dichotomous random variables have been the object of many foundational findings in quantum mechanics. Here, we ask the question: if one chooses a cyclic system "at random" (uniformly within…
We present a proof for a conjecture previously formulated by Dzhafarov, Kujala, and Larsson (Foundations of Physics, in press, arXiv:1411.2244). The conjecture specifies a measure for the degree of contextuality and a criterion (necessary…
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…
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 deals with three traditional ways of defining contextuality: (C1) in terms of (non)existence of certain joint distributions involving measurements made in several mutually exclusive contexts; (C2) in terms of relationship between…