Related papers: Contextuality is About Identity of Random Variable…
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…
A primary goal in recent research on contextuality has been to extend this concept to cases of inconsistent connectedness, where observables have different distributions in different contexts. This article proposes a solution within the…
Random variables representing measurements, broadly understood to include any responses to any inputs, form a system in which each of them is uniquely identified by its content (that which it measures) and its context (the conditions under…
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…
Cyclic systems of dichotomous random variables have played a prominent role in contextuality research, describing such experimental paradigms as the Klyachko-Can-Binicoglu-Shumovky, Einstein-Podolsky-Rosen-Bell, and Leggett-Garg ones in…
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.,…
From behavioral sciences to biology to quantum mechanics, one encounters situations where (i) a system outputs several random variables in response to several inputs, (ii) for each of these responses only some of the inputs may "directly"…
Contextuality and nonlocality are non-classical properties exhibited by quantum statistics whose implications profoundly impact both foundations and applications of quantum theory. In this paper we provide some insights into logical…
The definition of the conditional probability is very important in the theory of the probability. This definition is based on the fact, that random events can be simultaneously measurable. This paper deal with the problem of conditioning…
Bell inequalities may only be derived, if hidden variables do not depend on the experimental settings. The stochastic independence of hidden and setting variables is called: freedom of choice, free will, measurement independence or no…
Contextuality is a particular quantum phenomenon that has no analogue in classical probability theory. Given two independent systems, a natural question is how to represent such a situation as a single test space. In other words, how…
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,…
Nowadays contextuality is the hotest topic of quantum foundations and, especially, foundations of quantum information theory. This notion is characterized by the huge diversity of approaches and interpretations. One of the strongest trends…
Contextuality is one way of capturing the non-classicality of quantum theory. The contextual nature of a theory is often witnessed via the violation of non-contextuality inequalities---certain linear inequalities involving probabilities of…
Contextuality is a defining feature that separates the quantum from the classical descriptions of physical systems. Within the marginal-scenario framework, noncontextual models are characterized by the existence of a single joint…
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…
Contextuality is a non-classical behaviour that can be exhibited by quantum systems. It is increasingly studied for its relationship to quantum-over-classical advantages in informatic tasks. To date, it has largely been studied in…
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.,…
The Contextuality-by-Default (CbD) theory allows one to separate contextuality from context-dependent errors and violations of selective influences (aka "no-signaling" or "no-disturbance" principles). This makes the theory especially…
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…