Related papers: Contextuality and Informational Redundancy
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…
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…
Contextuality was originally defined only for consistently connected systems of random variables (those without disturbance/signaling). Contextuality-by-Default theory (CbD) offers an extension of the notion of contextuality to…
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…
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,…
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…
Recently there has been much interest and progress in extending the definition of contextuality to systems with disturbance. We prove that such an endeavor cannot simultaneously satisfy the following principles: (1) any deterministic system…
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…
The Contextuality-by-Default approach to determining and measuring the (non)contextuality of a system of random variables requires that every random variable in the system be represented by an equivalent set of dichotomous random variables.…
This is a non-technical introduction into theory of contextuality. More precisely, it presents the basics of a theory of contextuality called Contextuality-by-Default (CbD). One of the main tenets of CbD is that the identity of a random…
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…
The notion of (non)contextuality pertains to sets of properties measured one subset (context) at a time. We extend this notion to include so-called inconsistently connected systems, in which the measurements of a given property in different…
This paper provides a framework for characterizing sequential scenarios, allowing for the identification of contextuality given empirical data, and then provides precise operational interpretations in terms of the possible hidden variable…
We introduce a new notion, that of a contextuality profile of a system of random variables. Rather than characterizing a system's contextuality by a single number, its overall degree of contextuality, we show how it can be characterized by…
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.…
We discuss three measures of the degree of contextuality in contextual systems of dichotomous random variables. These measures are developed within the framework of the Contextuality-by-Default (CbD) theory, and apply to inconsistently…
Contextuality means non-existence of a joint distribution for random variables recorded under mutually incompatible conditions, subject to certain constraints imposed on how the identity of these variables may change across these…
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…
Traditionally categorical data analysis (e.g. generalized linear models) works with simple, flat datasets akin to a single table in a database with no notion of missing data or conflicting versions. In contrast, modern data analysis must…
Contextuality is a key characteristic that separates quantum from classical phenomena and an important tool in understanding the potential advantage of quantum computation. However, when assessing the quantum resources available for quantum…