Related papers: Contextuality-by-Default: A Brief Overview of Idea…
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 rigorous general definition of quantum probability is given, which is valid for elementary events and for composite events, for operationally testable measurements as well as for inconclusive measurements, and also for non-commuting…
In this paper, following an elementary line of thought which somewhat differs from the usual one, we prove once more that any deterministic theory predictively equivalent to quantum mechanics unavoidably exhibits a contextual character. The…
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…
Recent crowdsourcing experiments have shown that true contextuality of the kind found in quantum mechanics can also be present in human behavior. In these experiments simple human choices were aggregated over large numbers of respondents,…
We introduce contextual behavioural metrics (CBMs) as a novel way of measuring the discrepancy in behaviour between processes, taking into account both quantitative aspects and contextual information. This way, process distances by…
Contextuality is regarded as a non-classical feature, challenging our everyday intuition; quantum contextuality is currently seen as a resource for many applications in quantum computation, being responsible for quantum advantage over…
The Principle of Complementarity of Probabilities based on of noncommutative probability is introduced.
The recurring context in which objects appear holds valuable information that can be employed to predict their existence. This intuitive observation indeed led many researchers to endow appearance-based detectors with explicit reasoning…
The emergence of open data portals necessitates more attention to protecting sensitive data before datasets get published and exchanged. To do so effectively, we observe the need to refine and broaden our definitions of sensitive data, and…
Contextuality is a necessary resource for universal quantum computation and non-contextual quantum mechanics can be simulated efficiently by classical computers in many cases. Orders of Planck's constant, $\hbar$, can also be used to…
Contextuality is a central feature distinguishing quantum from classical probability theories, but its operational meaning is often stated only qualitatively. In this Letter, we study a simple information-theoretic question: how much…
As a phenomenon encompassing measurement incompatibility and Bell nonlocality, quantum contextuality is not only central to our understanding of quantum mechanics, but also an essential resource in many quantum information processing tasks.…
This paper presents a simple generalization of causal consistency suited to any object defined by a sequential specification. As causality is captured by a partial order on the set of operations issued by the processes on shared objects…
Within the framework of generalized noncontextuality, we introduce a general technique for systematically deriving noncontextuality inequalities for any experiment involving finitely many preparations and finitely many measurements, each of…
We formalize the general principle of significance with respect to binary relations which is a universal tool for description and analysis of various situations in and apart from mathematics. We derive the basic properties and focus on a…
Based on rectangle theory of formal concept and set covering theory, the concept reduction preserving binary relations is investigated in this paper. It is known that there are three types of formal concepts: core concepts, relative…
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…
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…
The question of what should be meant by a measurement is tackled from a mathematical perspective whose physical interpretation is that a measurement is a fundamental process via which a finite amount of classical information is produced.…