Related papers: Classical logic, classical probability, and quantu…
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…
Alternative partial Boolean structures, implicit in the discussion of classical representability of sets of quantum mechanical predictions, are characterized, with definite general conclusions on the equivalence of the approaches going back…
Relativistic causality, namely, the impossibility of signaling at superluminal speeds, restricts the kinds of correlations which can occur between different parts of a composite physical system. Here we establish the basic restrictions…
Partition logics -- non-Boolean event structures obtained by pasting Boolean algebras -- provide a natural language for situations in which a system has a definite latent state but can be accessed and resolved only through mutually…
Bell's theorem shows that the reasonable relativistic causal principle known as "local causality" is not compatible with the predictions of quantum mechanics. It is not possible maintain a satisfying causal principle of this type while…
Document ranking based on probabilistic evaluations of relevance is known to exhibit non-classical correlations, which may be explained by admitting a complex structure of the event space, namely, by assuming the events to emerge from…
In his article in Science, Nicolas Gisin claimed that quantum correlations emerge from outside space time. We explain that they are due to space time symmetries. This paper is a critical review of metaphysical conclusions found in many…
Contextuality and entanglement are valuable resources for quantum computing and quantum information. Bell inequalities are used to certify entanglement; thus, it is important to understand why and how they are violated. Quantum mechanics…
This note is concerned with a formal analysis of the problem of non-monotonic reasoning in intelligent systems, especially when the uncertainty is taken into account in a quantitative way. A firm connection between logic and probability is…
We introduce a contextual quantum system comprising mutually complementary observables organized into two or more collections of pseudocontexts with the same probability sums of outcomes. These pseudocontexts constitute non-orthogonal bases…
We show one can use classical fields to modify a quantum optics experiment so that Bell's inequalities will be violated. This happens with continuous random variables that are local, but we need to use the correlation matrix to prove there…
We explore correlation polytopes to derive a set of all Boole-Bell type conditions of possible classical experience which are both maximal and complete. These are compared with the respective quantum expressions for the…
We study the contextuality of a three-level quantum system using classical conditional entropy of measurement outcomes. First, we analytically construct the minimal configuration of measurements required to reveal contextuality. Next, an…
Recently, the author and Bob Coecke have introduced a categorical formulation of Quantum Mechanics. In the present paper, we shall use it to open up a novel perspective on No-Cloning. What we shall find, quite unexpectedly, is a link to…
We describe a mathematical language for determining all possible patterns of contextuality in the dependence of stochastic outputs of a system on its deterministic inputs. The central notion is that of all possible couplings for…
Correlations in Bell and noncontextuality inequalities can be expressed as a positive linear combination of probabilities of events. Exclusive events can be represented as adjacent vertices of a graph, so correlations can be associated to a…
Our aim in this paper is to point out a surprising formal connection, between two topics which seem on face value to have nothing to do with each other: relational database theory, and the study of non-locality and contextuality in the…
Reichenbach's principle states that in a causal structure, correlations of classical information can stem from a common cause in the common past or a direct influence from one of the events in correlation to the other. The difficulty of…
The study of causal relations has recently been applied to the quantum realm, leading to the discovery that not all physical processes have a definite causal structure. While indefinite causal processes have previously been experimentally…
It is one of the most remarkable features of quantum physics that measurements on spatially separated systems cannot always be described by a locally causal theory. In such a theory, the outcomes of local measurements are determined in…