Related papers: Probability Bracket Notation: the Unified Expressi…
We continue the development of a so called contextual statistical model (here context has the meaning of a complex of physical conditions). It is shown that, besides contexts producing the conventional trigonometric $\cos$-interference,…
As inductive inference and machine learning methods in computer science see continued success, researchers are aiming to describe ever more complex probabilistic models and inference algorithms. It is natural to ask whether there is a…
Contextuality, the impossibility of assigning a single random variable to represent the outcomes of the same measurement procedure under different experimental conditions, is a central aspect of quantum mechanics. Thus defined, it appears…
Automata with monitor counters, where the transitions do not depend on counter values, and nested weighted automata are two expressive automata-theoretic frameworks for quantitative properties. For a well-studied and wide class of…
Probabilistic programming is related to a compositional approach to stochastic modeling by switching from discrete to continuous time dynamics. In continuous time, an operator-algebra semantics is available in which processes proceeding in…
The notion of probability plays an important role in almost all areas of science and technology. In modern mathematics, however, probability theory means nothing other than measure theory, and the operational characterization of the notion…
In this paper analogically as quadratic stochastic operators and processes we define cubic stochastic operator (CSO) and cubic stochastic processes (CSP). These are defined on the set of all probability measures of a measurable space. The…
We introduce an operator system, universal for the probabilistic models of a contextuality scenario, and identify its maximal C*-cover via the right C*-algebra of a canonical ternary ring of operators, arising from a hypergraph version of…
The problem of defining quantum probabilities of composite events is considered. This problem is of high importance for the theory of quantum measurements and for quantum decision theory that is a part of measurement theory. We show that…
We use the machinery of a conditional probability space (R\'enyi, 1955) to obtain an Agreement Theorem (Aumann, 1976) under general conditions. A conditional probability space (CPS) is a family of probability measures defined relative to a…
The probability of necessity (PN), which quantifies the probability that an observed event would not have occurred in the absence of the treatment, is a central estimand in attribution analysis. While PN has been extensively studied for…
The dynamics of a quantum system, undergoing unitary evolution and continuous monitoring, can be described in term of quantum trajectories. Although the averaged state fully characterises expectation values, the entire ensamble of…
Symplectic and optical joint probability representations of quantum mechanics are considered, in which the functions describing the states are the probability distributions with all random arguments (except the argument of time ). The…
Three extensions and reinterpretations of nonclassical probabilities are reviewed. (i) We propose to generalize the probability axiom of quantum mechanics to self-adjoint positive operators of trace one. Furthermore, we discuss the…
We present a domain-theoretic framework for probabilistic programming that provides a constructive definition of conditional probability and addresses computability challenges previously identified in the literature. We introduce a novel…
Given a normalized state-vector $\psi $, we define the conditional expectation $\mathbb{E }_{\psi } (A | B ) $ of a Hermitian operator $A $ with respect to a strongly commuting family of self-adjoint operators $B $ as the best…
Kolmogorov's setting for probability theory is given an original generalization to account for probabilities arising from Quantum Mechanics. The sample space has a central role in this presentation and random variables, i.e., observables,…
We address the statistics of continuous weak linear measurement on a few-state quantum system that is subject to a conditioned quantum evolution. For a conditioned evolution, both the initial and final states of the system are fixed: the…
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…
The notion of context (complex of physical conditions) is basic in this paper. We show that the main structures of quantum theory (interference of probabilities, Born's rule, complex probabilistic amplitudes, Hilbert state space,…