Related papers: Representation theorem for obsevables on a quantum…
In the quantum-Bayesian approach to quantum foundations, a quantum state is viewed as an expression of an agent's personalist Bayesian degrees of belief, or probabilities, concerning the results of measurements. These probabilities obey the…
Quantum theory can be viewed as a generalization of classical probability theory, but the analogy as it has been developed so far is not complete. Whereas the manner in which inferences are made in classical probability theory is…
A rigorous theory of quantum state reduction, the state change of the measured system caused by a measurement conditional upon the outcome of measurement, is developed fully within quantum mechanics without leading to the vicious circle…
A probabilistic propositional logic, endowed with an epistemic component for asserting (non-)compatibility of diagonizable and bounded observables, is presented and illustrated for reasoning about the random results of projective…
Bayes' rule $\mathbb{P}(B|A)\mathbb{P}(A)=\mathbb{P}(A|B)\mathbb{P}(B)$ is one of the simplest yet most profound, ubiquitous, and far-reaching results of classical probability theory, with applications in any field utilizing statistical…
This paper introduces a novel type theory and logic for probabilistic reasoning. Its logic is quantitative, with fuzzy predicates. It includes normalisation and conditioning of states. This conditioning uses a key aspect that distinguishes…
We develop a new framework of uncertainty variables to model uncertainty. An uncertainty variable is characterized by an uncertainty set, in which its realization is bound to lie, while the conditional uncertainty is characterized by a set…
Scientific theories need to be testable by observations, say using Bayes' theorem. A complete theory needs at least the three parts of dynamical laws for specified physical variables, the correct solution of the dynamical laws (boundary…
We review recent work that employs the framework of logical inference to establish a bridge between data gathered through experiments and their objective description in terms of human-made concepts. It is shown that logical inference…
We analyse a quantum-like Bayesian Network that puts together cause/effect relationships and semantic similarities between events. These semantic similarities constitute acausal connections according to the Synchronicity principle and…
We develop a systematic approach to quantum probability as a theory of rational betting in quantum gambles. In these games of chance the agent is betting in advance on the outcomes of several (finitely many) incompatible measurements. One…
In this paper we will study a function of simultaneus measurements for quantum events (s-map) which will be compared with the conditional states on an orthomodular lattice as a basic structure for quantum logic.
Complex phase factors are viewed not only as redundancies of the quantum formalism but instead as remnants of unitary transformations under which the probabilistic properties of observables are invariant. It is postulated that a quantum…
We state a quantum version of Bayes's rule for statistical inference and give a simple general derivation within the framework of generalized measurements. The rule can be applied to measurements on N copies of a system if the initial state…
This is an attempt to create a consistent and non-trivial extension of quantum theory, describing in detail the quantum measurement process. A tentative but concrete model is presented, based on the concept of multiple…
The fundamental algebraic concepts of quantum mechanics, as expressed by many authors, are reviewed and translated into the framework of the relatively new non-distributive system of Boolean fractions (also called conditional events or…
Predictions for measurement outcomes in physical theories are usually computed by combining two distinct notions: a state, describing the physical system, and an observable, describing the measurement which is performed. In quantum theory,…
In this article we provide a substantial discussion on the statistical concept of conditional independence, which is not routinely mentioned in most elementary statistics and mathematical statistics textbooks. Under the assumption of…
This paper presents a framework for Quantum causal modeling based on the interpretation of causality as a relation between an observer's probability assignments to hypothetical or counterfactual experiments. The framework is based on the…
We develop a new interpretation of quantum theory by combining insights from extended Wigner's friend scenarios and quantum causal modelling. In this interpretation, which synthesizes ideas from relational quantum mechanics and consistent…