Quantum probability

Quantum Probability Explanations for Probability Judgment ‘Errors’

A quantum probability model is introduced and used to explain human probability judgment errors including the conjunction, disjunction, inverse, and conditional fallacies, as well as unpacking effects and partitioning effects. Quantum probability theory is a general and coherent theory based on a set of (von Neumann) axioms which relax some of the constraints underlying classic (Kolmogorov) pro...

Quantum Probability Spaces

Classical and Quantum Probability

We follow the development of probability theory from the beginning of the last century, emphasising that quantum theory is really a generalisation of this theory. The great achievements of probability theory, such as the theory of processes, generalised random fields, estimation theory and information geometry, are reviewed. Their quantum versions are then described.

Quantum Probability Theory

The mathematics of classical probability theory was subsumed into classical measure theory by Kolmogorov in 1933. Quantum theory as nonclassical probability theory was incorporated into the beginnings of noncommutative measure theory by von Neumann in the early thirties, as well. To precisely this end, von Neumann initiated the study of what are now called von Neumann algebras and, with Murray,...

Fuzzy Quantum Probability Theory

This paper surveys some of the recent results that have been obtained in fuzzy quantum probability theory. In this theory fuzzy events are represented by quantum effects and fuzzy random variables are represented by quantum measurements. Probabilities, conditional probabilities and sequential products of effects are discussed. The relationship between the law of total probability and compatibil...