Elements of quantum probability

Abstract

This is an introductory article presenting some basic ideas of quantum probability. From a discussion of simple experiments with polarized light and a card game we deduce the necessity of extending the body of classical probability theory. For a class of systems, containing classical systems with finitely many states, a probabilistic model is developed. It can describe, in particular, the polarization experiments. Some examples of ‘quantum coin tosses’ are discussed, closely related to V.F.R. Jones’ approach to braid group representations, to spin relaxion, and to nuclear magnetic resonance. In an appendix we indicate the steps which lead to the full mathematical model of quantum probability.