Quantum Probability

From Qwiki

Quantum probability or non-commutative probability is an extension of probability theory wide enough to allow for quantum mechanical models.

A quantum probability space is a von Neumann algebra (of bounded operators on a Hilbert space) together with a normal state on it. It generalizes the classical notion of a probability space, and reduces to it if the algebra is commutative.

The theory is based on ideas of von Neumann and Segal, and was developed in the 60's and 70's of the 20th century for the benefit of constructive quantum field theory and quantum statistical mechanics, where these notions arise naturally.

The, basically European, development of Quantum probability has been laid down in the series Quantum Probability and Related Topics, later called Quantum Probability Communications.