Foundations of non-commutative probability theory (Extended abstract)

Abstract

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, are defined in a natural way.The mystery presented by the algebraic equations satisfied by (non-commuting) observables that cannot be observed in the same states is elucidated.

13 pages, Presented at TARK '09, Stanford, July 2009

References in corpus (3)

• A presentation of Quantum Logic based on an "and then" connective
• Quantic Superpositions and the Geometry of Complex Hilbert Spaces
• Similarity-Projection structures: the logical geometry of Quantum Physics