Syllabus
C*-algebras (mainly finite dimensional). Events, random variables and product spaces in quantum theory.
The interpretation of quantum probability. Representations of algebras.
Completely positive maps. Paradoxes of quantum mechanics.
Quantum teleportation. Quantum cryptography.
Annotation
Introduction to quantum probability theory, which is a noncommutative extension of probability theory. After a review of the basic concepts
(events, random variables, product spaces) in the new set-up, the course turns its attention to the interpretation of quantum mechanics, as well as typical quantum effects such as quantum teleportation, quantum cryptography, etc. The course is meant for students in mathematics with an interest in probability, as well as students in physics with an interest in rigorous mathematics.