What is Quantum Probability?
Guest Lecturer Greg Kuperberg, UC Davis
Abstract: Quantum mechanics is difficult for many people to understand because it is difficult to believe. The heart of the problem is quantum probability, which is an entirely rigorous theory; nonetheless even many working mathematicians have trouble believing it. (Quantum field theory is far from entirely rigorous, but that is a very different issue that I will not discuss.) In the past 15 years or so, quantum probability has greatly expanded as a mathematical topic in the guise of quantum computation and quantum information theory. In this talk, I will discuss some of the ideas of quantum probability, quantum computation, and quantum information, using the language of pure mathematics. A particular theme is that a good scientific interpretation of quantum probability can be exactly matched to basic ideas in operator algebras.