Conditional probability, three-slit experiments, and the Jordan algebra structure of quantum mechanics

Understand

Most quantum logics do not allow for a reasonable calculus of conditional probability.

• However, those ones which do so provide a very general and rich mathematical structure, including classical probabilities, quantum mechanics as well as Jordan algebras.
• This structure exhibits some similarities with Alfsen and Shultz's non-commutative spectral theory, but these two mathematical approaches are not identical.
• Barnum, Emerson and Ududec adapted the concept of higher-order interference, introduced by Sorkin in 1994, into a general probabilistic framework.