I returned this weekend from the meeting on Foundations of Probability and Physics at the University of Vaxjo in Sweden. There were many interesting talks, so I'll just mention a few of them that I found particularly inspiring.
– Giacomo Mauro d'Ariano explained his axiomatization of quantum theory, inspired by observations from quantum state and process tomography. One of the nice features of this is that he gives an operational definition of the adjoint. Why the observables of QM should form an algebra from an operational point of view has been a topic of recent debate amongst foundational people here at Perimeter, so this could be a piece of the puzzle.
– Rüdiger Schack explained what it might mean for quantum randomness to be "truly random" from a Bayesian point of view, using the concept of "inside information" that he has developed with Carlton Caves.
– Philip Goyal gave another axiomatization of quantum theory. I'm not sure whether the framework he uses is that well-motivated (especially the sneaky way that complex numbers are introduced). On the other hand, one of his axioms has the flavor of an "epistemic constraint", which gels nicely with ideas that have been expressed earlier by Chris Fuchs and Rob Spekkens.