> There is nothing to report until there is an experiment that people can hold up saying "see! we found it! This part is deterministic not probabilistic!".
To add a bit more on top of my earlier comment: I believe Deutsch would point out that all experiments that have ever been done do corroborate the determinism of quantum phenomena.
Experimental tests are only ever understood in terms of theory, and quantum theory, which Deutsch identifies with the many worlds "interpretation", says that the world evolves according to Schrodinger's equation. Other "interpretations" of quantum theory are actually rival theories that fall at the first hurdle of being worse theories. To Deutsch, a bad theory is one that is easy to vary -- in this case, for example, the "Copenhagen interpretation" says that QM -- i.e. Schrodinger's equation -- is true, except when you measure something -- and then it says that you're not allowed to ask what that means. Why not? You're just not, OK?
This may sound like sophistry, but it isn't. Consider a closely analogous case:
Denying that experimental tests of QM have corroborated that theory -- which is a deterministic theory -- is like saying that dinosaur bones are not evidence of dinosaurs because none of the experimental tests distinguish the theory that dinosaurs really existed from the one that says that God put the bones there: true, but that theory is ruled out because it's a bad explanation (easy to vary: why God, for example?).