Ah, you've put your finger on just why I have trouble believing in the determinism fairy (deterministic QM). Randomness, like entropy, is opaque -- information or structure that is dispersed isn't retrievable or reconstructible.
Your implication seems quite sound to me, and it might be fun to tease out some of the other consequences. There might even be a neat reductio ad absurdum nested in there (i.e., a proof that QM cannot be contained in a deterministic theory). Then we'd know that to violate the HUP or otherwise make QM deterministic, we have to violate one of the axioms said proof requires -- that's assuming anyone still has an appetite for the problem.
I ought to take Max's advice and think about this post for three days or so, it's soooo half-baked :-)
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