Turing machine as an abstract concept is known to not hold a solution to the halting problem. There's no question about that, the only question is how the abstract concept assumptions pertain to the real world (infinite tape? maybe a problem, maybe not?; is the execution speed bounded? or maybe we can somehow count to infinity by exponentially increasing the speed? things like that).

On the other hand nobody has any clue what the quantum measurement / wave function collapse actually is. There are theories/interpretations but no truly satisfying answers in the same way as for example Newton's equations were a satisfying answer to the elliptical movement of planets, even though we later found out in the 20th century that F ~ 1/r^2 was actually an approximation.

We simply don't know, and we have no idea when shall we know.

Bell's inequalities talk about "measurements". But measurement's aren't real.