The Schrodinger equation almost always predicts that a particle has some particular amplitude at many different locations. However, if you try to detect a particle, you will never find it at more than one location. Furthermore, once the particle is detected at one particular location, you need to update the Schrodinger equation to give it amplitude 1 at that location and 0 everywhere else - if you don't perform this nonlinear update and instead use the old wave-function, the predictions for further experiments will be completely off.
Now, the physical interpretation of this collapse varies wildly between different interpretations of QM, but some variant of it is always required - otherwise, the observations simply do not match the math. We don't yet have any theory consistent with QM that can make predictions without applying the Born rule.
As far as we know for now, [a variant of [0] ] this one is the wrong claim: we do have algorithms (Shor's, Grover's) that are faster on Quantum Computers than any known classical algorithm.
Of course, we do not yet have any proof that a faster classical algorithm can't exist, so the possibility remains open that this claim remains true. BUT, if this claim turns out to be true, then it is extremely likely that either one or both of the other 2 claims will immediately turn out to be wrong.
[0] I would note that the "exponential" part is somewhat of a red herring. If there is any kind of asymptotic speed-up that QCs fundamentally have over classical computers, even if it's just quadratic, then the larger point will remain valid.
> In a sense, the sci-fi concept of the ansible, where quantum collapse effects are exploited for FTL signaling, is more plausible than the view where quantum systems collapse instantly, but cannot be exploited for FTL.
This is also what rubs me the wrong way about entanglement, and seems a very tantalizing thread to pull at if one wanted a more fundamental theory. The other thread of course is the measurement problem.