Less sensational than the claim that quantum physics allows for magic is the claim that quantum mechanics explains free will. Unfortunately for those who make it, this claim is no truer.
The logic behind this claim runs something like this:
For thousands of years, philosophers and theologians have been debating determinism vs. free will.
Quantum theory implies that nature is fundamentally random; you can start a quantum mechanical system from the exact same starting conditions over and over again, and it will evolve differently each time. There may be only finitely many end states, but there is no way to predict before hand how a given trial will end.
Therefore, the universe is non-deterministic.
Therefore everyone has free will.
The problem here is the logical fallacy known as false dilemma: we are implicitly assuming that there are only two possibilities: determinism or free will. When we think about it, though, this assumption is clearly unreasonable. It is perfectly possible for reality to behave in a way that is both completely random and completely beyond Human control.
Put another way, suppose that you have to pick between an apple and an orange for breakfast one morning: by some extremely improbable turn of events, your decision is governed by the behaviour of a single electron in your brain; if it moves to the left, you will pick the orange, if it moves to the right, you will pick the apple. Your behaviour will then be non-deterministic; however, you still have no actual say over which way the electron moves.
That’s not to say, of course, that quantum theory rules out free will; just that it doesn’t predict it.