I agree with abgematcht. If you argue whether the world is deterministic or QM is coherent, it is still obvious that we are controlled by our composed particles. If you argue that we're complex enough enough to control it, well...isn't it the particles that make us complex? The circularity makes it so that it appears that there's free will, but not really. Ergo, free will is impossible w/o non-physical implications. I don't think this can be argued, and I don't know why people do.
"What I meant to say, of course, is that the brain is physical reality and may thus be part of a "system" where the question that was asked applies,. But if there is a mind, and it is not physical, then it doesn't matter what QM do to the brain, or it only matters insofar as there is indeed a relation between brain (physical) and mind (mental)."
Cachimbo, maybe...it's obvious that the brain has impact on decisions. You can say it's linked to a mind, but from my pov I'd rather say it's linked to the soul. However, I'm not saying that souls are the explanation for the apparent QM. The randomness in experiments is just physics. However, the randomness of particles in the brain appears to be part of the QM when it's not. A decision would be affected by triggering a randomness caused by the soul that leads to a chain reaction of particle movements in the brain that lead to a choice. It's undetectable because of the QM. So, I believe in free will linked to the supernatural, making it neither provable or unprovable.
Also, I believe that God can alter particles outside of the brain to influence what's called "miracles." Kind of radical thinking...but you could hypothetically test a miracles to see if atoms were moving in unpredictable ways. Except the QM makes this type of supernatural influence undetectable also. Don't ask me why, it's God's business.
Anyways, that's just a religious spin on QM and freewill.