The Strong Free Will Theorem

[…] our theorem asserts that if experimenters have a certain freedom, then particles have exactly the same kind of freedom. Indeed, it is natural to suppose that this latter freedom is the ultimate explanation of our own.
[…] It may well be true that classically stochastic processes such as tossing a (true) coin do not help in explaining free will, but […] adding randomness also does not explain the quantum mechanical effects described in our theorem. It is precisely the “semi-free” nature of twinned particles, and more generally of entanglement, that shows that something very different from classical stochasticism is at play here.
Although the FWT [Free Will Theorem] suggests to us that determinism is not a viable option, it nevertheless enables us to agree with Einstein that “God does not play dice with the Universe.” In the present state of knowledge, it is certainly beyond our capabilities to understand the connection between the free decisions of particles and humans, but the free will of neither of these is accounted for by mere randomness.
[…] determinism may formally be shown to be consistent, there is no longer any evidence that supports it, in view of the fact that classical physics has been superseded by quantum mechanics, a non-deterministic theory. The import of the free will theorem is that it is not only current quantum theory, but the world itself that is non-deterministic, so that no future theory can return us to a clockwork universe.

http://www.ams.org/notices/200902/rtx090200226p.pdf
Cf. http://www.sciencenews.org/view/generic/id/35391/title/Math_Trek__Do_subatomic_particles_have_free_will%3F