I want to understand the Gottesman-Knill theorem, which basically says that using some subclass of unitary transformations (from the Clifford group) there is no quantum speed-up ie. we can simulate the system efficiently on a classical computer.
I want to understand the claims presented in http://core.ac.uk/download/pdf/11923581.pdf . The author says that the reason that using only Clifford group brings efficient classical simulation is because the transformations in Clifford group inlcude only rotations of the Bloch sphere by multiples of $\pi/2$. He then goes on to explain that these transformations don't violate Bell's inequalities (specifically CHSH inequalities):
In an entangled quantum system, no amount of $k\pi/2$ transformations of one of the constituent systems will cause it to take on an orientation with respect to the other subsystems that is not a multiple of $\pi/2$ (unless it was so oriented initially).And as we have seen above, the statistics of compound states for which the difference in orientation between subsystems is a multiple of $\pi/2$ are capable in general of being reproduced by a classical hidden variables theory.
I wan't to know if this claim is correct and first of all, I would be happy if someone explained this to me on an example. I heard that stabilizer formalism can violate Bell's inequalities so this is all weird to me.
PS. My basic intention is to have a clearer picture of why some subclass of transformations can be efficiently simulated classicaly and I thought this would be a nice way to understand it (if of course it is true). If anyone has any other ideas as to how to explain the Gottesman-Knill (besides stabilizer formalism), I would be very happy.