No-hidden-variables proof for two spin- particles preselected and postselected in unentangled states

It is a well-known fact that all the statistical predictions of quantum mechanics on the state of any physical system represented by a two-dimensional Hilbert space can always be duplicated by a noncontextual hidden-variables model. In this paper, I show that, in some cases, when we consider an additional independent (unentangled) two-dimensional system, the quantum description of the resulting composite system cannot be reproduced using noncontextual hidden variables. In particular, a no-hidden-variables proof is presented for two individual spin- particles preselected in an uncorrelated state |A〉⊗|B〉 and postselected in another uncorrelated state |a〉⊗|B〉, |B〉 being the same state for the second particle in both preselection and postselection.