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No hidden variables proof for two spin 1/2 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-1/2 particles preselected in an uncorrelated state AB and postselected in another uncorrelated state aB, B being the same state for the second particle in both preselection and postselection.