  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.
