  The noncontextual hidden variables models in $d=2$, such as the ones
constructed by Bell and by Kochen and Specker, have difficulties in accounting
for the conditional measurement of two non-orthogonal projectors. An idea of
branching in the hidden variables space, which provides a means to realize the
notion of reduction effectively and describe the state preparation, is
suggested as a way to resolve the difficulties associated with the conditional
measurement.
