  The question of a hidden variable interpretation of quantum contextuality in
the Mermin-Peres square is considered. The Kochen-Specker theorem implies that
quantum mechanics may be interpreted as a contextual hidden variable theory. It
is shown that such a hidden variable description can be viewed as either
contextual in the random variables mapping hidden states to observable outcomes
or in the probability measure on the hidden state space. The latter view
suggests that this apparent contextuality may be interpreted as a simple
consequence of measurement disturbance, wherein the initial hidden state is
altered through interaction with the measuring device, thereby giving rise to a
possibly different final hidden variable state from which the measurement
outcome is obtained. In light of this observation, a less restrictive and,
arguably, more reasonable definition of noncontextuality is suggested. To prove
that such a description is possible, an explicit and, in this sense,
noncontextual hidden variable model is constructed which reproduces all quantum
theoretic predictions for the Mermin-Peres square. A critical analysis of some
recent and proposed experimental tests of contextuality is also provided.
Although the discussion is restricted to a four-dimensional Hilbert space, the
approach and conclusions are expected to generalize to any Hilbert space.
