  We explore a particular way of reformulating quantum theory in classical
terms, starting with phase space rather than Hilbert space, and with actual
probability distributions rather than quasiprobabilities. The classical picture
we start with is epistemically restricted, in the spirit of a model introduced
by Spekkens. We obtain quantum theory only by combining a collection of
restricted classical pictures. Our main challenge in this paper is to find a
simple way of characterizing the allowed sets of classical pictures. We present
one promising approach to this problem and show how it works out for the case
of a single qubit.
