  We give a complete characterization of the (non)classicality of all
stabilizer subtheories. First, we prove that there is a unique nonnegative and
diagram-preserving quasiprobability representation of the stabilizer subtheory
in all odd dimensions, namely Gross's discrete Wigner function. This
representation is equivalent to Spekkens' epistemically restricted toy theory,
which is consequently singled out as the unique noncontextual ontological model
for the stabilizer subtheory. Strikingly, the principle of noncontextuality is
powerful enough (at least in this setting) to single out one particular
classical realist interpretation. Our result explains the practical utility of
Gross's representation by showing that (in the setting of the stabilizer
subtheory) negativity in this particular representation implies generalized
contextuality. Since negativity of this particular representation is a
necessary resource for universal quantum computation in the state injection
model, it follows that generalized contextuality is also a necessary resource
for universal quantum computation in this model. In all even dimensions, we
prove that there does not exist any nonnegative and diagram-preserving
quasiprobability representation of the stabilizer subtheory, and, hence, that
the stabilizer subtheory is contextual in all even dimensions.
