  We develop a systematic coarse graining procedure for systems of $N$ qubits.
We exploit the underlying geometrical structures of the associated discrete
phase space to produce a coarse-grained version with reduced effective size.
Our coarse-grained spaces inherit key properties of the original ones. In
particular, our procedure naturally yields a subset of the original measurement
operators, which can be used to construct a coarse discrete Wigner function.
These operators also constitute a systematic choice of incomplete measurements
for the tomographer wishing to probe an intractably large system.
