  The characterization of quantum polarization of light requires knowledge of
all the moments of the Stokes variables, which are appropriately encoded in the
multipole expansion of the density matrix. We look into the cumulative
distribution of those multipoles and work out the corresponding extremal pure
states. We find that SU(2) coherent states are maximal to any order whereas the
converse case of minimal states (which can be seen as the most quantum ones) is
investigated for a diverse range of the number of photons. Taking advantage of
the Majorana representation, we recast the problem as that of distributing a
number of points uniformly over the surface of the Poincare sphere.
