We capitalize on a multipolar expansion of the polarisation density matrix,
in which multipoles appear as successive moments of the Stokes variables. When
all the multipoles up to a given order K vanish, we can properly say that the
state is Kth-order unpolarized, as it lacks of polarization information to
that order. First-order unpolarized states coincide with the corresponding
classical ones, whereas unpolarized to any order tally with the quantum notion
of fully invariant states. In between these two extreme cases, there is a rich
variety of situations that are explored here. The existence of \textit{hidden}
polarisation emerges in a natural way in this context.Comment: 7 pages, 3 eps-color figures. Submitted to PRA. Comments welcome