  The degree of polarization of a quantum state can be defined as its
Hilbert-Schmidt distance to the set of unpolarized states. We demonstrate that
the states optimizing this degree for a fixed average number of photons
$\bar{N}$ present a fairly symmetric, parabolic photon statistics, with a
variance scaling as $\bar{N}^2$. Although no standard optical process yields
such a statistics, we show that, to an excellent approximation, a highly
squeezed vacuum can be considered as maximally polarized.
