Maximally polarized states for quantum light fields
  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. 
L. L. Sanchez-Soto, E. C. Yustas, G. Bjork, and A. B. Klimov