  A universal and optimal method for the polarimetry of light with arbitrary
photon statistics is presented. The method is based on the continuous
maximum-likelihood positive operator-valued measure (ML-POVM) for pure
polarization states over the surface of the Bloch sphere. The success
probability and the mean fidelity are used as the figures of merit to show its
performance. The POVM is found to attain the collective bound of polarization
estimation with respect to the mean fidelity. As demonstrations, explicit
results for the N photon Fock state, the phase-randomized coherent state
(Poisson distribution), and the thermal light are obtained. It is found that
the estimation performances for the Fock state and the Poisson distribution are
almost identical, while that for the thermal light is much worse. This suggests
that thermal light leaks less information to an eavesdropper and hence could
potentially provide more security in polarization-encoded quantum communication
protocols than a single-mode laser beam as customarily considered. Finally,
comparisons against an optimal adaptive measurement with classical
communications are made to show the better and more stable performance of the
continuous ML-POVM.
