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A universal and optimal method for the polarimetry of light with arbitraryphoton statistics is presented. The method is based on the continuousmaximum-likelihood positive operator-valued measure (ML-POVM) for purepolarization states over the surface of the Bloch sphere. The successprobability and the mean fidelity are used as the figures of merit to show itsperformance. The POVM is found to attain the collective bound of polarizationestimation with respect to the mean fidelity. As demonstrations, explicitresults for the N photon Fock state, the phase-randomized coherent state(Poisson distribution), and the thermal light are obtained. It is found thatthe estimation performances for the Fock state and the Poisson distribution arealmost identical, while that for the thermal light is much worse. This suggeststhat thermal light leaks less information to an eavesdropper and hence couldpotentially provide more security in polarization-encoded quantum communicationprotocols than a single-mode laser beam as customarily considered. Finally,comparisons against an optimal adaptive measurement with classicalcommunications are made to show the better and more stable performance of thecontinuous ML-POVM.

Universal Optimal Estimation of the Polarization of Light with Arbitrary Photon Statistics