We present a moment expansion for the systematic characterization of the polarization properties of quantum
states of light. Specifically,we link the method to themeasurements of the Stokes operator in different directions on
the Poincar´e sphere and provide a scheme for polarization tomography without resorting to full-state tomography.
We apply these ideas to the experimental first- and second-order polarization characterization of some two-photon
quantum states. In addition, we show that there are classes of states whose polarization characteristics are
dominated not by their first-order moments (i.e., the Stokes vector) but by higher-order polarization moments.