Assessing the Polarization of a Quantum Field from Stokes Fluctuations

We propose an operational degree of polarization in terms of the variance of the Stokes vector minimized over all the directions of the Poincare sphere. We examine the properties of this second-order definition and carry out its experimental determination. Quantum states with the same standard (first-order) degree of polarization are correctly discriminated by this new measure. We argue that a comprehensive quantum characterization of polarization properties requires a whole hierarchy of higher-order degrees.