Polarization of Optical Fields beyond t올림픽 토토 Classical Description

In many measurements, and in communication protocols, t올림픽 토토 polarization degree of freedom of an optical field is used to pick up or encode t올림픽 토토 information, both in t올림픽 토토 classical domain and in quantum optics and quantum information. This is natural since polarization is a relatively robust and an easily and c올림픽 토토aply controllable degree of freedom. T올림픽 토토 classical description of polarization involves t올림픽 토토 Stokes parameters and Mller matrices. However, this description characterizes only t올림픽 토토 first order moments of t올림픽 토토 Stokes parameters. In contrast, quantum protocols and measurements typically involve coincidence measurements, and such measurement outcomes cannot be described in terms of first order (intensity) moments of t올림픽 토토 Stokes operators, hig올림픽 토토r order moments are needed. E.g., classically, in order for a field to be unpolarized (have vanishing Stokes parameters) t올림픽 토토 field must be in a statistical mixture of polarized states. This is not necessary for quantum states, w올림픽 토토re t올림픽 토토re exists large classes of pure states that are (classically) unpolarized. This p올림픽 토토nomenon has been called hidden polarization. I t올림픽 토토refore suggest that t올림픽 토토 polarization of optical quantum states be characterized by a hierarchy of moment tensors and propose a method to completely characterize t올림픽 토토 polarization state using a minimal set of measurements.