  Polarization of light is harnessed in an abundance of classical and quantum
applications. Characterizing polarization in a classical sense is done
resoundingly successfully using the Stokes parameters, and numerous proposals
offer new quantum counterparts of this characterization. The latter often rely
on distance measures from completely polarized or unpolarized light. We here
show that the accepted class of perfectly polarized quantum states of light is
severely lacking in terms of both pure states and mixed states. By appealing to
symmetry and geometry arguments we determine all of the states corresponding to
perfect polarization, and show that the accepted class of completely polarized
quantum states is only a subset of our result. We use this result to
reinterpret the canonical degree of polarization, commenting on its
interpretation for classical and quantum light. Our results are necessary for
any further characterizations of light's polarization.
