I went to school with Mel Siegel, a physisist at Carnegie Mellon. I asked Mel for a simple explanation of polarized light in terms of quantum theory. In this case that’s the construct that light can be explained in terms of it being a particle — a photon. Here’s what he wrote:
Polarization maps one-to-one to angular momentum (spin) of h/2pi per photon (i.e., 1 in fundamental units).
The one subtlety is that whereas for particles with non-zero mass it could project to +1, 0, or -1, for photons — because they travel at the speed of light — only +1 and -1 are allowed.
These correspond to the two circular polarizations. If I remember the convention correctly, +1 is called left and -1 is called right.
Linear polarization is then a suitably phase-shifted equally-weighted mixture of left and right.
You can visualize this by imagining an uncomplicated emitting atom (e.g., an idealized alkali metal) in a weak magnetic field (Zeeman effect): as the viewing angle goes smoothly from aligned with to aligned against the magnetic field the polarization goes smoothly from one circular polarization to linear polarization to the other circular polarization, being elliptical in between, of course.