How much information can ride on a light ray? --- and what geometry and probability on complex projective spaces has to do with this

Imagine communication via a single ray of (nearly) monochromatic light by modulating (in time) the intensity and polarization.  These two attributes are computed at the receiver from the photocurrents generated by several photodiodes (fed by a bespoke linear optical circuit). What are the maximum achievable bit rate (per Hz of bandwidth) and the best receiver design when limited by the inevitable (photocurrent) thermal noise?
I will give an introduction to the mathematics of this basic question, from the classical principles of Shannon's information theory to a novel geometric optimization problem.  An asymptotic bit rate formula in terms of a new special function and globally optimal receivers offering 4x capacity improvement are the tangible outcomes. No special background is expected of the audience.

(This work is a part of a joint project with MSU's EE and is funded by U.S. Air Force.)