  Information theory establishes the ultimate limits on performance for noisy
communication systems [Shannon48]. An accurate model of a physical
communication device must include quantum effects, but typically including
these makes the theory intractable. As a result communication capacities are
not known, even for transmission between two users connected by an
electromagnetic waveguide subject to gaussian noise. Here we present an exactly
solvable model of communications with a fully quantum electromagnetic field.
This allows us to find explicit expressions for all the point-to-point
capacities of a noisy quantum channel, with implications for quantum key
distribution, and fiber optical communications. We also develop a theory of
quantum communication networks by solving some rudimentary quantum networks for
broadcasting and multiple access. When possible, we compare the predictions of
our new model with those of the orthodox quantum gaussian model and in all
cases we find capacities in agreement to within a constant number of bits.
Thus, in the limit of high signal to noise ratios our simple model captures the
relevant physics of gaussian models while remaining amenable to detailed
analysis,
