Quantum Communications Made Easy: Deterministic Models of Bosonic Channels

Abstract: 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,