Multiple-user quantum information theory for optical communication channels

Abstract

Research in the past decade has established capacity theorems for point-to-point bosonic channels with additive thermal noise, under the presumption of a conjecture on the minimum output von Neumann entropy. In the first part of this thesis, we evaluate the optimum capacity for free-space line-of-sight optical communication using Gaussian-attenuation apertures. Optimal power allocation across all the spatiotemporal modes is studied, in both the far-field and near-field propagation regimes. We establish the gap between ultimate capacity and data rates achievable using classical encoding states and structured receivers. The remainder of the thesis addresses the ultimate capacity of bosonic broadcast channels, i.e., when one transmitter is used to send information to more than one receiver. We show that when coherent-state encoding is employed in conjunction with coherent detection, the bosonic broadcast channel is equivalent to the classical degraded Gaussian broadcast channel whose capacity region is known. We draw upon recent work on the capacity region of the two-user degraded quantum broadcast channel to establish the ultimate capacity region for the bosonic broadcast channel, under the presumption of another conjecture on the minimum output entropy. We also generalize the degraded broadcast channel capacity theorem to more than two receivers, and prove that if the above conjecture is true, then the rate region achievable using a coherent-state encoding with optimal joint-detection measurement at the receivers would be the ultimate capacity region of the bosonic broadcast channel with loss and additive thermal noise. We show that the minimum output entropy conjectures restated for Wehrl entropy, are immediate consequences of the entropy power inequality (EPI).

(cont.) We then show that an EPI-like inequality for von Neumann entropy would imply all the minimum output entropy conjectures needed for our channel capacity results. We call this new conjectured result the Entropy Photon-Number Inequality (EPnI).