On the capacity of bosonic channels

Abstract

The capacity of the bosonic channel with additive Gaussian noise is unknown, but there is a known lower bound that is conjectured to be the capacity. We have quantified the gap that exists between this known achievable rate and rates achievable by the known methods of detection including direct, heterodyne, and homodyne detection. We have also quantified these capacities in the case of multiple independent spatial modes in terms of spectral and photon efficiency. Furthermore, we have considered the ergodic and outage capacities of fading channel models for far-field and near-field propagation through atmospheric turbulence. For the far field, good models for the transmissivity statistics are known. For the near field we establish bounds on these capacities, and we show that these bounds are reasonably tight. Finally, we extend the results for ergodic capacity to the case of multiple spatial modes where a turbulent atmosphere results in crosstalk between different spatial modes.