  Semiclassical models for multiple-user optical communication cannot assess
the ultimate limits on reliable communication as permitted by the laws of
physics. In all optical communications settings that have been analyzed within
a quantum framework so far, the gaps between the quantum limit to the capacity
and the Shannon limit for structured receivers become most significant in the
low photon-number regime. Here, we present a quantum treatment of a
multiple-transmitter multiple-receiver multi-spatial-mode free-space
interference channel with diffraction-limited loss and a thermal background. We
consider the performance of a laser-light (coherent state) encoding in
conjunction with various detection strategies such as homodyne, heterodyne, and
joint detection. Joint detection outperforms both homodyne and heterodyne
detection whenever the channel exhibits "very strong" interference. We
determine the capacity region for homodyne or heterodyne detection when the
channel has "strong" interference, and we conjecture the existence of a joint
detection strategy that outperforms the former two strategies in this case.
Finally, we determine the Han-Kobayashi achievable rate regions for both
homodyne and heterodyne detection and compare them to a region achievable by a
conjectured joint detection strategy. In these latter cases, we determine
achievable rate regions if the receivers employ a recently discovered
min-entropy quantum simultaneous decoder.
