  Previous work on the classical information capacities of bosonic channels has
established the capacity of the single-user pure-loss channel, bounded the
capacity of the single-user thermal-noise channel, and bounded the capacity
region of the multiple-access channel. The latter is a multi-user scenario in
which several transmitters seek to simultaneously and independently communicate
to a single receiver. We study the capacity region of the bosonic broadcast
channel, in which a single transmitter seeks to simultaneously and
independently communicate to two different receivers. It is known that the
tightest available lower bound on the capacity of the single-user thermal-noise
channel is that channel's capacity if, as conjectured, the minimum von Neumann
entropy at the output of a bosonic channel with additive thermal noise occurs
for coherent-state inputs. Evidence in support of this minimum output entropy
conjecture has been accumulated, but a rigorous proof has not been obtained. In
this paper, we propose a new minimum output entropy conjecture that, if proved
to be correct, will establish that the capacity region of the bosonic broadcast
channel equals the inner bound achieved using a coherent-state encoding and
optimum detection. We provide some evidence that supports this new conjecture,
but again a full proof is not available.
