  We show that when coherent-state encoding is employed in conjunction with
coherent detection, the Bosonic broadcast channel is equivalent to a classical
degraded Gaussian broadcast channel whose capacity region is dual to that of
the classical Gaussian multiple-access channel. We further show that if a
minimum output-entropy conjecture holds true, then the ultimate classical
information capacity of the Bosonic broadcast channel can be achieved by a
coherent-state encoding. We provide some evidence in support of the conjecture.
