  Determining the ultimate classical information carrying capacity of
electromagnetic waves requires quantum-mechanical analysis to properly account
for the bosonic nature of these waves. Recent work has established capacity
theorems for bosonic single-user, broadcast, and wiretap channels, under the
presumption of two minimum output entropy conjectures. Despite considerable
accumulated evidence that supports the validity of these conjectures, they have
yet to be proven. Here we show that the preceding minimum output entropy
conjectures are simple consequences of an Entropy Photon-Number Inequality,
which is a conjectured quantum-mechanical analog of the Entropy Power
Inequality (EPI) from classical information theory.
