The long-standing conjectures of the optimality of Gaussian inputs and additivity are solved for a broad class of gauge-covariant or contravariant bosonic Gaussian channels (which includes in particular thermal, additive classical noise, and amplifier channels) restricting to the class of states with finite second moments. We show that the vacuum is the input state which minimizes the entropy at the output of such channels. This allows us to show also that the classical capacity of these channels (under the input energy constraint) is additive and is achieved by Gaussian encodings.
|Number of pages||19|
|Journal||Communications in Mathematical Physics|
|Early online date||27 Aug 2014|
|Publication status||Published - 31 Mar 2015|