  A long-standing problem on the classical capacity of bosonic Gaussian
channels has recently been resolved by proving the minimum output entropy
conjecture. It is also known that the ultimate capacity quantified by the
Holevo bound can be achieved asymptotically by using an infinite number of
channels. However, it is less understood to what extent the communication
capacity can be reached if one uses a finite number of channels, which is a
topic of practical importance. In this paper, we study the capacity of Gaussian
communication, i.e., employing Gaussian states and Gaussian measurements to
encode and decode information under a single-channel use. We prove that the
optimal capacity of single-channel Gaussian communication is achieved by one of
two well-known protocols, i.e., coherent-state communication or squeezed-state
communication, depending on the energy (number of photons) as well as the
characteristics of the channel. Our result suggests that the coherent-state
scheme known to achieve the ultimate information-theoretic capacity is not a
practically optimal scheme for the case of using a finite number of channels.
We find that overall the squeezed-state communication is optimal in a
small-photon-number regime whereas the coherent-state communication performs
better in a large-photon-number regime.
