Capacity With Energy Constraint in Coherent State Channel

In this paper, we consider two kinds of energy constraints when the output state is a coherent state. Conventional constraint is a constraint on the total energy per a single communication mode. This paper proposes another energy constraints, which is a constraint on the total energy during a fixed period. The first setting can be easily dealt with by using the conventional capacity formula. This paper analyzes the second setting when the number of communication modes is or is not limited.