On approximation of infinite-dimensional quantum channels

We develop an approximation approach to infinite-dimensional quantum channels based on a detailed investigation of continuity properties of entropic characteristics of quantum channels and operations (trace-nonincreasing completely positive maps) as functions of a pair channel, input state. Obtained results are then applied to the problems of continuity of the chi-capacity as a function of a channel, strong additivity of the chi-capacity for infinite-dimensional channels, and approximating representation for the convex closure of the output entropy of an arbitrary quantum channel.