On approximation of quantum channels

We develop an approximation approach to infinite dimensional quantum channels based on detailed investigation of the continuity properties of entropic characteristics of quantum channels and operations (trace-nonincreasing completely positive maps) as functions of a pair ``channel, input state''. The obtained results are then applied to the following problems: continuity of the $\chi$-capacity as function of a channel; strong additivity of the $\chi$-capacity for infinite dimensional channels; the analytical expression for the convex closure of the output entropy of arbitrary quantum channel.