2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/210770We 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 $χ$-capacity as function of a channel; strong additivity of the $χ$-capacity for infinite dimensional channels; the analytical expression for the convex closure of the output entropy of arbitrary quantum channel.26 pagesQuantum Physicstext