Abstract
We prove that for any infinite-dimensional quantum channel the entropic disturbance (defined as difference between the χ-quantity of a generalized ensemble and that of the image of the ensemble under the channel) is lower semicontinuous on the natural set of its definition. We establish a number of useful corollaries of this property, in particular, we prove the continuity of the output χ-quantity and the existence of χ-optimal ensemble for any quantum channel under the energy-type input constraint.