Continuity bounds for information characteristics of quantum channels depending on input dimension

We show how to use properties of the quantum conditional mutual information to obtain continuity bounds for information characteristics of quantum channels depending on their input dimension. First we prove tight estimates for variation of the output Holevo quantity with respect to simultaneous variations of a channel and of an input ensemble. Then we obtain tight continuity bounds for output conditional mutual information for a single channel and for $n$ copies of a channel. As a result tight and close-to-tight continuity bounds for basic capacities of quantum channels depending on the input dimension are obtained. They complement the Leung-Smith continuity bounds depending on the output dimension.