  The tight, in a sense, lower estimates of diamond-norm distance from a given
quantum channel to the sets of degradable, antidegradable and
entanglement-breaking channels are obtained via the tight continuity bounds for
quantum mutual information and for relative entropy of entanglement in
finite-dimensional case. As an auxiliary result there are established lower
bounds of trace-norm distance from a given bipartite state to the set of all
separable states.
