  Quantitative analysis of discontinuity of basic characteristics of quantum
states and channels is presented.
  First we consider general estimates for discontinuity jump (loss) of the von
Neumann entropy for a given converging sequence of states. It is shown, in
particular, that for any sequence the loss of entropy is upper bounded by the
loss of mean energy (with the coefficient characterizing Hamiltonian of a
system).
  Then we prove that discontinuity jumps of several correlation and
entanglement measures in composite quantum systems are upper bounded by loss of
one of the marginal entropies (with a corresponding coefficient).
  We also analyse discontinuity of the output entropy of a quantum operation
and of basic information charateristics of a quantum channel with respect to
simultaneous variations of an input state and of a channel.
