On discontinuity of information characteristics of quantum systems and channels

Abstract

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.