On discontinuity of information characteristics of quantum systems and channels

TL;DR

This paper investigates the discontinuities in fundamental information measures of quantum states and channels, providing bounds on entropy loss and analyzing how these discontinuities affect quantum correlations and channel characteristics.

Contribution

It introduces quantitative bounds on the discontinuity jumps of quantum information measures and analyzes their behavior under state and channel variations.

Findings

Discontinuity jump of von Neumann entropy is bounded by mean energy loss.

Correlation and entanglement measure discontinuities are bounded by marginal entropy loss.

Output entropy discontinuity of quantum channels is characterized under input and channel variations.

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.