Continuity of characteristics of composite quantum systems

TL;DR

This paper develops new methods for analyzing the continuity of characteristics in composite quantum systems, extending existing techniques to both finite and infinite-dimensional cases and establishing new continuity bounds and conditions.

Contribution

It introduces a novel approximation method for local continuity conditions and generalizes the Alicki-Fannes-Winter approach for broader applicability.

Findings

Proved several general continuity theorems for quantum system characteristics.

Established uniform continuity bounds for key quantum system properties.

Extended existing methods to infinite-dimensional quantum systems.

Abstract

General methods of quantitative and qualitative continuity analysis of characteristics of composite quantum systems are described. Several modifications of the Alicki-Fannes-Winter method are considered, which make it applicable to a wide class of characteristics in both finite-dimensional and infinite-dimensional cases. A new approximation method for obtaining local continuity conditions for various characteristics of quantum systems is proposed and described in detail. This method allows us to prove several general results (Simon-type dominated convergence theorem, the theorem about preserving continuity under convex mixtures, etc.). Uniform continuity bounds and local continuity conditions for basic characteristics of composite quantum systems are presented. Along with the results obtained earlier by different authors, a number of new results proved by the proposed methods are described.