Continuity of characteristics of composite 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.

arXiv comment97 pages, any comments and references are still welcome

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Cited by in corpus (7)

• Continuity of quantum entropic quantities via almost convexity
• Continuity bounds on observational entropy and measured relative entropies
• Close-to-optimal continuity bound for the von Neumann entropy and other quasi-classical applications of the Alicki-Fannes-Winter technique
• Correlation measures of a quantum state and information characteristics of a quantum channel
• Entanglement cost for infinite-dimensional physical systems
• Continuity bounds for quantum entropies arising from a fundamental entropic inequality
• Unified framework for continuity of sandwiched Rényi divergences