The Alicki-Fannes-Winter technique in the quasi-classical settings: advanced version and its applications

TL;DR

This paper introduces an advanced version of the Alicki-Fannes-Winter (AFW) technique for quantum systems, providing improved bounds and applications to key quantum information measures.

Contribution

It develops a more powerful AFW-technique applicable to a broader range of quantum characteristics, enhancing analysis tools in quantum information theory.

Findings

Derived lower semicontinuity bounds for quantum entropies.

Established continuity bounds for quantum relative entropy.

Applied the technique to quantify entanglement and energy functionals.

Abstract

We describe an advanced version of the AFW-technique proposed in [Lett. Math. Phys., 113, 121 (2023)],[Lobachevskii J. Math., 44(6), 2169 (2023)] which allows us to obtain lower semicontinuity bounds, continuity bounds and local lower bounds for characteristics of quantum systems and discrete random variables. We consider applications of the new version of the AFW-technique to several basic characteristics of quantum systems (the von Neumann entropy, the energy-type functionals, the quantum relative entropy, the conditional entropy and the entanglement of formation).