Local lower bounds on characteristics of quantum and classical systems

TL;DR

This paper develops methods to establish local lower bounds on properties of quantum and classical systems within a trace norm neighborhood, focusing on infinite-dimensional systems to better understand their characteristics.

Contribution

It introduces techniques for deriving local lower bounds on system characteristics in infinite-dimensional quantum and classical systems, expanding analysis tools in this domain.

Findings

Established local lower bounds for quantum systems

Extended methods to classical systems in trace norm neighborhoods

Focused on infinite-dimensional system analysis

Abstract

We consider methods for obtaining local lower bounds on characteristics of quantum (correspondingly, classical) systems, i.e. lower bounds valid in the trace norm $\epsilon$-neighborhood of a given state (correspondingly, probability distribution). The main attention is paid to infinite-dimensional systems.