# Advanced Alicki-Fannes-Winter method for energy-constrained quantum systems and its use

## TL;DR

This paper introduces a universal method for analyzing the continuity of entropic properties in energy-constrained quantum systems and channels, providing tight bounds and improving capacity approximation theorems.

## Contribution

It presents an advanced version of the Alicki-Fannes-Winter method for better continuity bounds in energy-constrained quantum information theory.

## Key findings

- Provides asymptotically tight continuity bounds for quantum characteristics.
- Extends the uniform finite-dimensional approximation theorem.
- Applicable to multi-mode quantum oscillators and channels.

## Abstract

We describe an universal method for quantitative continuity analysis of entropic characteristics of energy-constrained quantum systems and channels. It gives asymptotically tight continuity bounds for basic characteristics of quantum systems of wide class (including multi-mode quantum oscillators) and channels between such systems under the energy constraint. The main application of the proposed method is the advanced version of the uniform finite-dimensional approximation theorem for basic capacities of energy-constrained quantum channels.