Quantum Doeblin coefficients

A simple upper bound on contraction coefficients

verfasst von

Christoph Hirche

Abstract

Contraction coefficients give a quantitative strengthening of the data processing inequality. As such, they have many natural applications whenever closer analysis of information processing is required. However, it is often challenging to calculate these coefficients. As a remedy we discuss a quantum generalization of Doeblin coefficients. These give an efficiently computable upper bound on many contraction coefficients. We prove several properties and discuss generalizations and applications. In particular, we give additional stronger bounds. One especially for PPT channels and one for general channels based on a constraint relaxation. Additionally, we introduce reverse Doeblin coefficients that bound certain expansion coefficients.

Organisationseinheit(en)

Institut für Informationsverarbeitung

Typ

Aufsatz in Konferenzband

Seiten

557-562

Anzahl der Seiten

6

Publikationsdatum

07.07.2024

Publikationsstatus

Veröffentlicht

Peer-reviewed

Ja

ASJC Scopus Sachgebiete

Theoretische Informatik, Information systems, Modellierung und Simulation, Angewandte Mathematik

Elektronische Version(en)

https://doi.org/10.48550/arXiv.2405.00105 (Zugang: Offen)
https://doi.org/10.1109/ISIT57864.2024.10619667 (Zugang: Geschlossen)