Quantum Doeblin coefficients

A simple upper bound on contraction coefficients

authored by

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.

Organisation(s)

Institute of Information Processing

Type

Conference contribution

Pages

557-562

No. of pages

6

Publication date

07.07.2024

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Theoretical Computer Science, Information Systems, Modelling and Simulation, Applied Mathematics

Electronic version(s)

https://doi.org/10.48550/arXiv.2405.00105 (Access: Open)
https://doi.org/10.1109/ISIT57864.2024.10619667 (Access: Closed)