Quantum Doeblin coefficients: A simple upper bound on contraction coefficients

TL;DR

This paper introduces quantum Doeblin coefficients, providing an efficient way to upper bound contraction coefficients in quantum information processing, with applications to PPT channels and general channels.

Contribution

It presents a quantum generalization of Doeblin coefficients that are efficiently computable and offers new bounds and properties for quantum channels.

Findings

Quantum Doeblin coefficients are efficiently computable upper bounds.

New bounds for PPT channels and general channels are established.

Reverse Doeblin coefficients bound expansion coefficients.

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.