Lower Bounds on Error Exponents via a New Quantum Decoder

TL;DR

This paper introduces a novel quantum decoding method that establishes new lower bounds on error exponents in classical-quantum channel coding, especially tight for classical channels near capacity.

Contribution

The paper presents a new quantum decoder based on a variant of the pretty good measurement, providing improved lower bounds on error exponents in both one-shot and asymptotic regimes.

Findings

New lower bounds on error exponents for quantum channel coding

Bounds expressed via measured and sandwiched channel Rènyi mutual information

Bounds are tight for classical channels near capacity

Abstract

We introduce a new quantum decoder based on a variant of the pretty good measurement, but defined via an alternative matrix quotient. We use this decoder to show new lower bounds on the error exponent both in the one-shot and asymptotic regimes for the classical-quantum and the entanglement-assisted channel coding problem. Our bounds are expressed in terms of measured (for the one-shot bounds) and sandwiched (for the asymptotic bounds) channel R\'enyi mutual information of order between 1/2 and 1. Our results are not comparable with some previously established bounds for general instances, yet they are tight (for rates close to capacity) when the underlying channel is classical.