A Holevo-type bound for a Hilbert Schmidt distance measure

TL;DR

This paper introduces a new Holevo-type bound using the Hilbert-Schmidt norm, providing an intuitive and natural upper limit on classical information transmission over quantum channels.

Contribution

It presents a novel version of the Holevo bound employing the Hilbert-Schmidt norm instead of the traditional divergence measure.

Findings

Establishes a bound on classical mutual information using the Hilbert-Schmidt norm.

Provides a more natural and intuitive relation between classical and quantum information measures.

Abstract

We prove a new version of the Holevo bound employing the Hilbert-Schmidt norm instead of the Kullback-Leibler divergence. Suppose Alice is sending classical information to Bob using a quantum channel, while Bob is performing some projective measurement. We bound the classical mutual information in terms of the Hilbert-Schmidt norm by its quantum Hilbert-Schmidt counterpart. This constitutes a Holevo-type upper bound on the classical information transmission rate via a quantum channel. The resulting inequality is rather natural and intuitive relating classical and quantum expressions using the same measure.