Regularized maximum pure-state input-output fidelity of a quantum channel

TL;DR

This paper studies the maximum pure-state input-output fidelity of quantum channels, establishing bounds and exact values for specific channels, which advances understanding of quantum channel capacities.

Contribution

It introduces regularizations of the fidelity measure and proves their relation to the maximum output norm, including exact results for Pauli channels.

Findings

Asymptotic regularization is lower bounded by maximum output norm.

For Pauli channels, the regularized fidelity equals the maximum output norm.

Provides insights into quantum channel capacity measures.

Abstract

As a toy model for the capacity problem in quantum information theory we investigate finite and asymptotic regularizations of the maximum pure-state input-output fidelity $F(\cal N$) of a general quantum channel $\cal N$. We show that the asymptotic regularization $\tilde F(\cal N$) is lower bounded by the maximum output $\infty$-norm $\nu_\infty(\cal N)$ of the channel. For $\cal N$ being a Pauli channel we find that both quantities are equal.