Fast convergence of Dynamic Capacities of GNS-Symmetric Quantum Channels

TL;DR

This paper establishes exponential convergence bounds for classical and quantum capacities of GNS-symmetric quantum channels, aiding in understanding their information transmission efficiency over time.

Contribution

It provides explicit exponential convergence bounds for capacities of GNS-symmetric channels, linking them to entropic properties and practical error correction performance.

Findings

Exponential convergence bounds for capacities of GNS-symmetric channels.

Bounds expressed in terms of entropic properties of the channels.

Application to quantifying active versus passive error correction.

Abstract

We consider a quantum system described by a quantum channel $\Phi$ that is applied at every time step and study the time evolution of its information capacities. When $\Phi$ is a GNS-symmetric channel (this includes Pauli channels, for example), we give explicit exponential convergence bounds for the classical and quantum capacities. These bounds are in terms of entropic properties of $\Phi$. We further illustrate how these results help quantify the performance of active versus passive error-correction setups.