Fast convergence of Dynamic Capacities of GNS-Symmetric Quantum Channels

Preprint, 2026

We consider a quantum system described by a quantum channel Φ that is applied at every time step and study the time evolution of its information capacities. When Φ 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 Φ. We further illustrate how these results help quantify the performance of active versus passive error-correction setups.