Convergence rates for quantum evolution & entropic continuity bounds in infinite dimensions

TL;DR

This paper develops stronger continuity bounds for quantum dynamics and entropy in infinite-dimensional systems, with applications to quantum speed limits, channels, and thermodynamics, based on energy constraints and spectral analysis.

Contribution

It introduces extended energy-constrained norms and explicit continuity bounds for quantum evolution and entropy in infinite dimensions, advancing theoretical understanding.

Findings

Stronger continuity bounds for quantum dynamics in infinite dimensions.

Explicit entropy bounds based on Hamiltonian spectra.

Applications to quantum channels and thermodynamic processes.

Abstract

By extending the concept of energy-constrained diamond norms, we obtain continuity bounds on the dynamics of both closed and open quantum systems in infinite-dimensions, which are stronger than previously known bounds. We extensively discuss applications of our theory to quantum speed limits, attenuator and amplifier channels, the quantum Boltzmann equation, and quantum Brownian motion. Next, we obtain explicit log-Lipschitz continuity bounds for entropies of infinite-dimensional quantum systems, and classical capacities of infinite-dimensional quantum channels under energy-constraints. These bounds are determined by the high energy spectrum of the underlying Hamiltonian and can be evaluated using Weyl's law.