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

Understand

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.