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

Banff International Research Station for Mathematical Innovation and Discovery

How fast do infinite-dimensional quantum systems evolve Do entropies of infinite-dimensional quantum systems satisfy continuity bounds If so, what are the corresponding convergence rates These are the questions that will addressed in this talk. 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. Our results have interesting applications including quantum speed limits, attenuator and amplifier channels, the quantum Boltzmann equation, and quantum Brownian motion. We also 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 Weylâ s law. This is joint work with Simon Becker.

Mathematics; Quantum theory; Operator theory; Mathematical physics

video/mp4

Author affiliation: Cambridge University

2020-01-21

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/73354

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/