Convergence Rates for Quantum Evolution and Entropic Continuity Bounds in Infinite Dimensions
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Peer-reviewed
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Authors
Becker, Simon
Datta, Nilanjana
Abstract
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.
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Article
Journal Title
Communications in Mathematical Physics
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Journal ISSN
0010-3616
1432-0916
1432-0916
Volume Title
374
Publisher
Springer Berlin Heidelberg
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Sponsorship
Engineering and Physical Sciences Research Council (GB) (EP/L016516/1)