Convergence Rates for Quantum Evolution and Entropic Continuity Bounds in Infinite Dimensions


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Type
Article
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Authors
Becker, S 
Datta, N 
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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Keywords
quant-ph, quant-ph, math-ph, math.MP
Journal Title
Communications in Mathematical Physics
Conference Name
Journal ISSN
0010-3616
1432-0916
Volume Title
374
Publisher
Springer Science and Business Media LLC
Sponsorship
Engineering and Physical Sciences Research Council (EP/L016516/1)