Author:
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.
Funder
Engineering and Physical Sciences Research Council
Publisher
Springer Science and Business Media LLC
Subject
Mathematical Physics,Statistical and Nonlinear Physics
Reference65 articles.
1. Alicki, R.: A search for a border between classical and quantum worlds. Phys. Rev. A 65, 034104 (2002)
2. Alicki, R.: Invitation to quantum dynamical semigroups. In: Garbaczewski, P., Olkiewicz, R. (eds.) Dynamics of Dissipation. Lecture Notes in Physics, vol. 597. Springer, Berlin (2002)
3. Arnold, A., Sparber, C.: Quantum dynamical semigroups for diffusion models with Hartree interaction. Commun. Math. Phys. 2004(251), 179–207 (2004)
4. Bounit, H., Fadili, A.: Favard spaces and admissibility for Volterra systems with scalar kernel. Electron. J. Differ. Equ. 2015(42), 1–21 (2015)
5. Benatti, F., Narnhofer, H.: Entropy behaviour under completely positive maps. Lett. Math. Phys. 15, 325 (1988)
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