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

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.

51 pages

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Cited by in corpus (18)

• Energy-constrained discrimination of unitaries, quantum speed limits and a Gaussian Solovay-Kitaev theorem
• Strong convergence of quantum channels: continuity of the Stinespring dilation and discontinuity of the unitary dilation
• From Classical to Quantum: Uniform Continuity Bounds on Entropies in Infinite Dimensions
• Advanced Alicki-Fannes-Winter method for energy-constrained quantum systems and its use
• Characterizing the performance of continuous-variable Gaussian quantum gates
• Continuity of characteristics of composite quantum systems
• Continuous-variable quantum state designs: theory and applications
• Attainability and lower semi-continuity of the relative entropy of entanglement, and variations on the theme
• On quantum channels and operations preserving finiteness of the von Neumann entropy
• Extreme points of the set of quantum states with bounded energy
• Uniform continuity bounds for characteristics of multipartite quantum systems
• Close-to-optimal continuity bound for the von Neumann entropy and other quasi-classical applications of the Alicki-Fannes-Winter technique
• Optimal gain sensing of quantum-limited phase-insensitive amplifiers
• Infinite-Dimensional Programmable Quantum Processors
• A two-parameter entropy and its fundamental properties
• Energy-limited quantum dynamics
• Convergence Rates for the Trotter Splitting for Unbounded Operators
• Quantum-optimal information encoding using noisy passive linear optics