Energy-limited quantum dynamics

• URL: http://arxiv.org/abs/2405.10259v1
• Date: Thu, 16 May 2024 17:12:00 GMT
• Title: Energy-limited quantum dynamics
• Authors: Lauritz van Luijk,
• Abstract summary: We systematically study "energy-limited" channels and dynamics. By tracking the output energy, we observe that the energy-constrained operator and diamond norms of Shirokov and Winter satisfy submultiplicativity estimates. This makes for a powerful toolkit for quantitative analyses of dynamical problems in finite and infinite-dimensional systems.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We consider quantum systems with energy constraints. In general, quantum channels and continuous-time dynamics need not satisfy energy conservation. Physically meaningful channels, however, can only introduce a finite amount of energy to the system, and continuous-time dynamics may only increase the energy gradually over time. We systematically study such "energy-limited" channels and dynamics. For Markovian dynamics, energy-limitedness is equivalent to a single operator inequality in the Heisenberg picture. By tracking the output energy, we observe that the energy-constrained operator and diamond norms of Shirokov and Winter satisfy submultiplicativity estimates with respect to energy-limited channels. This makes for a powerful toolkit for quantitative analyses of dynamical problems in finite and infinite-dimensional systems. As an application, we derive state-dependent bounds for quantum speed limits and related problems that outperform the usual operator/diamond norm estimates, which have to account for fluctuations in high-energy states.

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