Quantum Speed Limit is Not Quantum

Abstract

The quantum speed limit (QSL), or the energy-time uncertainty relation, describes the fundamental maximum rate for quantum time evolution and has been regarded as being unique in quantum mechanics. In this study, we obtain a classical speed limit corresponding to the QSL using the Hilbert space for the classical Liouville equation. Thus, classical mechanics has a fundamental speed limit, and QSL is not a purely quantum phenomenon but a universal dynamical property of the Hilbert space. Furthermore, we obtain similar speed limits for the imaginary-time Schroedinger equations such as the master equation.

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Cited by in corpus (107)

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• Unified Approach to Classical Speed Limit and Thermodynamic Uncertainty Relation
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• Topological Speed Limit
• Quantum Speed Limits under Continuous Quantum Measurements
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• Decays of unstable quantum systems
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• Unified entropies and quantum speed limits for nonunitary dynamics
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• Entropy non-conservation and boundary conditions for Hamiltonian dynamical systems
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