Generalised quantum speed limit for arbitrary time-continuous evolution

Abstract

The quantum speed limit describes how quickly a quantum system can evolve in time from an initial state to a final state under a given dynamics. Here, we derive a generalised quantum speed limit (GQSL) for arbitrary time-continuous evolution using the geometrical approach of quantum mechanics. The GQSL is applicable for quantum systems undergoing unitary, non-unitary, completely positive, non-completely positive and relativistic quantum dynamics. This reduces to the well known standard quantum speed limit (QSL), i.e., the Mandelstam-Tamm bound when the quantum system undergoes unitary time evolution. Using our formalism, we then obtain a quantum speed limit for non-Hermitian quantum systems. To illustrate our findings, we have estimated the quantum speed limit for a time-independent non-Hermitian system as well as for a time-dependent non-Hermitian system namely the Bethe-Lamb Hamiltonian for general two-level system.

10 pages, 4 figures, close to published version

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• Speed limits and thermodynamic uncertainty relations for quantum systems governed by non-Hermitian Hamiltonian
• Energetic cost for speedy synchronization in non-Hermitian quantum dynamics
• Quantum Speed Limits Based on Schatten Norms: Universality and Tightness
• A geometrical description of non-Hermitian dynamics: speed limits in finite rank density operators
• Family of Exact and Inexact Quantum Speed Limits for Completely Positive and Trace-Preserving Dynamics
• Three perspectives on entropy dynamics in a non-Hermitian two-state system
• Generalized Entropic Quantum Speed Limits
• Probing the quantum speed limit and entanglement in flavor oscillations of neutrino-antineutrino system in curved spacetime
• Propagation-Distance Limit for a Classical Nonlocal Optical System
• Influence of gravity on the quantum speed limit in neutrino oscillations
• A unified fidelity-based framework for quantum speed limits in open quantum systems