Quantum Speed Limits For Open System Dynamics Based On Representation Basis Dependent \boldsymbolℓ^p_w-Seminorm

2025/08/23 by Chau, H. F., Li, Jinjie
#FOS: Physical sciences #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.2508.17053

Abstract

We report a family of quantum speed limits (QSLs) that give evolution time lower bounds between an initial and a final state whose separation is described by a certain representation basis dependent norm derived from the weighted ℓ^p_w-seminorm. These QSLs are applicable to open, closed, time-dependent, or time-independent systems in finite-dimensional Hilbert spaces. They can be extended to infinite-dimensional systems as well. Crucially, these QSLs are valid for arbitrary operators, not just density matrices. When compared to the existing QSLs applied to pure state time-independent Hamiltonian evolution, qubit spontaneous emission, high-fidelity gate implementation, and operator coherence or dephasing, ours consistently show improved sharpness in most cases, along with greater universality and still retaining computational efficiency.

Citations

• Generalized Entropic Quantum Speed Limits
• Quantum Speed limit on the production of quantumness of observables
• Quantum speed limit for Kirkwood-Dirac quasiprobabilities
• Variational Optimization on Lie Groups, with Examples of Leading (Generalized) Eigenvalue Problems
• Geometric Optimization Methods for Adaptive Filtering
• Quantum-Enhanced Measurements: Beating the Standard Quantum Limit
• The maximum speed of dynamical evolution

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