Quantum Speed Limits For Open System Dynamics Based On A Representation-Basis-Dependent $\boldsymbol{\ell^{p}_{w}}$-Seminorm

TL;DR

This paper introduces a family of quantum speed limits based on a basis-dependent norm, applicable to various quantum systems, providing tighter bounds and greater universality than existing limits.

Contribution

The authors develop a new class of quantum speed limits using a representation basis-dependent $oldsymbol{ ext{ell}^{p}_{w}}$-seminorm, applicable to diverse quantum dynamics and operators.

Findings

The new QSLs outperform existing bounds in multiple quantum evolution scenarios.

They are valid for arbitrary operators under mild conditions.

The approach offers improved sharpness and universality with computational efficiency.

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 $\ell^{p}_{w}$-seminorm. These QSLs are applicable to open, closed, time-dependent, or time-independent systems in finite-dimensional Hilbert spaces whose density matrices are piecewise time differentiable. They can be extended to systems over separable Hilbert spaces as well. Crucially, these QSLs are valid for arbitrary operators, not just density matrices, provided that a modest technical condition is fulfilled. When compared to the existing QSLs applied to pure state time-independent Hamiltonian evolution, qubit spontaneous emission, high-fidelity gate implementation, coherent state photon loss and operator coherence or dephasing, ours consistently show improved sharpness in most cases, along with greater universality and still retaining computational efficiency.