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Tight Quantum Speed Limit for Ergotropy Charging in the N-Qubit Dicke Battery

Quantum Physics 2026-03-18 v2 Mathematical Physics math.MP

Abstract

We derive and analytically prove a tight quantum speed limit (QSL) for ergotropy charging in the NN-qubit Dicke quantum battery: the first-passage time to normalised ergotropy ϵ\epsilon satisfies τ(ϵ)Nϵ/(2λnˉ)\tau^{*}(\epsilon) \geq \sqrt{N\epsilon}/(2\lambda\sqrt{\bar{n}}), where λ\lambda is the coupling and nˉ\bar{n} is the mean charger photon number. The bound follows from an exact perturbative identity ϵ(t)=Aλ2nˉt2+O((λt)4)\epsilon(t) = A\lambda^2\bar{n}t^2 + \mathcal{O}((\lambda t)^4), where A=4/NA=4/N is the short-time ergotropy coefficient, combined with a global upper bound proved analytically for all NN. The composite parameter ΓN=2λnˉ/N\Gamma_N = 2\lambda\sqrt{\bar{n}/N} is the unique figure of merit for charging speed; all protocols collapse onto ΓNτϵ\Gamma_N \tau^{*} \geq \sqrt{\epsilon}, with the bound saturated to within 1% at small ϵ\epsilon.

Keywords

Cite

@article{arxiv.2603.10415,
  title  = {Tight Quantum Speed Limit for Ergotropy Charging in the N-Qubit Dicke Battery},
  author = {Anass Jad and Abderrahim El Allati},
  journal= {arXiv preprint arXiv:2603.10415},
  year   = {2026}
}