arXiv:2603.10415

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

Anass Jad, Abderrahim El Allati

quant-phmath-phSubmitted Mar 11, 2026• Announced Mar 12, 2026• 0 citations• Revised Mar 17, 2026 (v2)

Abstract

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

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arXiv:2603.10415

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

Anass Jad, Abderrahim El Allati

quant-phmath-phSubmitted Mar 11, 2026• Announced Mar 12, 2026• 0 citations• Revised Mar 17, 2026 (v2)

arXiv HTML PDF

Abstract

We derive and analytically prove a tight quantum speed limit (QSL) for ergotropy charging in the

N

-qubit Dicke quantum battery: the first-passage time to normalised ergotropy

ε

satisfies

τ^{*}(ε) \geq \sqrt{Nε}/(2λ\sqrt{\bar{n}})

, where

λ

is the coupling and

\bar{n}

is the mean charger photon number. The bound follows from an exact perturbative identity

ε(t) = Aλ^2\bar{n}t^2 + \mathcal{O}((λt)^4)

, where

A=4/N

is the short-time ergotropy coefficient, combined with a global upper bound proved analytically for all

N

. The composite parameter

Γ_N = 2λ\sqrt{\bar{n}/N}

is the unique figure of merit for charging speed; all protocols collapse onto

Γ_N τ^{*} \geq \sqrtε

, with the bound saturated to within 1% at small

ε

Related papers

Asymptotic freedom in the dephased charging of quantum batteries

Chayan Purkait, B. Prasanna Venkatesh, Gentaro Watanabe A

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Po-Rong Lai, Jhen-Dong Lin, Yi-Te Huang +2 more

We propose charging protocols for quantum batteries based on quantum superpositions of trajectories. Specifically, we consider that a qubit (the battery) interacts with multiple cavities or a single cavity at various positions, where the cavities act as chargers. Further, we introduce a quantum control prepared in a quantum superposition state, allowing the battery to be simultaneously charged by multiple cavities (the multiple-charger protocol) or a single cavity with different entry positions (the single-charger protocol). To assess the battery's performance, we evaluate the maximum extractable work, referred to as ergotropy. The primary discovery lies in the quick charging effect, wherein we prove that the increase in ergotropy stems from the quantum coherence initially present in the quantum control. Moreover, the induced “Dicke-type interference effect” in the single-charger protocol can further lead to a “perfect charging phenomenon”, enabling a complete conversion of the stored energy into extractable work across the entire charging process, with just two entry positions in superposition. Furthermore, we propose circuit models for these charging protocols and conduct proof-of-principle demonstrations on IBMQ and IonQ quantum processors. The results validate our theoretical predictions, demonstrating a clear enhancement in ergotropy. Published by the American Physical Society 2024We propose charging protocols for quantum batteries based on quantum superpositions of trajectories. Specifically, we consider that a qubit (the battery) interacts with multiple cavities or a single cavity at various positions, where the cavities act as chargers. Further, we introduce a quantum control prepared in a quantum superposition state, allowing the battery to be simultaneously charged by multiple cavities (the multiple-charger protocol) or a single cavity with different entry positions (the single-charger protocol). To assess the battery's performance, we evaluate the maximum extractable work, referred to as ergotropy. The primary discovery lies in the quick charging effect, wherein we prove that the increase in ergotropy stems from the quantum coherence initially present in the quantum control. Moreover, the induced “Dicke-type interference effect” in the single-charger protocol can further lead to a “perfect charging phenomenon”, enabling a complete conversion of the stored energy into extractable work across the entire charging process, with just two entry positions in superposition. Furthermore, we propose circuit models for these charging protocols and conduct proof-of-principle demonstrations on IBMQ and IonQ quantum processors. The results validate our theoretical predictions, demonstrating a clear enhancement in ergotropy. Published by the American Physical Society 2024

arXiv:2307.09010Physical Review ResearchMay 7, 202425 citations

We derive and analytically prove a tight quantum speed limit (QSL) for ergotropy charging in the

N

-qubit Dicke quantum battery: the first-passage time to normalised ergotropy

ε

satisfies

τ^{*}(ε) \geq \sqrt{Nε}/(2λ\sqrt{\bar{n}})

, where

λ

is the coupling and

\bar{n}

is the mean charger photon number. The bound follows from an exact perturbative identity

ε(t) = Aλ^2\bar{n}t^2 + \mathcal{O}((λt)^4)

, where

A=4/N

is the short-time ergotropy coefficient, combined with a global upper bound proved analytically for all

N

. The composite parameter

Γ_N = 2λ\sqrt{\bar{n}/N}

is the unique figure of merit for charging speed; all protocols collapse onto

Γ_N τ^{*} \geq \sqrtε

, with the bound saturated to within 1% at small

ε

N

is small (

N=10

), far below the thermodynamic limit, and the charging power follows a behavior consistent with that of the stored energy.

We explore coherent ergotropy extraction in quantum batteries from a resource-geometric point of view. For an initial state

ρ

, we quantify the coherent extraction process by the coherent ergotropy

\mathcal{E}_c(ρ)

and the coherent extraction distance

D_c^{\rm ext}(ρ)

between the active state

σ_ρ

and the passive state

P_ρ

. This defines the geometric power capacity

Π_c(ρ)=\mathcal{E}_c(ρ)/D_c^{\rm ext}(ρ)

, which measures the coherent ergotropy released unit minimal unitary distance. We prove that, for any driving Hamiltonian satisfying

\|V_t\|\leqν

, the actual coherent discharging power is bounded by

P_c^{\rm ext}(ρ;V_t)\leq νΠ_c(ρ)

, showing that

Π_c(ρ)

is a capacity under unit driving norm rather than the power of a particular protocol. General bounds on

Π_c(ρ)

are derived by combining relative entropy bounds on coherent ergotropy with geometric bounds on the coherent extraction distance. We also formulate coherence measure induced bounds and protocol-corrected capacities involving the effective speed of a given Hamiltonian. Qubit and qutrit examples demonstrate that

Π_c(ρ)

captures a resource-geometric feature of coherent discharging beyond coherent ergotropy or coherence measures alone.

We consider a central-spin battery where

{N}_{b}

central spins serve as battery cells and

{N}_{c}

bath spins serve as charging units. It is shown that the energy stored in the battery that can be extractable is quantified by the ergotropy, and that battery-charger entanglement is quantified via the Von Neumann entropy. By using an exact approach to a one-cell and two-cell battery, our analytical results suggest that, during the charging process, the extractable work slowly increases before the battery-charger entanglement reaches its maximum and then it will rapidly increase when the entanglement begins to decrease. In particular, we rigorously show that there is an inverse relationship between the extractable work and the entanglement at the end of the charging process. Moreover, we investigate different approaches to realize optimal work extraction without wasted energy. Among them a central-spin battery with an unpolarized Dicke state as the charger possesses a universal charging time $\ensuremath{\propto}1/{N}_{c}$, large extractable work and

\sqrt{{N}_{c}}

-improvement of charging power compared with the battery in the Tavis-Cummings limit. The above-mentioned results have also been numerically verified in multicell batteries. Our results pave the way to improve extractable work storage in the central-spin battery and highlight a competitive relation between the extractable work and the battery-charger entanglement.