Collective quantum batteries (QBs) demonstrate remarkable acceleration in charging dynamics compared to their individual counterparts, underscoring the pivotal contribution of quantum correlations to advanced energy storage paradigms. A fundamental challenge lies in identifying QBs that exhibit genuine quantum advantages derived from multipartite entanglement. In this Letter, based on numerical and analytical evidence, we conjecture a universal bound on the charging rate for fully charging schemes, which is determined by the maximum entanglement depth arising during the charging dynamics. Here, the charging rate quantifies the intrinsic evolution speed of the charging process, appropriately normalized against the quantum speed limit (QSL). We analytically validate this conjecture in three distinct scenarios: (i) fully charging schemes saturating the QSL, (ii) fully parallel charging schemes, and (iii) the SU(2) fully charging schemes. Moreover, we establish a novel lower bound for entanglement depth detection, facilitating numerical verification of our proposed conjecture. By defining the genuine quantum charging advantage as the ratio between entanglement-enhanced charging rates and the maximum achievable non-entangling charging rate, we demonstrate that the charging rate constitutes a robust indicator of genuine quantum advantages.
Collective quantum batteries (QBs) demonstrate remarkable acceleration in charging dynamics compared to their individual counterparts, underscoring the pivotal contribution of quantum correlations to advanced energy storage paradigms. A fundamental challenge lies in identifying QBs that exhibit genuine quantum advantages derived from multipartite entanglement. In this Letter, based on numerical and analytical evidence, we conjecture a universal bound on the charging rate for fully charging schemes, which is determined by the maximum entanglement depth arising during the charging dynamics. Here, the charging rate quantifies the intrinsic evolution speed of the charging process, appropriately normalized against the quantum speed limit (QSL). We analytically validate this conjecture in three distinct scenarios: (i) fully charging schemes saturating the QSL, (ii) fully parallel charging schemes, and (iii) the SU(2) fully charging schemes. Moreover, we establish a novel lower bound for entanglement depth detection, facilitating numerical verification of our proposed conjecture. By defining the genuine quantum charging advantage as the ratio between entanglement-enhanced charging rates and the maximum achievable non-entangling charging rate, we demonstrate that the charging rate constitutes a robust indicator of genuine quantum advantages.
Can collective quantum effects make a difference in a meaningful thermodynamic operation? Focusing on energy storage and batteries, we demonstrate that quantum mechanics can lead to an enhancement in the amount of work deposited per unit time, i.e., the charging power, when N batteries are charged collectively. We first derive analytic upper bounds for the collective quantum advantage in charging power for two choices of constraints on the charging Hamiltonian. We then demonstrate that even in the absence of quantum entanglement this advantage can be extensive. For our main result, we provide an upper bound to the achievable quantum advantage when the interaction order is restricted; i.e., at most k batteries are interacting. This constitutes a fundamental limit on the advantage offered by quantum technologies over their classical counterparts.
Complete quantum charging provides a sharp setting in which to ask how much multipartite entanglement is forced by speed itself. For a closed N-qubit battery evolving from ∣↓⟩⊗N to ∣↑⟩⊗N under a time-independent Hamiltonian, we exactly solve the pure-state depth-constrained speed problem. If the realized trajectory has entanglement depth at most k, then the largest possible QSL-normalized rate η=τQSL/T is ηmax(k)=⌈N/k⌉−1/2. Conversely, an observed rate η certifies trajectory entanglement depth at least ⌈N/⌊η−2⌋⌉. The mechanism is block orthogonalization: under a fixed product partition, complete charging forces all blocks to orthogonalize simultaneously, and the quantum speed limit converts this counting constraint into the speed bound. Balanced cluster-flip evolutions saturate the bound, establishing an exact integer staircase frontier. Thus fast complete charging cannot be explained by many small independently charging blocks; in particular, crossing the threshold η>1/2 certifies, for N>1, the generation of genuine N-partite entanglement.
We investigate charging dynamics in many-body quantum batteries by examining the relationship between instantaneous charging power and the emergence of bipartite, tripartite, and multipartite quantum correlations across different battery--charger configurations. We find that the charging power reaches its maximum before the correlation measures peak, revealing a temporal separation between rapid energy transfer and the buildup of quantum correlations. We further study the role of interaction structure using local and many-body charging Hamiltonians for both unconstrained and constrained charging protocols, in which the total available charging resources are fixed to scale proportionally with the number of spins, thereby isolating the influence of interaction geometry and particle participation on the charging dynamics. In the unconstrained case, the enhanced charging energy observed for higher-order interactions originates primarily from the larger energy scale of the corresponding charging Hamiltonian. Under constrained conditions, however, increasing the interaction order alone provides no advantage over parallel charging when interaction and local spin-flip contributions are balanced, whereas interaction-dominated protocols significantly enhance charging performance, highlighting the importance of collective many-body dynamics. Fully collective interactions yield the largest enhancement in charging power together with stronger multipartite correlations, while partially collective interactions provide only limited improvements. Finally, extending the interaction range through next-nearest-neighbor couplings suppresses the charging power, demonstrating that, under constrained energetic resources, charging performance is governed primarily by interaction structure, particle participation, and collective many-body dynamics rather than by interaction order alone.
Quantum batteries (QBs) exploit principles of quantum mechanics to accelerate the charging process and aim to achieve optimal energy storage. However, analytical results for investigating these problems remain lacking due to the challenges associated with nonequilibrium dynamics. In this work we analytically investigate a central-spin QB model in which Nb spin-21 battery cells interact with Nc spin-21 charger units, using m initially excited charger units as a resource. By employing the invariant subspace method and the shifted Holstein-Primakoff transformation, we identify four scenarios in which optimal energy storage can be achieved: (i) ${N}_{b}\ensuremath{\ll}m\ensuremath{\ll}{N}_{c}$, (ii) $m\ensuremath{\ll}{N}_{b}\ensuremath{\ll}{N}_{c}$, (iii) $m\ensuremath{\ll}{N}_{c}\ensuremath{\ll}{N}_{b}$, and (iv) ${N}_{b}\ensuremath{\ll}m=k{N}_{c} [k\ensuremath{\in}(0,1)]$. In these cases, optimal storage is ensured by the SU(2) symmetry emerging from the charging dynamics. The first three cases map the central-spin QB to different Tavis-Cummings (TC) QBs, while the fourth corresponds to the non-TC limit. We analytically determine the charging time and demonstrate that in the fully charging cases (i) and (iv), the collective charging exhibits an Nb-fold enhancement in speedup compared to the parallel charging scheme. Additionally, we numerically observe a unified charging behavior when m=Nc, showing that asymptotically optimal energy storage is possible when Nb=m=Nc. In this case, we find a collective charging enhancement scaling as Nb0.8264. The origin of the collective charging advantage in central-spin quantum batteries is also analyzed through the quantum speed limit and a multipartite entanglement witness. Our results highlight the crucial role of dynamically emergent SU(2) symmetry in providing an analytical understanding of nonequilibrium charging dynamics in QBs.
A quantum battery is expected to outperform its classical counterpart due to quantum effects. Usually, in a quantum battery made of N cells, quantum advantage is demonstrated through super-extensive scaling of the upper bound to the charging power with N. In this work, we show that potential quantum advantage as measured by the power bounds need not translate to tangible advantage in practice. We demonstrate this by considering an all-to-all coupled spin-chain model of a quantum battery with 2-local interactions. It exhibits super-extensive charging when analyzed using the upper bound derived from the uncertainty principle. Unlike the previously studied models, the contribution to this apparent quantum advantage is twofold—arising from both the battery and the charger. The model is also experimentally friendly, as it does not require global couplings and yet generates genuine multipartite entanglement. However, we demonstrate that the potential quantum advantage in this scenario is not tangible by employing a tighter upper bound on power. Additionally, we show that even this tighter bound can fail in a range of physical situations and indicate a quantum enhancement that is intangible in practice. Hence, we argue that actual power transferred must be evaluated along with proper characterization of the resources before claiming quantum advantage.
We demonstrate the possibility of a genuine quantum advantage in the efficiency of quantum batteries by analyzing a model that enables a consistent comparison between quantum and classical regimes. Our system consists of N harmonic oscillator cells coupled to a common thermal reservoir, evolving through Gaussian states. We define the global efficiency as the ratio of extractable work (ergotropy) to stored energy, and derive analytical bounds that distinguish, in order of increasing efficiency, regimes characterized by classical squeezing, quantum squeezing without entanglement, and genuine entanglement. Moreover, numerical simulations support the emergence of a similar hierarchy for the thermodynamic efficiency, defined as the ratio between ergotropy and the total thermodynamic cost of the charging process.