Bounds on the charging power of quantum batteries in direct charging protocols are often interpreted as charging-side constraints. Although the locality of the charging Hamiltonian is known to restrict attainable power in certain protocols, whether battery locality is itself operationally necessary has remained unresolved. Here we show that it is necessary for spin batteries whose interactions do not pairwise commute. We construct commuting and noncommuting high-locality batteries with identical interaction supports and local energy scale, driven by the same charging. The commuting battery saturates the battery-locality-independent bound, whereas the noncommuting battery exceeds it by a parametrically growing factor, demonstrating that this bound cannot apply generally. The enhanced norm of the commutator is dynamically attained from a suitable joint state supported entirely in the battery ground-energy sector, although this state may be correlated with the auxiliary fermionic degrees of freedom. Our results establish battery locality as an operational resource enabled by noncommuting battery interactions.
Bounds on the charging power of quantum batteries in direct charging protocols are often interpreted as charging-side constraints. Although the locality of the charging Hamiltonian is known to restrict attainable power in certain protocols, whether battery locality is itself operationally necessary has remained unresolved. Here we show that it is necessary for spin batteries whose interactions do not pairwise commute. We construct commuting and noncommuting high-locality batteries with identical interaction supports and local energy scale, driven by the same charging. The commuting battery saturates the battery-locality-independent bound, whereas the noncommuting battery exceeds it by a parametrically growing factor, demonstrating that this bound cannot apply generally. The enhanced norm of the commutator is dynamically attained from a suitable joint state supported entirely in the battery ground-energy sector, although this state may be correlated with the auxiliary fermionic degrees of freedom. Our results establish battery locality as an operational resource enabled by noncommuting battery interactions.
Quantum batteries can outperform their classical counterparts through collective quantum effects, yet the conditions enabling such advantage remain unclear. Using a generic class of free-fermionic chargers we prove that global operators are insufficient for scalable superextensive charging and that a cumulative hierarchy of many-body operators is required, with the structure of the battery determining the degree of advantage. This is obtained by relating the charging power to the norm of the commutator between the battery and charger Hamiltonians and deriving an upper bound only capturing noncommuting terms. Moreover, we revisit the concept of participation number and propose an effective definition that accounts for the relative strength of the contributing terms, correlating it with the charging power scaling. Not limited to quadratic Hamiltonians, our results establish cumulative locality as a key resource for quantum charging advantage.
Quantum batteries have emerged as a platform for investigating whether quantum effects can accelerate energy storage beyond classical limits. Although a variety of charging schemes have reported signatures of quantum advantage, the fundamental physical requirements for achieving superextensive charging power remain insufficiently understood. Here, we show that, in addition to Hamiltonian locality, a key structural property, g-extensiveness, quantifying the distribution of interaction energy across lattice sites places a fundamental bound on charging performance in spin-lattice models. We prove that superextensive power scaling is possible only when the interaction-energy distribution becomes increasingly nonuniform, with the maximal local weight growing with system size. This criterion explains why many previously studied protocols fail to exhibit superextensive power, even when the Hamiltonians involve large participation numbers. We further demonstrate that this condition is realized in an experimentally relevant interacting model, where, despite fixed interaction order, the charging power scales superextensively. Our results establish g-extensiveness as a necessary resource for quantum advantage in direct-charging protocols and provide a systematic framework for identifying and engineering physically feasible quantum batteries capable of outperforming classical counterparts in charging power.
We establish a general implementation-independent approach to assess the potential advantage of using highly entangled quantum states between the initial and final states of the charging protocol to enhance the maximum charging power of quantum batteries. It is shown that the impact of entanglement on power can be separated from both the global quantum speed limit associated with an optimal choice of driving Hamiltonian and the energy gap of the batteries. We then demonstrate that the quantum state advantage of battery charging, defined as the power obtainable for given quantum speed limit and battery energy gap, is not an entanglement monotone. A striking example we provide is that, counterintuitively, independent thermalization of the local batteries, completely destroying any entanglement, can lead to larger charging power than that of the initial maximally entangled state. Highly entangled states can thus also be potentially disadvantageous when compared to product states. We also demonstrate that taking the considerable effort of producing highly entangled states, such as W or k-locally entangled states, is not sufficient to obtain quantum-enhanced scaling behavior with the number of battery cells. Finally, we perform an explicit computation for a Sachdev–Ye–Kitaev battery charger to demonstrate that the quantum state advantage allows the instantaneous power to exceed its classical bound.
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.
Hamiltonian k-Locality is the Key Resource for Powerful Quantum Battery Charging
Storing and extracting energy using quantum degrees of freedom is a promising approach to leveraging quantum effects in energy science. Early experimental efforts have already demonstrated its potential to surpass the charging power of existing technologies. In this context, it is crucial to identify the specific quantum effects that can be exploited to design the most efficient quantum batteries and push their performance to the ultimate limit. While entanglement has often been considered a key factor in enhancing charging (or discharging) power, our findings reveal that it is not as critical as previously thought. Instead, three parameters emerge as the most significant in determining the upper bound of instantaneous charging power: the locality of the battery and charger Hamiltonians, and the maximum energy storable in a single unit cell of the battery. To derive this new bound, we have also addressed several open questions previously noted in the literature but lacks an explanation. This bound provides a foundation for designing the most powerful charger-battery systems, where combined optimization of both components offers enhancements that cannot be achieved by manipulating only one of them.
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.