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arXiv:2501.12000

Hamiltonian $k$-Locality is the Key Resource for Powerful Quantum Battery Charging

Anupam Sarkar, Sibasish Ghosh A

Published Jan 21, 2025• 0 citations
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.2501.12000

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Hamiltonian kkk-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.
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.
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.
Quantum batteries provide a platform for investigating energy storage and extraction in quantum many-body systems. Here, we study a charging protocol in which battery and chargoid roles are assigned to different Hamiltonian components of a standalone many-body spin system. By externally controlling the contribution of the intrinsic battery Hamiltonian during charging, we reveal a tunable competition between intrinsic and charging dynamics. We find that suppressing the intrinsic battery contribution can substantially enhance both the maximum stored energy and charging power, with the magnitude of the enhancement determined by the interaction structure and range. We further investigate the protocol in a Markovian open-system setting that incorporates energy relaxation and pure dephasing. While environmental effects generally degrade charging performance, they can instead enhance energy-storage and energy-extraction dynamics in certain interacting systems. The enhancement associated with the controlled suppression of the intrinsic battery dynamics remains robust in the presence of environmental coupling.
We consider a central-spin battery where Nb{N}_{b}Nb​ central spins serve as battery cells and Nc{N}_{c}Nc​ 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 Nc\sqrt{{N}_{c}}Nc​​-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.
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.