Battery Locality Is Necessary in Noncommuting Quantum Charging Bounds

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.