A theoretical study identifies the condition that allows a quantum battery to charge faster than any classical scheme could permit. Using a generic class of free-fermionic chargers, the authors show that global operators alone are not enough to achieve scalable superextensive charging: a cumulative hierarchy of many-body operators is required, and the structure of the battery determines the degree of advantage attainable.

The starting point is a relation between charging power and the norm of the commutator between the battery and charger Hamiltonians. From there, the researchers derive an upper bound that captures only the noncommuting terms, isolating the part of the Hamiltonian that genuinely contributes to fast charging. The idea of cumulative locality is that the quantum advantage does not depend on an operator being global, but on how many-body contributions accumulate and reinforce each other.

As a complementary tool, the work revisits the concept of participation number, commonly used to describe delocalized states, and proposes an effective definition that accounts for the relative strength of the contributing terms. This measure correlates with the scaling of charging power, making it possible to predict when a given system will exhibit a quantum advantage.

The results are not limited to quadratic Hamiltonians, so cumulative locality is established as a key resource for quantum charging advantage. The practical consequence is a criterion for designing quantum batteries and chargers: coupling the battery to a global operator is not enough, the appropriate many-body hierarchy must be built. The framework opens the door to comparing concrete device proposals and to studying how the topology of the coupling constrains performance.