Exact Entanglement-Depth Speed Frontier for Complete Quantum Charging

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 ket{downarrow}^{otimes N} to ket{uparrow}^{otimes 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=τ_{rm QSL}/T is η_max(k)=lceil N/krceil^-1/2. Conversely, an observed rate η certifies trajectory entanglement depth at least bigllceil N/lfloor η^-2rfloorbigrrceil. 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/sqrt2 certifies, for N>1, the generation of genuine N-partite entanglement.