  Quantum measurements are key to quantum metrology. Constrained by
experimental capabilities, collective measurements on a large number of copies
of metrological probes can pose significant challenges. Therefore, the locality
in quantum measurements must be considered. In this work, we propose a method
dubbed as the "iterative matrix partition" approach to elucidate the underlying
structures of optimal local measurements, with and without classical
communications, that saturate the quantum Cram\'er-Rao Bound (qCRB).
Furthermore, we find that while exact saturation is possible for all two-qubit
pure states, it is generically restrictive for multi-qubit pure states.
However, we demonstrate that the qCRB can be universally saturated in an
approximate manner through adaptive coherent controls, as long as the initial
state is separable and the Hamiltonian allows for interaction. Our results
bridge the gap between theoretical proposals and experiments in many-body
metrology and can find immediate applications in noisy intermediate-scale
quantum devices.
