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Estimation of unknown qubit elementary gates and alignment of referenceframes are formally the same problem. Using quantum states made out of $N$qubits, we show that the theoretical precision limit for both problems, whichbehaves as $1/N^{2}$, can be asymptotically attained with a covariant protocolthat exploits the quantum correlation of internal degrees of freedom instead ofthe more fragile entanglement between distant parties. This cuts by half thenumber of qubits needed to achieve the precision of the dense covariant codingprotocol

Quantum reverse engineering and reference-frame alignment without nonlocal correlations