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