Quantum reverse engineering and reference-frame alignment without nonlocal correlations

The estimation of unknown qubit elementary gates and alignment of reference frames without nonlocal correlations, were discussed. The theoretical precision limit, which behaves as 1/N2, can be approximately attained with a covariant protocol was obtained by using quantum states made out of N qubits. It was observed that the internal 'α' degrees of freedom associated to repeated irreducible representations in the Clebsch-Gordan series do not transform under the SU(2) group of rotations. Such degrees of freedom can be entangled to proper SU(2) degrees of freedom to provide an outstanding improvement over some known estimation and communication protocols.