Optimal quantum learning of a unitary transformation

ArXiv identifier: 
Giulio Chiribella
A. Bisio, G. Chiribella, G. M. D'Ariano, S. Facchini, P. Perinotti

We prove that the optimal strategy to store an unknown group transformation into a quantum memory is to apply the available uses in parallel on a suitable entangled state. The optimal retrieving strategy is the incoherent, ``measure-and-rotate'' strategy, in which the quantum memory is measured and a unitary depending on the outcome is performed. The same result holds for approximate re-alignment of reference frames for quantum communication.