Discrimination between evolution operators

Under broad conditions, evolutions due to two different Hamiltonians are shown to lead at some moment to orthogonal states. For two spin-1/2 systems subject to precession by different magnetic fields the achievement of orthogonalization is demonstrated for every scenario but a special one. This discrimination between evolutions is experimentally much simpler than procedures proposed earlier based on either sequential or parallel application of the unknown unitaries. A lower bound for the orthogonalization time is proposed in terms of the properties of the two Hamiltonians.