Distinguishing $n$ Hamiltonians on $C^n$ by a single measurement

If an experimentalist wants to decide which one of n possible Hamiltonians acting on an n-dimensional Hilbert space is present, he can conjugate the time evolution by an appropriate sequence of known unitary transformations in such a way that the different Hamiltonians result in mutual orthogonal final states. We present a general scheme providing an approximation for such a sequence.