Finding a state among a complete set of orthogonal states

We consider the problem to single out a particular state among 2ⁿ orthogonal pure states. As it turns out, in general the optimal strategy is not to measure the particles separately, but to consider joint properties of the n-particle system. The required number of propositions is n. There exist 2ⁿ! equivalent operational procedures to do so. We enumerate some configurations for three particles, in particular the Greenberger-Horne-Zeilinger (GHZ) and W states, which are specific cases of a unitary transformation. For the GHZ case, an explicit physical meaning of the projection operators is discussed.