A three state invariant
  For triples of probability measures, pure quantum states and mixed quantum states we obtain the exact constraints on the fidelities of pairs in the sequence. We show that it is impossible to decide between a quantum model, either pure or mixed, and a classical model on the basis of the fidelities alone. Next, we introduce a quantum three state invariant called phase and show that any sequence of pure quantum states is uniquely reconstructible given the fidelities and phases. 
M. Fannes D. Vanpeteghem