  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.
