  The decay of ortho-positronium into three photons produces a physical
realization of a pure state with three-party entanglement. Its quantum
correlations are analyzed using recent results on quantum information theory,
looking for the final state which has the maximal amount of GHZ-like
correlations. This state allows for a statistical dismissal of local realism
stronger than the one obtained using any entangled state of two spin one-half
particles.
