Sufficient conditions for three-particle entanglement and their tests in recent experiments

We point out a loophole problem in some recent experimental claims to produce three-particle entanglement. The problem consists in the question whether mixtures of two-particle entangled states might suffice to explain the experimental data. In an attempt to close this loophole, we review two sufficient conditions that distinguish between N-particle states in which all N particles are entangled to each other and states in which only M particles are entangled (with $M<N).\mathrm{}$ It is shown that three recent experiments to obtain three-particle entangled states [Bouwmeester et al., Phys. Rev. Lett. 82, 1345 (1999); Pan et al., Nature 403, 515 (2000); and Rauschenbeutel et al., Science 288, 2024, (2000)] do not meet these conditions. We conclude that the question whether these experiments provide confirmation of three-particle entanglement remains unresolved. We also propose modifications of the experiments that would make such confirmation feasible.