Conditions for the confirmation of three-particle non-locality

Abstract

The notion of genuine three-particle non-locality introduced by Svetlichny \cite{Svetlichny} is discussed. Svetlichny's inequality which can distinguish between genuine three-particle non-locality and two-particle non-locality is analyzed by reinterpreting it as a frustrated network of correlations. Its quantum mechanical maximum violation is derived and a situation is presented that produces the maximum violation. It is shown that the measurements performed in recent experiments to demonstrate GHZ entanglement \cite{Bouwmeester}, \cite{Pan} do not allow this inequality to be violated, and hence can not be taken as confirmation of genuine three-particle non-locality. Modifications to the experiments that would make such a confirmation possible are discussed.

minor revisions, references added