Detection efficiency in the loophole-free violation of Svetlichny's inequality

Svetlichny's inequality (SI) is a Bell-like inequality, the violation of which can be used to confirm the existence of genuine multipartite correlations. However, poor detector efficiency can possibly cause a so-called detection loophole in actual Svetlichny experiments. We derive an alternative SI to deal with this loophole. If the experimental data can violate this SI, it must result in loophole-free violation of the original SI. We show that the minimum detection efficiency needed for a loophole-free violation of the tripartite SI is about 0.97. For the general case of n particles, we give the analytic expression of the needed detection efficiency, and find that its value monotonically and rapidly approaches 1 as the number of particles increases. © 2012 American Physical Society.