  We prove that the threshold detection efficiency for a loophole-free Bell
experiment using an $n$-qubit Greenberger-Horne-Zeilinger state and the
correlations appearing in the $n$-partite Mermin inequality is $n/(2n-2)$. If
the detection efficiency is equal to or lower than this value, there are local
hidden variable models that can simulate all the quantum predictions. If the
detection efficiency is above this value, there is no local hidden variable
model that can simulate all the quantum predictions.
