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We consider Bell experiments with N spatially separated qubits where loss ispresent and restrict to two measurement settings per site. We note theMermin-Ardehali-Belinskii-Klyshko (MABK) Bell inequalities do not present atight bound for the predictions of local hidden variable (LHV) theories. TheHolder-type Bell inequality derived by Cavalcanti, Foster, Reid and Drummondprovides a tighter bound, for high losses. We analyse the actual tight boundfor the MABK inequalities, given the measure W=\prod_{k=1}^{N}\eta_{k} ofoverall detection efficiency, where \eta_{k} is the efficiency at the site k .Using these inequalities, we confirm that the maximally entangledGreenberger-Horne-Zeilinger state enables loophole-free falsification of LHVtheories provided \prod_{k=1}^{N}\eta_{k}>2^{(2-N)}, which implies a symmetricthreshold efficiency of \eta\rightarrow50%, as N\rightarrow\infty .Furthermore, loophole-free violations remain possible, even when the efficiencyat some sites is reduced well below 0.5, provided N>3 .

Two-setting multi-site Bell inequalities for loophole-free tests with up to 50% loss