Violation of local realism vs detection efficiency

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We put bounds on the minimum detection efficiency necessary to violate local realism in Bell experiments. These bounds depends of simple parameters like the number of measurement settings or the dimensionality of the entangled quantum state. We derive them by constructing explicit local-hidden variable models which reproduce the quantum correlations for sufficiently small detectors efficiency.
6 pages, revtex. Modifications in the discussion for many parties in section 3, small erros and typos corrected, conclusions unchanged

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