Hardy’s approach, Eberhard’s inequality, and supplementary assumptions

Hardy's formulation of the Einstein-Podolsky-Roser paradox and the usual formulation based on Bell-type inequalities are compared. The role of the supplementary assumptions in an experimental test based on Hardy's approach is discussed. It is proved that even in Hardy's approach the supplementary assumptions play a fundamental role in refusing Einstein locality on the basis of the experimental results. The lowest value of quantum efficiency for a loophole-free experiment based on Hardy's approach is deduced.