It is argued that Hardy-type proposals assume either nonlocality at detection, and then beg the question, or "local empty waves" (local hidden variables), and then have to accept "many worlds" and cannot prove nonlocality.
For a system of n spin-21 particles and for two measurement possibilities for each particle there is always a state showing Hardy's nonlocality. Mixed states of an n- (n>3) particle system can only show Hardy's nonlocality. Product states for any n never show nonlocality.
We generalize Hardy's proof of nonlocality to the case of bipartite mixed statistical operators, and we exhibit a necessary condition which has to be satisfied by any given mixed state $\ensuremath{\sigma}$ in order that a local and realistic hidden variable model exists which accounts for the quantum mechanical predictions implied by $\ensuremath{\sigma}$. Failure of this condition will imply both the impossibility of any local explanation of certain joint probability distributions in terms of hidden variables and the nonseparability of the considered mixed statistical operator. Our result can be also used to determine the maximum amount of noise, arising from imperfect experimental implementations of the original Hardy's proof of nonlocality, in presence of which it is still possible to put into evidence the nonlocal features of certain mixed states.