I derive separability inequalities for Bell correlations of observables in arbitrary pure or mixed $N$ Qudit states in $D^N$-dimensional state space. I find states (a continuum of states if $D>3$) including maximally entangled states which violate these inequalities by a factor $2^{ N-1}$ ; local reality Bell inequalities are much weaker, their maximum violation being by a factor $2^{ (N-1)/2}$. The separability inequalities allow tests of entanglement of unknown states using only the measured correlations .
Categories: quant-ph