Tight multisetting Bell’s inequalities
Which quantum states do not allow a local realistic description? This question still remains open, mainly because our present tools to test local realism are not optimal. Most of Bell’s inequalities are for the case in which only two measurement settings can be chosen by each observer, for example the Clauser-Horne-Shimony-Holt or Mermin inequalities. On the other hand, no efficient method for the derivation of Bell’s inequalities with more than two measurement settings per observer is known. A general way is to define the facets of the correlation polytope. Yet, this is computationally hard NP-problem.
In 2004 we derived tight Bell's inequalities for N>2 observers involving more than two alternative measurement settings. We gave a necessary and sufficient condition for a general quantum state to violate the new inequalities. Most importantly, the new inequalities are violated by some classes of states, for which all standard Bell's inequalities with two measurement settings per observer are satisfied.
W. Laskowski, T. Paterek, M. Zukowski &C. Brukner
Tight multipartite Bell’s inequalities involving many measurement settings
