Multipartite bound entanglement and three-setting Bell inequalities

It was shown by Dur [Phys. Rev. Lett. $87,$ 230402 (2001)] that N $(N>~4)$ qubits described by a certain one-parameter family $\mathcal{F}$ of bound entangled states violate the Mermin-Klyshko inequality for $N>~8.$ In this paper we prove that the states from the family $\mathcal{F}$ violate Bell inequalities derived by Żukowski and Kaszlikowski [Phys. Rev. A $56,$ R1682 (1997)], in which each observer measures three noncommuting sets of orthogonal projectors, for $N>~7.$ We also derive a simple one-parameter family of entanglement witnesses that detect entanglement for all the states belonging to $\mathcal{F}.$ It is possible that these entanglement witnesses could be generated by some Bell inequalities.