Multipartite bound entanglement and multisetting Bell inequalities

Dür Phys. Rev. Lett. 87 230402 (2001) constructed N-qubit bound entangled states which violate a Bell inequality for N≥8, and his result was recently improved by showing that there exists an N-qubit bound entangled state violating the same Bell inequality if and only if N≥6 [ Phys. Rev. A 79 032309 (2009)]. On the other hand, it has been also shown that the states which Dür considered violate Bell inequalities different from the inequality for N≥6. In this paper, by employing different forms of Bell inequalities, in particular, a specific form of Bell inequalities with M settings of the measuring apparatus for sufficiently large M, we prove that there exists an N-qubit bound entangled state violating the M-setting Bell inequality if and only if N≥4.