Quadratic Bell inequalities as tests for multipartite entanglement

This letter presents quantum mechanical inequalities which distinguish, for systems of $N$ spin-$\half$ particles ($N>2$), between fully entangled states and states in which at most $N-1$ particles are entangled. These inequalities are stronger than those obtained by Gisin and Bechmann-Pasquinucci [Phys.\ Lett. A {\bf 246}, 1 (1998)] and by Seevinck and Svetlichny [quant-ph/0201046].