  We derive a single general Bell inequality which is a necessary and
sufficient condition for the correlation function for N particles to be
describable in a local and realistic picture, for the case in which
measurements on each particle can be chosen between two arbitrary dichotomic
observables. We also derive a necessary and sufficient condition for an
arbitrary N-qubit mixed state to violate this inequality. This condition is a
generalization and reformulation of the Horodeccy family condition for two
qubits.
