All-versus-nothing inseparability for two pairs of entangled atoms

It is shown that Cabello’s nonlocality without inequalities for two pairs of singlet states [A. Callebo, Phys. Rev. Lett. 87, 010403 (2001)] can be realized in two pairs of trapped atoms based on Innsbruck ion group. The reasoning mainly lies in that controlled NOT (CNOT) gate can be realized between two atoms in ion trap.