Perfect Test of Entanglement for Two-level Systems

A 3-setting Bell-type inequality enforced by the indeterminacy relation of complementary local observables is proposed as an experimental test of the 2-qubit entanglement. The proposed inequality has an advantage of being a sufficient and necessary criterion of the separability. Therefore any entangled 2-qubit state cannot escape the detection by this kind of tests. It turns out that the orientation of the local testing observables plays a crucial role in our perfect detection of the entanglement.