We derive a Bell inequality for testing violation of local realism. Quantum nonlocality of several four-qubit states is investigated. These include the Greenberger-Zeilinger-Horne (GHZ) state, $W$ state, linear cluster state, and the state $\mid \chi ⟩$ that has recently been proposed in [Phys. Rev. Lett. 96, 060502 (2006)]. The Bell inequality is optimally violated by $\mid \chi ⟩$ but not violated by the GHZ state. The linear cluster state also violates the Bell inequality though not optimally. The state $\mid \chi ⟩$ can thus be discriminated from the linear cluster state by using the inequality. Different aspects of four-partite entanglement are also studied by considering the usefulness of a family of four-qubit mixed states as resources for two-qubit teleportation. Our results generalize those in [Phys. Rev. Lett. 72, 797 (1994)].

• Received 17 November 2006

DOI:https://doi.org/10.1103/PhysRevA.75.032332