  Cluster states are multi-particle entangled states with special entanglement
properties particularly suitable for quantum computation. It has been shown
that cluster states can exhibit Greenberger-Horne-Zeilinger (GHZ)-type
non-locality even when some of their qubits have been lost. In the present
work, we generated a four-photon mixed state, which is equivalent to the
partial, qubit-loss state of an N-qubit cluster state up to some local
transformations. By using this mixed state, we then realize a GHZ-type
violation of local realism. Our results not only demonstrate a mixed state's
GHZ-type non-locality but also exhibit the robustness of cluster states under
qubit-loss conditions.
