The non-locality of cluster states

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Abstract
We investigate cluster states of qubits under the standpoint of their non-local properties. We demonstrate that a Greenberger-Horne-Zeilinger (GHZ) argument holds for any cluster state: more precisely, it holds for any partial, thence {\em mixed}, state of a small number of connected qubits (five, in the case of one-dimensional lattices). For the 4-qubit cluster state, we also provide a new Bell inequality that is maximally violated by this state and is not violated by the four-qubit GHZ state.

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