General Greenberger-Horne-Zeilinger theorem of cluster states
Abstract
In this paper, we show that there are eight distinct forms of the Greenberger-Horne-Zeilinger (GHZ) argument for the four-qubit cluster state |φ4> and forty eight distinct forms for the five-qubit cluster state |φ5> in the case of the one-dimensional lattice. The proof is obtained by regarding the pair qubits as a single object and constructing the new Pauli-like operators. The method can be easily extended to the case of the N-qubit system and the associated Bell inequalities are also discussed. Consequently, we present a complete construction of the GHZ theorem for the cluster states of N-qubit in the case of the one-dimensional lattice.
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