General Greenberger-Horne-Zeilinger theorem of cluster states

Details General Greenberger-Horne-Zeilinger theorem of cluster states General Greenberger-Horne-Zeilinger theorem of cluster states

2008-12-29

arxiv.org/abs/0812.4915v1

Physics

Quantum Physics

7 pages, 2 figures, We believe the paper may be of particular interest to the readers of your journal because the study it rep

Scientific paper

In this paper, we show that there are eight distinct forms of the Greenberger-Horne-Zeilinger (GHZ) argument for the four-qubit cluster state $|\phi_4>$ and forty eight distinct forms for the five-qubit cluster state $|\phi_5>$ 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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