Entanglement Classification of Restricted Greenberger-Horne-Zeilinger Symmetric States in Four-Qubit System

Abstract

Similar to the three-qubit Greenberger-Horne-Zeilinger (GHZ) symmetry we explore the four-qubit GHZ symmetry group and its subgroup called restricted GHZ symmetry group. While the set of symmetric states under the whole group transformation is represented by three real parameters, the set of symmetric states under the subgroup transformation is represented by two real parameters. After comparing the symmetric states for whole and subgroup, the entanglement is examined for the latter set. It is shown that the set has only two SLOCC classes, $L_{ab{c}_2}$ and $G_{abcd}$. Extension to the multi-qubit system is briefly discussed.

11 pages, 1 figure v2: 16 pages, 3 figures, almost re-written including title, author, abstract, etc v3: final version, will appear in PRA

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Cited by in corpus (1)

• Locality of three-qubit Greenberger-Horne-Zeilinger-symmetric states