Entanglement Classification of extended Greenberger-Horne-Zeilinger-Symmetric States

Abstract

In this paper we analyze entanglement classification of extended Greenberger-Horne-Zeilinger-symmetric states ${\rho }^{ES}$, which is parametrized by four real parameters $x$, $y_1$, $y_2$ and $y_3$. The condition for separable states of ${\rho }^{ES}$ is analytically derived. The higher classes such as bi-separable, W, and Greenberger-Horne-Zeilinger classes are roughly classified by making use of the class-specific optimal witnesses or map from the extended Greenberger-Horne-Zeilinger symmetry to the Greenberger-Horne-Zeilinger symmetry. From this analysis we guess that the entanglement classes of ${\rho }^{ES}$ are not dependent on $y_j(j=1,2,3)$ individually, but dependent on $y_1+y_2+y_3$ collectively. The difficulty arising in extension of analysis with Greenberger-Horne-Zeilinger symmetry to the higher-qubit system is discussed.

16 pages, 6 figures

References in corpus (2)

• Four-qubit entanglement from string theory
• Entanglement of three-qubit Greenberger-Horne-Zeilinger-symmetric states