Greenberger-Horne-Zeilinger Symmetry in Four Qubit System

2016/11/30 by Park, DaeKil
#FOS: Physical sciences #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.1611.09999

Abstract

Like a three-qubit Greenberger-Horne-Zeilinger(GHZ) symmetry we explore a corresponding symmetry in the four-qubit system, which we call GHZ₄ symmetry. While whole GHZ-symmetric states can be represented by two real parameters, the whole set of the GHZ₄-symmetric states is represented by three real parameters. In the parameter space all GHZ₄-symmetric states reside inside a tetrahedron. We also explore a question where the given SLOCC class of the GHZ₄-symmetric states resides in the tetrahedron. Among nine SLOCC classes we have examined five SLOCC classes, which results in three linear hierarchies L_abc2 ⊂ L_a4 ⊂ L_a2b2 ⊂ G_abcd, L_a₂0_3⊕1 ⊂ G_abcd, and L_0_3⊕10_3⊕1 ⊂ G_abcd which hold, at least, in the whole set of the GHZ₄-symmetric states. Difficulties arising in the analysis of the remaining SLOCC classes are briefly discussed.

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