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Open Quantum Systems Decoherence Entanglement Theory Quantum Correlations

Greenberger-Horne-Zeilinger Symmetry in Four Qubit System

arXiv

Authors: DaeKil Park

Year

2016

Paper ID

42127

Status

Preprint

Abstract Read

~2 min

Abstract Words

146

Citations

N/A

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 subset L_a₄ subset L_{a_2b₂} subset G_abcd, L_{a₂₀_{3oplusbar{1}}} subset G_abcd, and L_{0_{3oplusbar{1}}0_{3oplusbar{1}}} subset 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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Like a three-qubit Greenberger-Horne-Zeilinger(GHZ) symmetry we explore a corresponding symmetry in the four-qubit system, which we call GHZ4 symmetry.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1611.09999 [2] arXiv https://arxiv.org/abs/1611.09999 [3] Publisher https://arxiv.org/abs/1611.09999

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