Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Greenberger-Horne-Zeilinger Symmetry in Four Qubit System   Like a three-qubit Greenberger-Horne-Zeilinger(GHZ) symmetry we explore a
corresponding symmetry in the four-qubit system, which we call GHZ$_4$
symmetry. While whole GHZ-symmetric states can be represented by two real
parameters, the whole set of the GHZ$_4$-symmetric states is represented by
three real parameters. In the parameter space all GHZ$_4$-symmetric states
reside inside a tetrahedron. We also explore a question where the given SLOCC
class of the GHZ$_4$-symmetric states resides in the tetrahedron. Among nine
SLOCC classes we have examined five SLOCC classes, which results in three
linear hierarchies $L_{abc_2} \subset L_{a_4} \subset L_{a_2b_2} \subset
G_{abcd}$, $L_{a_20_{3\oplus\bar{1}}} \subset G_{abcd}$, and
$L_{0_{3\oplus\bar{1}}0_{3\oplus\bar{1}}} \subset G_{abcd}$ which hold, at
least, in the whole set of the GHZ$_4$-symmetric states. Difficulties arising
in the analysis of the remaining SLOCC classes are briefly discussed.

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The categories of this paper are: bayes-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: gr-qc
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The categories of this paper are: q-alg
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The categories of this paper are: chao-dyn
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The categories of this paper are: patt-sol
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The categories of this paper are: physics
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: nlin
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The categories of this paper are: q-bio
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The categories of this paper are: hep-lat