Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rotational covariance and GHZ contradictions for three or more particles
  of any dimension   Greenberger-Horne-Zeilinger (GHZ) states are characterized by their
transformation properties under a continuous symmetry group, and $N$-body
operators that transform covariantly exhibit a wealth of GHZ contradictions. We
show that local or noncontextual hidden variables cannot duplicate this
covariance for any state-changing transformations, and we extract specific GHZ
contradictions from discrete subgroups, with no restrictions on particle number
$N$ or dimension $d$ except for the fundamental requirement that $N \geq 3$ for
nonprobabilistic contradictions. However, the specific contradictions fall into
three regimes distinguished by increasing demands on the number of measurement
operators required for the proofs. We introduce new methods of proof that
define these regimes. The first recovers theorems equivalent to those found
recently by Ryu et. al. \cite{RLZL}, the first operator-based theorems for all
odd dimensions, $d$, covering many (but not all) particle numbers $N$ for each
$d$. The second and third produce new theorems that fill all remaining gaps
down to $N=3$, for every $d$. The common origin of all such GHZ contradictions
is that the GHZ states and measurement operators transform according to
different representations of the symmetry group, which has an intuitive
physical interpretation.

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The categories of this paper are: eess
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The categories of this paper are: chem-ph
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The categories of this paper are: supr-con
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The categories of this paper are: nlin
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ex
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-th
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The categories of this paper are: math-ph
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The categories of this paper are: adap-org
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The categories of this paper are: hep-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: econ
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The categories of this paper are: dg-ga
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-ex