Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Entanglement in SU(2)-invariant quantum systems: The positive partial
  transpose criterion and others   We study entanglement in mixed bipartite quantum states which are invariant
under simultaneous SU(2) transformations in both subsystems. Previous results
on the behavior of such states under partial transposition are substantially
extended. The spectrum of the partial transpose of a given SU(2)-invariant
density matrix $\rho$ is entirely determined by the diagonal elements of $\rho$
in a basis of tensor-product states of both spins with respect to a common
quantization axis. We construct a set of operators which act as entanglement
witnesses on SU(2)-invariant states. A sufficient criterion for $\rho$ having a
negative partial transpose is derived in terms of a simple spin correlator. The
same condition is a necessary criterion for the partial transpose to have the
maximum number of negative eigenvalues. Moreover, we derive a series of sum
rules which uniquely determine the eigenvalues of the partial transpose in
terms of a system of linear equations. Finally we compare our findings with
other entanglement criteria including the reduction criterion, the majorization
criterion, and the recently proposed local uncertainty relations.

10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
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The categories of this paper are: adap-org
2
The categories of this paper are: math
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
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The categories of this paper are: econ
31
The categories of this paper are: ao-sci