Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Equivalence classes and canonical forms for two-qutrit entangled states
  of rank four having positive partial transpose   Let E' denote the set of non-normalized two-qutrit entangled states of rank
four having positive partial transpose (PPT). We show that the set of SLOCC
equivalence classes of states in E', equipped with the quotient topology, is
homeomorphic to the quotient R/A_5 of the open rectangular box R in the
Euclidean space R^4 by an action of the alternating group A_5. We construct an
explicit map omega: Omega -> E', where Omega is the open positive orthant in
R^4, whose image meets every SLOCC equivalence class E containeed in E'.
Although the intersection of the image of omega and E is not necessarily a
singleton set, it is always a finite set of cardinality at most 60. By abuse of
language, we say that any state in this intersection is a canonical form of
states rho in E. In particular, we show that all checkerboard PPT entangled
states can be parametrized up to SLOCC equivalence by only two real parameters.
We also summarize the known results on two-qutrit extreme PPT states and edge
states, and examine which other interesting properties they may have. Thus we
find the first examples of extreme PPT states whose rank is different from the
rank of its partial transpose.

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The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
8
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: comp-gas
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
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The categories of this paper are: q-bio
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The categories of this paper are: bayes-an
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The categories of this paper are: stat
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The categories of this paper are: cmp-lg