Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence Criterion of Genuine Tripartite Entanglement   In this paper, an intuitive mathematical formulation is provided to
generalize the residual entanglement for tripartite systems of qubits (Phys.
Rev. A \textbf{61}, 052306 (2000)) to the tripartite systems in higher
dimension. The spirit lies in the tensor treatment of tripartite pure states
(Phys. Rev. A \textbf{72}, 022333 (2005)). A distinct characteristic of the
present generalization is that the formulation for higher dimensional systems
is invariant under permutation of the subsystems, hence is employed as a
criterion to test the existence of genuine tripartite entanglement.
Furthermore, the formulation for pure states can be conveniently extended to
the case of mixed states by utilizing the kronecker product approximate
technique. As applications, we give the analytic approximation of the criterion
for weakly mixed tripartite quantum states and consider the existence of
genuine tripartite entanglement of some weakly mixed states.

14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph