Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Necessary and sufficient criterion for k-separability of N-qubit noisy
  GHZ states   A Multipartite entangled state has many different kinds of entanglement
specified by the number of partitions. The most essential example of
multipartite entanglement is the entanglement of multi-qubit
Greenberger-Horne-Zeilinger (GHZ) state in white noise. We explicitly construct
the entanglement witnesses for these states with stabilizer generators of the
GHZ states. For a $N$ qubit GHZ state in white noise, we demonstrate the
necessary and sufficient criterion of separability when it is divided into $k$
parties with $N\leq 2k-1$ for arbitrary $N$ and $k$. The criterion covers more
than a half of all kinds of partial entanglement for $% N $-qubit GHZ states in
white noise. For the rest of multipartite entanglement problems, we present a
method to obtain the sufficient conditions of separability. As an application,
we consider $N$ qubit GHZ state as a codeword of the degenerate quantum code
passing through depolarizing channel. We find that the output state is neither
genuinely entangled nor fully separable when the quantum channel capacity
reduces from positive to zero.

30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
2
The categories of this paper are: math
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph