Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Characterization and properties of weakly optimal entanglement witnesses   We present an analysis of the properties and characteristics of weakly
optimal entanglement witnesses, that is witnesses whose expectation value
vanishes on at least one product vector. Any weakly optimal entanglement
witness can be written as the form of $W^{wopt}=\sigma-c_{\sigma}^{max} I$,
where $c_{\sigma}^{max}$ is a non-negative number and $I$ is the identity
matrix. We show the relation between the weakly optimal witness $W^{wopt}$ and
the eigenvalues of the separable states $\sigma$. Further we give an
application of weakly optimal witnesses for constructing entanglement witnesses
in a larger Hilbert space by extending the result of [P. Badzi\c{a}g {\it et
al}, Phys. Rev. A {\bf 88}, 010301(R) (2013)], and we examine their geometric
properties.

31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
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The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an