Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal PPTES witnesses for states in $\mathbb C^n\otimes \mathbb C^n$   Recently, X. Qi and J. Hou [Phys. Rev. A 85, 022334 (2012)] provided optimal
entanglement witnesses without the spanning property. These witnesses are
associated to indecomposable positive linear maps, but it is not checked
whether partial transposes of these witnesses are also optimal. We show that
partial transposes of these entanglement witnesses have spanning property, and
these witnesses are indeed optimal PPTES witnesses (non-decomposable optimal
entanglement witnesses).

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The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
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The categories of this paper are: cond-mat
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The categories of this paper are: q-alg
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The categories of this paper are: patt-sol
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The categories of this paper are: supr-con
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The categories of this paper are: mtrl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: atom-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: adap-org
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The categories of this paper are: chao-dyn