Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Note on Locally Unextendible Non-Maximally Entangled Basis   We study the locally unextendible non-maximally entangled basis (LUNMEB) in
$H^{d}\bigotimes H^{d}$. We point out that there exists an error in the proof
of the main result of LUNMEB [Quant. Inf. Comput. 12, 0271(2012)], which claims
that there are at most $d$ orthogonal vectors in a LUNMEB, constructed from a
given non-maximally entangled state. We show that both the proof and the main
result are not correct in general. We present a counter example for $d=4$, in
which five orthogonal vectors from a specific non-maximally entangled state are
constructed. Besides, we completely solve the problem of LUNMEB for the case of
$d=2$.

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The categories of this paper are: math-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: plasm-ph
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The categories of this paper are: stat
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The categories of this paper are: math
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The categories of this paper are: eess
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The categories of this paper are: hep-ex
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The categories of this paper are: adap-org
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The categories of this paper are: bayes-an
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The categories of this paper are: q-bio
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The categories of this paper are: physics
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The categories of this paper are: q-alg
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: chem-ph