Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A completely entangled subspace of maximal dimension   A completely entangled subspace of a tensor product of Hilbert spaces is a
subspace with no non-trivial product vector. K. R. Parthasarathy determined the
maximum dimension possible for such a subspace. Here we present a simple
explicit example of one such space. We determine the set of product vectors in
its orthogonal complement and see that it spans whole of the orthogonal
complement. This way we are able to determine the minimum dimension possible
for an unextendible product basis (UPB) consisting of product vectors which are
linearly independent but not necessarily mutually orthogonal.

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The categories of this paper are: cmp-lg
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The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
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The categories of this paper are: hep-th
2
The categories of this paper are: math
15
The categories of this paper are: nucl-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
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The categories of this paper are: atom-ph