Existence of product vectors and their partial conjugates in a pair of spaces

Details Existence of product vectors and their partial conjugates in a pair of spaces Existence of product vectors and their partial conjugates in a pair of spaces

2011-07-06

arxiv.org/abs/1107.1023v3

J. Math. Phys. 52, 122201 (2011)

Physics

Quantum Physics

15 pages, to correct a technical problem in V2

Scientific paper

Let $D$ and $E$ be subspaces of the tensor product of the $m$ and $n$ dimensional complex spaces, with codimensions $k$ and \ell$, respectively. We show that if $k+\ellm+n-2$ then there may not exist such a product vector. If $k+\ell=m+n-2$ then both cases may occur depending on $k$ and $\ell$.

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