  We study the eigenvalue distributions for sums of independent rank-one
$k$-fold tensor products of large $n$-dimensional vectors. Previous results in
the literature assume that $k=o(n)$ and show that the eigenvalue distributions
converge to the celebrated Mar\v{c}enko-Pastur law under appropriate moment
conditions on the base vectors. In this paper, motivated by quantum information
theory, we study the regime where $k$ grows faster, namely $k=O(n)$. We show
that the moment sequences of the eigenvalue distributions have a limit, which
is different from the Mar\v{c}enko-Pastur law. As a byproduct, we show that the
Mar\v{c}enko-Pastur law limit holds if and only if $k=o(n)$ for this tensor
model. The approach is based on the method of moments.
