  The geometric measure of entanglement $E$ of an $m$ qubit quantum state takes
maximal possible value $m$. In previous work of Gross, Flammia, and Eisert, it
was shown that $E \ge m-O(\log m)$ with high probability as $m\to\infty$. They
showed, as a consequence, that the vast majority of states are too entangled to
be computationally useful. In this paper, we show that for $m$ qubit {\em
Boson} quantum states (those that are actually available in current designs for
quantum computers), the maximal possible geometric measure of entanglement is
$\log_2 m$, opening the door to many computationally universal states. We
further show the corresponding concentration result that $E \ge \log_2 m -
O(\log \log m)$ with high probability as $m\to\infty$. We extend these results
also to $m$-mode $n$-bit Boson quantum states.
