For Hilbert Spaces:
$$(|0\rangle + |1\rangle)\otimes (|0\rangle + |1\rangle) = |00\rangle + |01\rangle + |10\rangle + |11\rangle.$$
where all results are column vectors
\begin{eqnarray*} 0 &=& \langle 00|01\rangle, \\ &=& \langle 00|10\rangle, \\ &=& \langle 00|11\rangle, \end{eqnarray*}
etc. But for Geometric Algebra, the geometric product results in all orthogonal bivectors
$$(a_0 + a_1)*(b_0+b_1) = a_0\wedge b_0 + a_0\wedge b_1 + a_1\wedge b_0 + a_1\wedge b_1.$$
\begin{eqnarray*} 0 &=& \langle a_0\wedge b_0,a_0\wedge b_1\rangle, \\ &=& \langle a_0\wedge b_0,a_1\wedge b_0\rangle, \\ &=& \langle a_0\wedge b_0,a_1\wedge b_1\rangle, \end{eqnarray*}
etc. The questions is: Where did the bivectors go in the Hilbert space tensor product? this leads to different results for bell and magic states between the two representations.