  In this paper, we represent $n$-qubits as hypermatrices and consider various
applications to quantum entanglement. In particular, we use the higher-order
singular value decomposition of hypermatrices to prove that the $\pi$-transpose
is an LU invariant. Additionally, through our construction we show that the
matrix representation of the combinatorial hyperdeterminant of $2n$-qubits can
be expressed as a product of the second Pauli matrix, allowing us to derive a
formula for the combinatorial hyperdeterminant of $2n$-qubits in terms of the
$n$-tangle.
