  We provide a method to write down the density operator for any pure state of
multi-qubit systems in the multiparticle spacetime algebra (MSTA) introduced by
Doran, Gull, and Lasenby. Using the MSTA formulation, we analyze several
aspects of quantum mechanics in a geometrical way including the Bell inequality
and the dynamics of two coupled qubits. Lastly, we provide a natural way to
construct the local unitary invariants in the MSTA. Using these invariants, we
analyze the space of the two-qubit and three-qubit pure states with local and
non-local degrees of freedom separated.
