  Relying on the mathematical analogy of the pure states of a two-qubit system
with four-component Dirac spinors, we provide an alternative consideration of
quantum entanglement using the mathematical formulation of Cartan's pure
spinors. A result of our analysis is that the Cartan equation of two qubits
state is entanglement sensitive in a way that the Dirac equation for fermions
is mass sensitive. The Cartan equation for unentangled qubits is reduced to a
pair of Cartan equations for single qubits as the Dirac equation for massless
fermions separates into two Weyl equations. Finally, we establish a
correspondance between the separability condition in qubit geometry and the
separability condition in spinor geometry.
