Quantum entanglement as an aspect of pure spinor geometry

Abstract

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 Cartanʼs pure spinors. A result of our analysis is that the Cartan equation of a two-qubit state is entanglement sensitive in the same 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 correspondence between the separability condition in qubit geometry and the separability condition in spinor geometry.