Quantum entanglement as an aspect of pure spinor geometry
arXiv:1403.6419 · doi:10.1088/1751-8113/47/40/405301
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 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.
22 pages LaTeX. Accepted by J. of Phys. A. arXiv admin note: text overlap with arXiv:hep-th/0102049, arXiv:quant-ph/0108137, arXiv:1102.2544 by other authors