Pure Spinors, Impure Spinors and Quantum Mechanics

Tahir Manzoor, S. N. Hasan

Fernando Chamizo

Abstract The transformation law of the Pauli spinors under rotations, linked to 1/2-spin particles, leads to a mathematical problem that can be rephrased and solved in purely linear algebraic terms. We present it as a possible approach to be incorporated in a first course of quantum mechanics when introducing the concept of the spin. This concept was very elusive at early times and had an intricate development commonly overlooked in modern texts. We also take the opportunity to make some historical comments.

Andre G. Campos, Renán Cabrera, Denys I. Bondar +1 more

In nonrelativistic quantum mechanics, Hudson's theorem states that a Gaussian wave function is the only pure state corresponding to a positive Wigner function (WF). We explicitly construct non-Gaussian Dirac spinors with positive relativistic WFs. These pure relativistic states are coherent superpositions of particles and antiparticles, while the existence of positive WFs exclusive composed of particles is conjectured. These observations may open new directions in relativistic quantum information theory.

Stefanie Czischek

Vasileios I. Kiosses

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.