Qubits, Weyl spinors, quantum NOT gates, and dynamical decoupling

Abstract: An equivalence is established between orthogonal pure state qubits on the Bloch sphere and massless Weyl spinors, when the Bloch vector is taken as the physical three-momentum. A family of unitary, coordinate dependent transformations is obtained which connects orthogonal combinations of the basis states of a two-level quantum system. It is shown that a subset of these transformations possesses the novel feature of effecting a point inversion by means of a rotation. For qubits, these transformations act as quantum NOT/parity gates, and also as flipping operators that exactly cancel decoherence in a dynamical decoupling setting. For Weyl spinors they provide, at the relativistic quantum level, a unitary symmetry transformation for the Weyl equations.