  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.
