Chiral Basis for Qubits and Spin-Helix Decay

We propose a qubit basis composed of transverse spin helices with kinks. Unlike the usual computational basis, this chiral basis is well-suited for describing quantum states with nontrivial topology. Choosing appropriate parameters the operators of the transverse spin components, ${\sigma }_n^x$ and ${\sigma }_n^y$, become diagonal in the chiral basis, which facilitates the study of problems focused on transverse spin components. As an application, we study the temporal decay of the transverse polarization of a spin helix in the $XX$ model that has been measured in recent cold atom experiments. We obtain an explicit universal function describing the relaxation of helices of arbitrary wavelength.