The Geometry of Qubit Decoherence: Linear Versus Nonlinear Dynamics in the Bloch Ball

We present two complementary approaches to the Gorini–Kossakowski–Sudarshan–Lindblad equation for an open qubit. First, based on linearity, yields solutions illustrated by mixed-state trajectories in the Bloch ball, including non-random asymptotic fixed points and exceptional points. Second, exploiting the SU(2) symmetry, leads to a nonlinear dynamical system that separates angular dynamics from radial dissipation. This symmetry-based perspective presents a promising route toward generalization to open qudits.