We show that a cyclically controlled non-coherence-generating qubit channel generates a family of coaxial latitude circles labeled by two channel controls in the Bloch ball, whose scalar Uhlmann overlap develops a vortex–antivortex structure on the channel-parameter torus. With the preparation Hamiltonian and the pure input state held fixed, cyclic variation of the channel parameters induces a nontrivial Uhlmann phase, which we obtain in closed form for each output loop. The vortices are isolated zeros of the scalar overlap carrying opposite local winding; their total index vanishes on the control torus, consistent with the Poincar'e–Hopf theorem for the associated real two-component field. As the input-state orientation approaches its critical values, opposite-index vortices approach and annihilate in pairs through a tangency of the nodal sets, with a square-root separation law specific to this family of latitude circles. These are local defects of the scalar Uhlmann phase, rather than singularities of the matrix holonomy.