Antisymmetric Mueller generator as the universal origin of geometric phase in classical polarization and quantum two-level systems

We show that the antisymmetric Mueller generator provides a universal algebraic kernel for geometric phase in classical polarization optics and in quantum two-level systems. For any ideal retarder, the antisymmetric 3x3 block of its Mueller matrix (the antisymmetric generator of the adjoint SU(2) action on the Stokes vector) encodes the angular-velocity vector that drives the tangential motion on the Poincar\'e sphere and fully determines the Pancharatnam-Berry phase, while the symmetric block is geometrically neutral. The same antisymmetric generator governs the evolution of pure qubit states on the Bloch sphere. This unified viewpoint yields operational criteria to identify and control geometric-phase contributions from measured Mueller matrices and from qubit process tomography.