Antisymmetric Mueller Generator as the Universal Origin of Geometric Phase in Classical Polarization and Quantum Two-Level Systems

Abstract: We show that the antisymmetric part of the Mueller matrix of any ideal retarder uniquely determines the geometric phase observed in classical polarization optics. This antisymmetric block encodes the angular-velocity pseudovector that governs the tangential component of the Stokesvector motion on the Poincaré sphere and thus fully determines the associated geometric phase, while the symmetric block is geometrically neutral in the sense that it does not contribute to the phase. We further demonstrate that the same antisymmetric generator arises in the adjoint action of any SU(2) unitary operator and fully determines the geometric phase of a qubit, independently of adiabaticity or cyclicity. This identifies a single algebraic structure underlying geometric phases in both classical and quantum two-level systems and provides an operational criterion for isolating geometric-phase contributions either directly from measured Mueller matrices (classical case) or from the adjoint action reconstructed by qubit process tomography