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

TL;DR

This paper reveals that the antisymmetric Mueller generator universally encodes geometric phase information in classical polarization optics and quantum two-level systems, providing a unified algebraic framework for understanding and controlling geometric phases.

Contribution

It introduces the antisymmetric Mueller generator as a universal algebraic kernel for geometric phase in both classical and quantum two-level systems.

Findings

The antisymmetric 3x3 block of Mueller matrices encodes the angular-velocity vector for geometric phase.

The same antisymmetric generator governs pure qubit state evolution on the Bloch sphere.

Operational criteria are provided to identify and control geometric-phase contributions.

Abstract

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.