Polarized light and geometric phase in qg units: Stokes parameters, Mueller matrices and Stokes' theorem

Abstract

⟨ ⟩ The qang project describes qubits by measurement—level quantities, the qg values qgP = P [1]. This short note states two classical results in those units, implemented and checked in the qang library (pip install qang, version 0.6.0). First, a polarization state of light is a qubit: the normalized Stokes parameters are exactly the qg values, the degree of polarization P is the length of the qg vector, and a lossless Mueller matrix is the qg gate rule qg′ = qgU†PU . Malus's law becomes I = I0(1 + qgZ cos 2θ + qgX sin 2θ)/2 for any input state. Second, the — geometric phase of a closed loop on the Bloch (Poincaré) sphere is minus half the enclosed solid angle, which is Stokes' theorem for the Berry curvature. For a loop at constant qgZ the phase is (qgZ 1)/2 of a turn: it is fixed by qgZ alone. Nothing here is new physics. The contribution is the translation into qang's units and a set of 26 numerical checks, with the phase computed three independent ways.