  Mueller and Jones matrices have been thoroughly studied as mathematical tools
to describe the manipulation of the polarization state of classical light. In
particular, the most general physical transformation on the polarization state
has been represented as an ensemble of Jones matrices, as $\sum_i V_i \Phi
V^{\dagger}_i$. But this has generally been directly assumed without proof by
most authors. In this Letter, we derive this expression from simple physical
principles and the matrix theory of positive maps.
