  The Mueller-Stokes formalism which governs conventional polarization optics
is formulated for plane waves, and thus the only qualification one could demand
of a $4\times 4$ real matrix $M$ in order that it qualifies to be the Mueller
matrix of some physical system is that $M$ should map $\Omega^{({\rm pol})}$,
the positive cone of Stokes vectors, into itself. In view of growing current
interest in the characterization of partially coherent partially polarized
electromagnetic beams, there is need to extend this formalism to such beams
wherein the polarization and spatial dependence are generically inseparably
intertwined. This inseparability or non-quantum entanglement brings in
additional constraints that a pre-Mueller matrix $M$ mapping $\Omega^{({\rm
pol})}$ into itself needs to meet in order that it is an acceptable physical
Mueller matrix. These additional constraints are motivated and fully
characterized.
