  Previously a set of coupled first order differential equations were derived
for the decoherence of a pair of spatial mode entangled photons, propagating
along different paths through turbulence. Here we extend this analysis to the
situation where both photons travel along the same path, which introduces the
effect of multiple photon correlations. The resulting equation now contains
additional terms that take these multiphoton correlations into account. At the
same time, we provide a more thorough formulation of the quantized field,
starting from a Lorentz invariant formulation, which is then explicitly broken
by the choice of a particular propagation direction. The effect of the latter
improvement in the quantization on the form of the final equation is minimal.
