  In medical applications -- such as positron emission tomography (PET) --
$511$keV photons that experience Compton scattering are studied. We present a
consistent framework based on error-correction channels to fully describe the
quantum information-theoretic content of high energetic photons undergoing
Compton scattering, characterized by the Klein-Nishina formula in unoriented
matter. In this way, we can predict the expected spatial distribution of two or
more, pure or mixed, polarization entangled or unentangled photons. This
framework allows us to characterize the accessible and inaccessible information
for different parameter ranges. It also answers the question of how to describe
successive multi-photon scattering. In addition our formalism provides a
complete framework for dealing with single and all multi-partite errors that
can occur in the propagation, providing the basis for modeling future dedicated
experiments that will then have applications in medicine, such as reducing
errors in PET imaging.
