  We present a quantum information theoretic version of the Klein-Nishina
formula. This formulation singles out the quantity, the a priori visibility,
that quantifies the ability to deduce the polarisation property of single
photons. The Kraus-type structure allows a straightforward generalisation to
the multiphoton cases, relevant in the decay of positronium which is utilized
e.g. for metabolic PET-imaging (Positron-Emission-Tomograph). Predicted by
theory but never experimentally proven, the two- or three-photon states should
be entangled. We provide an experimentally feasible method to witness
entanglement for these processes via MUBs (Mutually Unbiased Bases), exploiting
Bohr's complementarity. Last but not least we present explicit cases
exemplifying the interrelation of geometry and entanglement including relations
to its potentiality for teleportation schemes or Bell inequality violations or
in future for detecting cancer in human beings.
