Abstract
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.
Highlights
We present a quantum information theoretic version of the Klein-Nishina formula
We provide an experimentally feasible method to witness entanglement for these processes via mutually unbiased basis (MUB) (Mutually Unbiased Bases), exploiting Bohr’s complementarity
Last but not least we present a case with non-trivial geometry, e.g. the decay of positronium into three photons that can be exploited by the new tomograph J-PET
Summary
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. This paper shows how the entanglement can be witnessed and provides a concise quantum information theoretic framework for describing high energetic photons undergoing Compton scattering processes. If this step is taken, observables sensitive to entanglement may become visible in living beings along with all the well-known benefits of a standard PET-scan. The prediction do not differ, we have to develop new tools to distinguish between separable and entangled states based on mutually unbiased bases or symmetric informationally complete measurements We apply this MUB-witness to the experimental setup typically exploited in PET scanners in hospitals. Details to symmetry considerations and entanglement as well as details on the witnesses are added before we conclude and give an outlook
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