  In the state-of-the-art Positron Emission Tomography (PET), information about
the polarization of annihilation photons is not available. Current PET systems
track molecules labeled with positron-emitting radioisotopes by detecting the
propagation direction of two photons from positron-electron annihilation.
However, annihilation photons carry more information than just the site where
they originated. Here we present a novel J-PET scanner built from plastic
scintillators, in which annihilation photons interact predominantly via the
Compton effect, providing information about photon polarization in addition to
information on photon direction of propagation. Theoretically, photons from the
decay of positronium in a vacuum are maximally entangled in polarization.
However, in matter, when the positron from positronium annihilates with the
electron bound to the atom, the question arises whether the photons from such
annihilation are maximally entangled. In this work, we determine the
distribution of the relative angle between polarization orientations of two
photons from positron-electron annihilation in a porous polymer. Contrary to
prior results for positron annihilation in aluminum and copper, where the
strength of observed correlations is as expected for maximally entangled
photons, our results show a significant deviation. We demonstrate that in
porous polymer, photon polarization correlation is weaker than for maximally
entangled photons but stronger than for separable photons. The data indicate
that more than 40% of annihilations in Amberlite resin lead to a non-maximally
entangled state. Our result indicates the degree of correlation depends on the
annihilation mechanism and the molecular arrangement. We anticipate that the
introduced Compton interaction-based PET system opens a promising perspective
for exploring polarization correlations in PET as a novel diagnostic indicator.
