  J-PET is the first positron-emission tomograph (PET) constructed from plastic
scintillators. It was optimized for the detection of photons from
electron-positron annihilation. Such photons, having an energy of 511 keV,
interact with electrons in plastic scintillators predominantly via the Compton
effect. Compton scattering is at most probable at an angle orthogonal to the
electric field vector of the interacting photon. Thus registration of multiple
photon scatterings with J-PET enables to determine the polarization of the
annihilation photons. In this contribution we present estimates on the physical
limitation in the accuracy of the polarization determination of $511$~keV
photons with the J-PET detector.
