Abstract: Background: Positron Emission Tomography (PET) is a medical imaging modality that utilizes positron-emitting isotopes for many diagnostic purposes. The positron annihilates with an electron, creating two photons of 511 keV energy and opposite momenta, entangled in their orthogonal polarizations. If each photon undergoes a Compton scattering process, the difference of their azimuthal scattering angles reflects the initial orthogonality of the polarizations, peaking at +/- 90 degrees. This correlation, not yet utilized in conventional PET scanners, offers an additional, energy-independent method for background discrimination. Methods: The correlation can be measured using single-layer Compton polarimeters, compatible with conventional PET architecture. We assembled a demonstrator with two such modules comprising 3 & times; 3 & times; 20 mm3 GAGG:Ce scintillating pixels in 16 & times; 16 matrix, read by silicon photomultipliers, mounted on a rotating gantry with 430 mm diameter. Results: This paper reports on the study of random background in measurements with Ga-68 source with activities 200-380 MBq. We compare polarization-correlated Compton events, having a two-hit signature, to conventional single-pixel hits. The signal-to-random background ratio (SBR) obtained in the polarization-correlated events is larger than the one for the single-pixel hits, for all selected event samples. We also demonstrate a correlation between the SBR and the polarimetric modulation factor. Conclusion: The random background suppression in the measurements of the polarization-correlated annihilation quanta is higher than in the standard PET modality, which could be a valuable resource for PET imaging. Since there is a correlation between the SBR and the polarimetric modulation factor, it could serve as an estimator of the random background.