Positron Emission Tomography (PET) is a widely-used imaging modality for medical research and clinical diagnosis. Imaging of the radiotracer is obtained from the detected hit positions of the two positron annihilation photons in a detector array. The image is degraded by backgrounds from random coincidences and in-patient scatter events which require correction. In addition to the geometric information, the two annihilation photons are predicted to be produced in a quantum-entangled state, resulting in enhanced correlations between their subsequent interaction processes. To explore this, the predicted entanglement in linear polarisation for the two photons was incorporated into a simulation and tested by comparison with experimental data from a cadmium zinc telluride (CZT) PET demonstrator apparatus. Adapted apparati also enabled correlation measurements where one of the photons had undergone a prior scatter process. We show that the entangled simulation describes the measured correlations and, through simulation of a larger preclinical PET scanner, illustrate a simple method to quantify and remove the unwanted backgrounds in PET using the quantum entanglement information alone.