In this article, we investigate quantum entanglement (QE) filtering to address the challenges in multi-isotope positron emission tomography (PET) or in PET studies utilizing radiotracers with dual- positron and prompt gamma emissions. Via GATE simulation, we demonstrate the efficacy of QE filtering using a one-of-a-kind cadmium zinc telluride (CZT) PET system - establishing its viability as a multimodal scanner and ability to perform QE filtering. We show the high Compton scattering probability in this CZT-based scanner with 44.2% of gammas undergoing a single scatter prior to absorption. Additionally, the overall system sensitivity as a standard PET scanner (11.29%), QE-PET scanner (6.81%), and Compton Camera (11.29%) is quantified. Further, we find a 23% decrease in the double Compton scatter (DCSc) frequency needed for QE filtering for each mm decrease in crystal resolution and an increase in mean absolute error (MAE) of their Δϕs from 6.8° for 1 mm resolution to 9.5° , 12.2° , and 15.3° for 2, 4, and 8 mm resolution, respectively. These results reinforce the potential of CZT detectors to lead next generation PET systems taking full advantage of the QE information of positron annihilation photons.