PET Simulation Study of Quantum Entangled Annihilation Photons for Application in Gamma-Positron Imaging

Leveraging quantum entanglement (QE) properties of annihilation photons is among new emerging techniques being investigated for improving spatial resolution and sensitivity in Positron Emission Tomography (PET). The double Compton scattering (DCSc) kinematics of coincident photons reveal the entangled annihilation photons via the polar and azimuthal scattering angles. This information can aid Gamma-Positron $(\beta+\gamma)$ imaging, which combines PET with the detection of prompt-gammas, in discriminating between annihilation photons and non-entangled promptgammas. Filtering annihilation photons from prompt-gammas using QE would reduce noise and improve spatial resolution in PET. In a GATE simulation of a Cadmium Zinc Telluride (CZT) PET system currently undergoing system calibration and scale-up at UC Santa Cruz, we report results on its capability in capturing the scattering kinematics of entangled annihilation photons for use in QE filtering. Here, we demonstrate the linearly orthogonal polarization enhancement ratio in the azimuthal scattering difference of entangled photons ($\mathrm{R}=2.035 \pm 0.020$). We then report that each mm decrease in detector crystal resolution leads to a 23% reduction in the quantity of captured DCSc events. This increases the mean absolute error (MAE) of the computed azimuthal scattering angle difference from 6.8° to $9.5^{\circ}, 12.2^{\circ}$, and 15.3° for 1, 2, 4, and 8 mm resolution. Our result demonstrates the capability of our CZT system to take advantage of entangled photons for use in yet-to-be-developed QE filtering techniques for $\beta+\gamma$ imaging while experimental verification is in progress.