Towards total-body modular PET for positronium and quantum entanglement imaging

The purpose of the reported research is (i) the elaboration of the new imaging method based on the in-vivo measurement of properties of positronium produced inside patient during positron emission tomography, and determination of correlations between properties of positronium inside the cancer tissues and histopathological characteristics of cancers, as well as (ii) exploration of possibilities of the determination of the linear polarization of annihilation photons and development of novel prognostic indicators for cancer diagnostics based on the quantum information from (multipartite) entanglement of photons originating from the positronium decay.During PET diagnosis positronium may be trapped inside free volumes between and within molecules of the examined patient. Currently, in the PET technique, the phenomenon of positronium production is neither recorded nor used for imaging. Yet in about 40% cases, the electron-positron annihilation proceeds in the tissue via creation of positronium. The properties of positronium (such as e.g. mean lifetime or ratio of decay rates into two and three photons) depend on the size of the free volumes between atoms and there are indications that they are correlated with the stage of the development of metabolic disorders of the human tissues. Therefore, an image of properties of positronium formed inside the human body may deliver new information complementary to SUV index and useful for the diagnosis.Moreover, recent theoretical studies have proven that the entanglement in the three-photon state from the decay of ortho-positronium survives surprisingly also for mixed scenarios expected in human tissues. Hence, detecting entanglement of photons originating from positronium may enable the extraction of quantum properties of the surrounding tissue environment.We discuss (i) results of the feasibility studies of the positronium mean-lifetime image reconstruction with the total-body PET scanner from plastic scintillators, as well as (ii) results of pilot studies of the mean lifetime of positronium in the healthy and tumorous tissues operated from the patients. Performed experiments show that properties of positronium atoms in uterine tissues operated from human patients reveals meaningful differences between healthy and tumorous tissues. We also discuss results of the feasibility studies of the polarization of annihilation photons with the J-PET tomograph in which annihilation photons interact predominantly via Compton scattering. Registration of both primary and scattered photons enables to determinate the linear polarization of the primary photon on the event by event basis and hence enables to witness the entanglement of annihilation photons in polarization based on Mutually Unbiased Bases. The performed simulations indicate that in the future with the total-body PET and improved time resolution it shall be feasible to reconstruct images of positronium properties in-vivo during the routine PET diagnosis.