  The J-PET detector, which consists of inexpensive plastic scintillators, has
demonstrated its potential in the study of fundamental physics. In recent
years, a prototype with 192 plastic scintillators arranged in 3 layers has been
optimized for the study of positronium decays. This allows performing precision
tests of discrete symmetries (C, P, T) in the decays of positronium atoms.
Moreover, thanks to the possibility of measuring the polarization direction of
the photon based on Compton scattering, the predicted entanglement between the
linear polarization of annihilation photons in positronium decays can also be
studied. Recently, a new J-PET prototype was commissioned, based on a modular
design of detection units. Each module consists of 13 plastic scintillators and
can be used as a stand-alone, compact and portable detection unit. In this
paper, the main features of the J-PET detector, the modular prototype and their
applications for possible studies with positron and positronium beams are
discussed. Preliminary results of the first test experiment performed on two
detection units in the continuous positron beam recently developed at the
Antimatter Laboratory (AML) of Trento are also reported.
