  The KLOE-2 detector records decays of quantum-entangled pairs of neutral
kaons produced in decays of phi mesons provided by the DAFNE accelerator at the
Laboratori Nazionali di Frascati, Italy. This system allows for a broad range
of studies of fundamental discrete symmetries including tests which are only
feasible with entangled neutral mesons. This work reports on the Lorentz
non-invariance and CPT violation searches with the KSKL->pi+pi-pi+pi- process
in the framework of the Standard Model Extension. Moreover, status and results
of quantum coherence tests with the same process are discussed. Finally, the
status of ongoing direct tests of T and CPT in neutral kaon transitions is
presented. For each of thereported studies, perspectives are discussed for the
KLOE-2 experiment, which is presently taking data.
