  This work concerned two experimental searches for the violation of
fundamental discrete symmetries in physical systems originating from
electron-positron interactions. The first study was a direct test of the
symmetry under reversal in time in transitions of neutral K mesons, performed
with quantum-entangled neutral kaon pairs. Data collected by the KLOE
experiment operating at the DAFNE collider in 2004-2005 were studied to select
events of the KsKl->pi e nu 3pi0 and KsKl->pi+pi- pi e nu processes and compare
their rates. Rates of each process identified by two time-ordered neutral kaon
decays, determined as a function of a difference between kaon decays, were used
to measure the asymptotic level of two T-violation sensitive ratios of double
kaon decay rates, yielding the values of R2=1.020+/-0.017stat+/-0.035syst and
R4=0.990+/-0.017stat+/-0.039syst. Although these results do not reach the
sensitivity needed to probe T violation, this measurement proves the required
reconstruction and analysis of the data is feasible and prospects exist for a
statistically significant T test with a larger dataset collected by the KLOE-2
experiment if certain systematic effects are eliminated. The second part of
this work comprised a demonstration of feasibility of using the J-PET detector
to search for non-vanishing angular correlations in the decays of
ortho-positronium atoms. Feasibility of identification of 3gamma events as well
as reconstruction of their origin points using a dedicated trilateration-based
method was demonstrated using MC simulations and a test measurement performed
with the J-PET detector.
