The entanglement of $K^0\bar{K^0}$ pairs produced in $\phi$-meson decays, in combination
with the unique properties of the neutral kaon system – such as flavour oscillations, charge-parity (CP)
and time-reversal (T ) violation – opens up new horizons in testing the basic principles
of quantum mechanics and its fundamental discrete symmetries T , CP, CPT.
The KLOE and KLOE-2 experiments at the Frascati Laboratories of INFN
collected at the DA$\Phi$NE collider an integrated luminosity of about 8 fb$^{-1}$,
corresponding to $\simeq 8 \times 10^{9}$ $K_SK_L$ entangled pairs produced.
This is the world largest available data sample of this kind
and represents a unique tool to improve the precision on these studies.
The seminar will illustrate the most recent KLOE-2 results, including:
(i) an improved search for decoherence and CPT violation effects that exploits EPR correlations
in the process $\phi\rightarrow K_S K_L \rightarrow\pi^+\pi^-\pi^+\pi^-$, and constraints
the parameters of various phenomenological models with a precision that reaches - for some of them -
the interesting level at which – in the most optimistic scenarios – quantum gravity effects might show up.
(ii) the first direct test of the T and CPT symmetries in neutral kaon transitions between flavor and CP eigenstates,
by studying the processes $\phi\rightarrow K_S K_L \rightarrow \pi^+\pi^- \, \pi e \nu$ and
$\phi\rightarrow K_S K_L \rightarrow \pi e \nu \, 3\pi^0$~;
(iii) a new measurement of the $K_S \rightarrow \pi e \nu $ branching fraction, that in combination
with the previous KLOE result improves the total precision by almost a factor of two, and allows
a new derivation of $f_+(0)|V_{us}|$.
M. Pepe-Altarelli, P. Silva