  The quantum interference between the decays of entangled neutral kaons is
studied in the process $\phi\rightarrow K_S K_L
\rightarrow\pi^+\pi^-\pi^+\pi^-$, which exhibits the characteristic
Einstein--Podolsky--Rosen correlations that prevent both kaons to decay into
$\pi^+\pi^-$ at the same time. This constitutes a very powerful tool for
testing at the utmost precision the quantum coherence of the entangled kaon
pair state, and to search for tiny decoherence and CPT violation effects, which
may be justified in a quantum gravity framework. The analysed data sample was
collected with the KLOE detector at DA$\Phi$NE, the Frascati $\phi$-factory,
and corresponds to an integrated luminosity of about 1.7 fb$^{-1}$, i.e. to
about $1.7 \times 10^9$ $\phi\rightarrow K_S K_L$ decays produced. From the fit
of the observed $\Delta t$ distribution, being $\Delta t$ the difference of the
kaon decay times, the decoherence and CPT violation parameters of various
phenomenological models are measured with a largely improved accuracy with
respect to previous analyses. The results are consistent with no deviation from
quantum mechanics and CPT symmetry, while for some parameters the precision
reaches the interesting level at which -- in the most optimistic scenarios --
quantum gravity effects might show up. They provide the most stringent limits
up to date on the considered models.
