Precision tests of Quantum Mechanics and CPT symmetry with entangled neutral kaons at KLOE

The quantum interference between the decays of entangled neutral kaons is a very powerful tool for testing the quantum coherence of the entangled kaon pair state. The search for decoherence and CPT violation effects, which may be justified in a quantum gravity framework, was performed. The studied process $\phi \to K_S K_L \to \pi^+ \pi^- \pi^+ \pi^-$ exhibits the characteristic Einstein–Podolsky–Rosen correlations that prevent both kaons to decay into $\pi^+ \pi^-$ at the same time. The result is based on data sample collected with the KLOE detector at DA$\Phi$NE and corresponds to an integrated luminosity of about 1.7 fb$^{-1}$ , i.e. to ∼1.7 $\times 10^9$ $\phi \to K_S K_L$ decays. The fit of the observed the difference of the kaon decay times with the decoherence and CPT violation parameters of various phenomenological models will be discussed. Independently, the comparison of neutral meson transition rates between flavour and CP eigenstates allows direct and model independent tests of time-reversal T and CPT symmetries, through ratios of rates of two classes of processes: $K_S K_L \to \pi^\pm e^\mp \nu, 3 \pi^0$ and $K_S K_L \to \pi^+ \pi^-, \pi^\pm e^\mp \nu$. In addition to this a straightforward extension to the case of CPT symmetry was performed providing us with the first model independent test of CPT symmetry violation in transitions of neutral kaons.