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 studied process 𝜙 → K S K L → 𝜋 + 𝜋 − 𝜋 + 𝜋 − exhibits the characteristic Einstein-Podolsky-Rosen correlations [1] that prevent both kaons to decay into 𝜋 + 𝜋 − at the same time. The newly published result is based on data sample collected with the KLOE detector at DAΦNE and corresponds to an integrated luminosity of about 1.7 fb −1 , i.e. to ∼ 1.7 × 10 9 𝜙 → K S K L decays. From the fit to the observed time difference distribution of the two kaon decays, the decoherence and CPT violation parameters of various phenomenological models are measured. A stringent upper limit on the branching ratio of the 𝜙 → K S K S , K L K L decay is also derived. 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 to be conducted, through ratios of rates of two classes of processes: K S K L → (𝜋 ± 𝑒 ∓ 𝜈) (3𝜋 0 ) and K S K L → (𝜋 + 𝜋 − ) (𝜋 ± 𝑒 ∓ 𝜈). In addition to this a straightforward extension to the case of CPT symmetry is performed providing the first model independent test of CPT symmetry violation in transitions of neutral kaons.