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In general any theoretical connection among the parameters describing T, CP or CPT violation, as given by the CPT theorem, does not imply a corresponding connection among the experimental results of the T, CP or CPT tests. In this paper the possibility to perform a direct test of time-reversal T symmetry in the neutral kaon system is discussed. It requires the exchange of in and out states of a transition process. The only existing result [1] for neutral kaons showing a non-zero asymmetry comparing the rates of a reference process (K → K) and its T conjugated one (K → K) cannot be considered a direct test, because the T and CP conjugated processes are identical in this case, and cannot be distinguished. In fact here direct test means a test whose outcome is independent of the result of any other discrete symmetry test, as discussed in detail in Refs. [3 7]. In order to implement such a direct test of the T symmetry, and also of the CPT symmetry which requires as well the inversion of in and out states, it has been suggested to exploit the Einstein-Podolsky-Rosen (EPR) entanglement of neutral mesons produced at a φ-factory (or B-factory) [4 7]. In fact in this case the initial state of the neutral kaon pair produced in φ → KK decay can be rewritten in terms of any pair of orthogonal states |K+〉 and |K−〉: |i〉 = 1 √ 2 {|K〉|K〉 − |K〉|K〉} =

Direct Test of T and CPT Symmetries with Entangled Neutral Mesons