The classicality concept is formulated. It is used to derive Wigner inequalities dependent on three instants. The possibility of testing experimentally violations of these inequalities in pure and mixed flavor states of a pair of neutral pseudoscalar mesons is studied. Within the Werner background model, it is shown that a violation of time-dependent Wigner inequalities may be observed even at a 50 $\%$ fraction of background processes.The classicality concept is formulated. It is used to derive Wigner inequalities dependent on three instants. The possibility of testing experimentally violations of these inequalities in pure and mixed flavor states of a pair of neutral pseudoscalar mesons is studied. Within the Werner background model, it is shown that a violation of time-dependent Wigner inequalities may be observed even at a 50 $$\%$$ fraction of background processes.

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