Recently a new class of time-dependent Bell inequalities in Wigner form was introduced. The structure of the inequalities allows experimental studies of quantum and open quantum systems in external fields. In this paper, we study the properties of the time-dependent Wigner inequalities using the time evolution of neutral pseudoscalar mesons with $CP$-violation effects taken into account. It is shown that it is always possible to find a range of parameters to test for violation in an experimentally accessible area. The effect of the relaxation of the inequalities for large time scales is demonstrated.
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Nikitin et al. (2015) studied this question.
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