Proposal for experimental test of the time-dependent Wigner inequalities for neutral pseudoscalar meson systems

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. 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.