Bell inequalities for entangled kaons and their unitary time evolution

Abstract

We investigate Bell inequalities for neutral kaon systems from $\ensuremath{\Phi}$ resonance decay to test local realism versus quantum mechanics. We emphasize the unitary time evolution of the states, which means we also include all decay product states, in contrast to other authors. Only this guarantees the use of the complete Hilbert space. We develop a general formalism for Bell inequalities including both arbitrary ``quasispin'' states and different times; finally, we analyze Wigner-type inequalities. They contain an additional term, a correction function h, as compared to the spin $1/2$ or photon case, which changes considerably the possibility of quantum mechanics to violate the Bell inequality. Examples for special ``quasispin'' states are given, especially those that are sensitive to the $\mathrm{CP}$ parameters $\ensuremath{\varepsilon}$ and ${\ensuremath{\varepsilon}}^{\ensuremath{'}}.$