Entropic Leggett-Garg inequality in neutrinos and B (K) meson systems

Abstract

Entropic Leggett-Garg inequality is studied in systems like neutrinos in the context of two and three flavor neutrino oscillations and in neutral $B_d$, $B_s$ and $K$ mesons. The neutrino dynamics is described with the matter effect taken into consideration. For the decohering $B/K$ meson systems, the effect of decoherence and CP violation have also been taken into account, using the techniques of open quantum systems. Enhancement in the violation with increase in the number of measurements has been found, in consistency with findings in spin-$s$ systems. The effect of decoherence is found to bring the deficit parameter $\mathcal{D}^{[n]}$ closer to its classical value zero, as expected. The violation of entropic Leggett-Garg inequality lasts for a much longer time in $K$ meson system than in $B_d$ and $B_s$ systems.