The interplay between the various measures of quantum correlations is well known in stable optical and electronic systems. Here we study such foundational issues in unstable quantum systems. Specifically we study meson-antimeson systems (Formula Presented), which are produced copiously in meson factories. In particular, the nonclassicality of quantum correlations which can be characterized in terms of nonlocality (which is the strongest condition), entanglement, teleportation fidelity or weaker nonclassicality measures like quantum discord are analyzed. We also study the impact of decoherence on these measures of quantum correlations, using the semigroup formalism. A comparison of these measures brings out the fact that the relations between them can be nontrivially different from those of their stable counterparts such as neutrinos. © Società Italiana di Fisica/Springer-Verlag 2016