  In bipartite quantum systems, entanglement correlations between the parties
exerts direct influence in the phenomenon of wave-particle duality. This effect
has been quantitatively analyzed in the context of two qubits by M. Jakob and
J. Bergou [Optics Communications 283(5) (2010) 827]. Employing a description of
the $K$-meson propagation in free space where its weak decay states are
included as a second party, we study here this effect in the kaon-antikaon
oscillations. We show that a new quantitative "triality" relation holds,
similar to the one considered by Jakob and Bergou. In our case, it relates the
distinguishability between the decay products states corresponding to the
distinct kaon propagation modes $K_S $, $K_L $, the amount of wave-like path
interference between these states, and the amount of entanglement given by the
reduced von Neumann entropy. The inequality can account for the complementarity
between strangeness oscillations and lifetime information previously considered
in the literature, therefore allowing one to see how it is affected by
entanglement correlations. As we will discuss, it allows one to visualize
clearly through the $K^{0}$$\overline{K}\,^{0}$ oscillations the fundamental
role of entanglement in quantum complementarity.
