  The Milburn dynamics of three nonresonant ultra-strongly coupled oscillators
are resolved by using symplectic geometry. We look at the Milburn dynamics of
virtual excitations and how they affect pairwise entanglement. It is found that
the dynamics of excitations and entanglement experience similar profiles
against time, physical parameters, and decoherence rate. Furthermore, we show
that the extinction of excitations entails separability, which demonstrates the
hierarchy between entanglement and virtual excitations. Additionally, we
analyze the effects of physical parameters on the redistribution of virtual
excitations among the three bi-partitions. As a result, we show the violation
of the monogamy of excitations as in quantum discord. This implies that
excitations can be considered as signatures of quantum correlations beyond
entanglement. Besides, we emphasize that our treatment can be used to model
coupled quantum circuits in real situations (with decoherence).
