“…Much scope is left to such a longstanding [14] kind of approach, in particular concerning the entanglement characterization of CV states. The analysis of Gaussian states based on symplectic invariants has provided remarkable insight into the entanglement properties of two-mode states [27] and could be, employing the techniques developed in this paper, extended to multimode settings and to the analysis of multipartite continuous variable entanglement [7,24,25,28], which has been lately drawing considerable attention [26,29,30,31]. At a more fundamental level, this paper is intended to shed further light on the constraints imposed by quantum mechanics on second moments of canonical operators and on the symplectic structure underlying the evolution of bosonic modes under quadratic Hamiltonians.…”