ENTANGLEMENT OF GAUSSIAN STATES Gerardo Adesso

4.6. Summary and further remarks 91
We are now going to show, in Chapter 5, how some of the results here derived
for two-mode states, can be extended for the investigation of bipartite entanglement
in multimode Gaussian states endowed with peculiar symmetric structures.
Last but not the least, the results collected in the present Chapter might prove
useful as well in the task of quantifying multipartite entanglement of Gaussian
states. For instance, we should mention here that any two-mode reduction of a
pure three-mode Gaussian state is a GLEMS, as we will show in Chapter 7 (this
straightforwardly follows from the phase-space Schmidt decomposition discussed in
Sec. 2.4.2.1). Therefore, one has then available the tools and can apply them to
investigate the sharing structure of multipartite CV entanglement of three-mode,
and, more generally, multimode Gaussian states, as we will do in Chapter 6.
Let us moreover mention that the experimental production and manipulation
of two-mode Gaussian entanglement will be discussed in Chapter 9.