ENTANGLEMENT OF GAUSSIAN STATES Gerardo Adesso

264 Conclusion and Outlook
compass which points towards the physics under investigation. However, the brief
hints summarized above concerning the study of non-Gaussian entanglement in its
actual infancy, seem to suggest at least two things. On one hand, that it is worth
taking the risk, as the possibilities offered by non-Gaussian states may be really
intriguing; on the other hand, that wise footpaths in the CV labyrinth may be
traced and followed back and forth, leading to physically insightful, novel results
on both fundamental and practical grounds, obtainable with a finite, accountable
complexity rise compared to the Gaussian case.
The most exciting challenge for me is to enter this huge, largely unexplored
treasure island aiming to draw a map first of its underworld (foundations), and
then of its colorful surface (applications). The structure and distribution of entanglement
in non-Gaussian states have to be understood, qualified and quantified
properly, at least in restricted families of states, in order to single out their usefulness
for quantum information (and not only) implementations. For instance, we
have learned (see Part III) how the monogamy constraint imposes a natural hierarchical
structure on multipartite entanglement of Gaussian states. In this context,
the promiscuity of some classes of Gaussian states was established, opening new
frontiers for the implementation of such resources for multiparty communication
purposes. Inspired by these results, and bearing in mind that Gaussian states are
extremal in the sense of possessing minimal entanglement compared to the non-
Gaussian cousins, it appears as an exciting perspective to look for exotic states
in the CV arena with an enhancedly promiscuous sharing structure of quantum
correlations, with a monogamy of entanglement stretched to its limits, and so with
exceptional predispositions for the transfer of quantum information.
These considerations, along with the few other examples mentioned above,
should suffice to convince the reader that CV entanglement of Gaussian and non-
Gaussian states, together with its applications in fundamental quantum mechanics,
quantum “multimedia”, and several other areas of physics, is a very active and
lively field of research, where more progress and new fascinating developments may
be forecast in the near future. The results of this Dissertation, while of inherent
fundamental interest for quantum information theory, are thus expected to play
— either directly or as premises for new advances — an increasingly important
role in the practical characterization of the physical processes which underlie these
multifaceted, sometimes stunningly revolutionary situations.