ENTANGLEMENT OF GAUSSIAN STATES Gerardo Adesso

Introduction 7
The companion Part V looks at entanglement from a practical perspective for
quantum information and communication implementations, and other less conventional
applications. Bipartite and multipartite teleportation-based communication
(including telecloning) with Gaussian states is studied in Chapter 12, where the
equivalence between optimal teleportation fidelity and shared entanglement is established,
together with an experimentally testable connection between teleportation
efficiency, multipartite entanglement, and promiscuous sharing structure. Entanglement
distribution and the investigation of the correlation range in many-body
harmonic rings with a Gaussian valence bond structure is addressed in Chapter 13.
The degradation of Gaussian entanglement as detected by accelerated observers is
instead investigated in Chapter 14, and interpreted in terms of an entanglement
re-distribution in multipartite form among accessible and unaccessible modes from
a non-inertial perspective.
Part VI concludes this Dissertation with a summary on the various applications
of Gaussian entanglement not covered by our personal research, a brief discussion
about recent advances in the qualification and quantification of entanglement in
non-Gaussian states — a field of investigation that is to a large extent yet to be
fully explored — and an overview on open problems and current research directions.
Appendix A contains some tools of symplectic analysis necessary for the structural
characterization of the covariance matrix of pure Gaussian states.