  This thesis deals with the study of quantum communication protocols with
Continuous Variable (CV) systems. Continuous Variable systems are those
described by canonical conjugated coordinates x and p endowed with infinite
dimensional Hilbert spaces, thus involving a complex mathematical structure. A
special class of CV states, are the so-called Gaussian states. With them, it
has been possible to implement certain quantum tasks as quantum teleportation,
quantum cryptography and quantum computation with fantastic experimental
success. The importance of Gaussian states is two-fold; firstly, its structural
mathematical description makes them much more amenable than any other CV
system. Secondly, its production, manipulation and detection with current
optical technology can be done with a very high degree of accuracy and control.
Nevertheless, it is known that in spite of their exceptional role within the
space of all Continuous Variable states, in fact, Gaussian states are not
always the best candidates to perform quantum information tasks. Thus
non-Gaussian states emerge as potentially good candidates for communication and
computation purposes.
