## Non-markovian quantum dynamics

##### Abstract

Quantum systems can necessarily be viewed as open systems. As in classical
physics, any realistic description of a system must take into account the cou-
pling to an environment that strongly in
uences the system itself. Since perfect
isolation of a quantum system is not feasible and the complete description of the
degrees of freedom of the environment is not possible, it is required a description
that accounts for these aspects. Furthermore, not all the degrees of freedom are
of interest in order to e ectively describe the system. Hence a probabilistic ap-
proach to a quantum evolution is most appropriate: the idea is to consider only
the degrees of freedom that are useful, thus reducing to a small set the number
of variables needed to describe the evolution of the system.
In last years the remarkable progress of quantum technologies opened up
new perspective in the investigation of the dynamics of open systems; in this
sense, particularly relevant are the techniques which allow to control the degrees
of freedom of the environment that in
uence the system of interest. Till now
the attention was focused on the methods to reduce the detrimental e ect on
the quantum properties of the system-environment interaction; namely, on the
methods allowing to make the system the more isolated as possible. On the
other hand, it has been experimentally checked that in situations requiring ef-
fective quantum transfer a system-environment coupling can become a resource:
an example is provided by e cient quantum-information processing , in which
the present thesis is speci cally framed. The question is that a set of approxi-
mations usually exploited in describing quantum evolution (collectively known
as Markovian approximation) are too strong to carefully manage some quantum
phenomena.
The aim of this thesis is twofold. On the one hand, the characterization
and quanti cation of non-Markovian content for continuous-variable quantum
systems; on the other hand, its possible usefulness as a resource in the frame-
work of Quantum Information. The attention is focused mainly on the class of
Gaussian states and Gaussian channels; this choice is motivated by their exper-
imental relevance, and by the advantage to pass from the in nite-dimensional
Hilbert space to a nite-dimensional Hilbert space because, in this case, we
can exploit the nite-dimensional matrix analysis. However, we consider also
some non-Gaussian resources, which are anyway needful for implementing uni-
versal quantum computation, an potentially more powerful for all the quantum
protocols. [edited by author]