  Quantum information is a common topic of research in many areas of quantum
physics, such as quantum communication and quantum computation, as well as
quantum thermodynamics. It can be encoded in discrete or continuous variable
systems, with the appropriated formalism to treat it generally depending on the
quantum system to be chosen. For continuous variable systems, it is convenient
to employ a quasi-probability function to represent quantum states and
non-classical signatures. The Wigner function is a special quasi-probability
function because it allows to describe a quantum system in the phase space very
similar to the classical one. In this work we consider some informational
aspects of two-mode continuous variables systems. In particular we illustrate
how the mutual information may be useful to transfer the non-Gaussianity
property between two states. Moreover, the coherence of a Gaussian state is
studied when the system is coupled to a thermal reservoir but also with an
extra single-mode Gaussian state. Our results may be, in principle,
investigated in trapped ions setups, where the two-mode system can be encoded
in the vibrational modes of the ion.
