  The quantum systems with finite-dimensional Hilbert space have several
applications and are intensively explored theoretically and experimentally. The
mathematical description of these systems follows the analogy with the usual
infinite-dimensional case. There exist finite versions for most of the elements
used in the continuous case, but (to our knowledge) there does not exist a
finite version corresponding to the mixed Gaussian states. Our aim is to fill
this gap. The definition we propose for the mixed discrete Gaussian states is
based on the explicit formulas we have obtained in the case of pure discrete
variable Gaussian states.
