  The linear time-dependent constants of motion of the parametric amplifier are
obtained and used to determine in the tomographic-probability representation
the evolution of a general two-mode Gaussian state. By means of the
discretization of the continuous variable density matrix, the von Neumann and
linear entropies are calculated to measure the entanglement properties between
the modes of the amplifier. The obtained results for the nonlocal correlations
are compared with those associated to a linear map of discretized symplectic
Gaussian-state tomogram onto a qubit tomogram. This qubit portrait procedure is
used to establish Bell-type's inequalities, which provide a necessary condition
to determine the separability of quantum states, which can be evaluated through
homodyne detection. Other no-signaling nonlocal correlations are defined
through the portrait procedure for noncomposite systems.
