  The discretization of the density matrix is proposed as a nonlinear positive
map for systems with continuous variables. This procedure is used to calculate
the entanglement between two modes through different criteria, such as Tsallis
entropy, von Neumann entropy and linear entropy and the logarithmic negativity.
As an example, we study the dynamics of entanglement for the two-mode squeezed
vacuum state in the parametric amplifier and show good agreement with the
analytic results. The loss of information on the system state due to the
discretization of the density matrix is also addressed.
