  We study the Separability of the noncommutative (NC) space coordinate degrees
of freedom with the generalized Peres-Horodecki separability criterion (Simon's
condition) for a bipartite Gaussian state. Non-symplectic nature of the
transformation between the usual commutative space and NC space restricts the
use of Simon's condition in NCS. We transform the NCS system to an equivalent
Hamiltonian in commutative space through Bopp shift, which enables the
utilization of the separability criterion in NC space. For afairly general
study, we consider a bilinear Hamiltonian with time-dependent (TD) parameters,
along with a TD external interaction, which is linear in field modes. The
system is transformed into canonical form keeping the intrinsic symplectic
structure ($Sp(4,\mathbb{R})$) intact. The solution of the TD-Schr\"{o}dinger
equation is obtained with the help of Lewis-Riesenfeld invariant method (LRIM).
Expectation values of the observables (thus the covariance matrix ) are
constructed from the states obtained from LRIM. It turns out that the existence
of the NC parameters in the oscillator determines the separability of the
states. In particular, for isotropic oscillators, the separability condition
for the bipartite Gaussian states depends on NC parameters. Moreover,
anisotropic parameter values for the oscillator affects the separability. In
other words, both the deformation parameters ($\theta,\;\eta$) and parameter
values of the oscillator are important for the separability of bipartite
states. Thus tuning the parameter values, one can destroy or recreate the
separability of states. With the help of toy models, we have demonstrated TD-NC
space parameters effect on separability.
