The bi-partite Gaussian state, corresponding to an anisotropic harmonic
oscillator in a noncommutative-space, is investigated with the help of the
Simon’s separability condition (generalized Peres-Horodecki criterion). It
turns out that, in order to exhibit the entanglement between the noncommutative
co-ordinates, the parameters (mass and frequency) have to satisfy an unique
constraint equation. Exact solutions for the system are obtained after
diagonalizing the model, keeping the intrinsic symplectic structure intact. It
is shown that, the identification of the entangled degrees of freedom is
possible by studying the Wigner quasiprobability distribution in phase-space.
We have shown that the co-ordinates are entangled only with the conjugate
momentum corresponding to other co-ordinates.