Tomographic entanglement indicators in a coupled oscillator model

We study entanglement in a simple model comprising two coupled linear harmonic oscillators of the same natural frequency. The system is separable in the center of mass (COM) and relative coordinates into two oscillators of frequency $\omega_c$ and $\omega_r$. We compute standard entanglement measures (subsystem linear entropy and subsystem von Neumann entropy) as well as several tomographic entanglement indicators (Bhattacharyya distance, Kullback-Leibler divergence and inverse participation ratio) as functions of the frequency ratio $\eta = \omega_c/\omega_r$, keeping the COM oscillator in the ground state. We demonstrate that, overall, the entanglement indicators reflect quite faithfully the variations in the standard measures. The entanglement is shown to be minimum at $\eta = 1$ and maximum as $\eta \to 0$ or $\infty$.