in the tomograms also reveal nonlinear correlations between the quadrature variables $X_{{\theta_{\textsc{a}}}}$ and $X_{{\theta_{\textsc{b}}}}$ (top panel). For instance, the tomogram slice on the top right shows a probability distribution that is essentially unimodal and symmetric about the origin with the annular structures diminished in magnitude. It is clear that this case is less correlated than the tomogram in the top left corner. This conforms to the observed trend in the extent of entanglement (compare $\xi_{\textsc{svne}}$ corresponding to $k=0$ and $k=2$ at $\omega_{1}=0$ in (b)). Again, in the bottom panel of the figure, the sub-structures in the patterns increase with increasing $k$, signifying a higher degree of nonlinear correlation. This is in consonance with the trend in the entanglement at $\omega_{1}=1$ ( (b)). We therefore expect ${\varepsilon_{\small\textsc{tei}}}$ and its averaged version $\xi_{\textsc{tei}}$ to be much better entanglement indicators than ${\varepsilon_{\small\textsc{pcc}}}$ and $\xi_{\textsc{pcc}}$. We also mention here that the current experimental techniques of testing CV entanglement based on the variances and covariances of suitably chosen observables [@ExptCVentang] are not as effective as calculating nonlinear correlators, for the same reason.

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![image](tomo_0_index_3_xp_vary_omega1_lambda_quarter.eps){width="30.00000%"} ![image](tomo_1_index_3_xp_vary_omega1_lambda_quarter.eps){width="30.00000%"} ![image](tomo_2_index_3_xp_vary_omega1_lambda_quarter.eps){width="30.00000%"}\
![image](tomo_0_index_4_xp_vary_omega1_lambda_quarter.eps){width="30.00000%"} ![image](tomo_1_index_4_xp_vary_omega1_lambda_quarter.eps){width="30.00000%"} ![image](tomo_2_index_4_xp_vary_omega1_lambda_quarter.eps){width="30.00000%"}

Our detailed investigations reveal that $\xi_{\textsc{tei}}$ and $\xi_{\textsc{ipr}}$ follow the trends in $\xi_{\textsc{svne}}$ reasonably 