2 (so that these states are Hamming-uncorrelated), if $k_{1}\neq k_{2}$. Participation ratios are valid measures of entanglement for superpositions of Hamming-uncorrelated states in spin systems [@ViolaBrown]. We have demonstrated in our earlier work that $\xi_{\textsc{ipr}}$ effectively mimics standard measures of entanglement in CV systems as well. In the present instance, the eigenstates $\ket{\psi_{N,k}}$ are superpositions of the states $\lbrace \ket{j,N-j} \rbrace$ which are Hamming-uncorrelated for different values of $j$. This is the reason for the usefulness of $\xi_{\textsc{ipr}}$ as an entanglement indicator even for larger values of $\lambda$.

![Correlation of $\xi_{\textsc{svne}}$ with $\xi$-indicators (left), with ${\varepsilon}$-indicators for the slice ${\theta_{\textsc{a}}}=0,{\theta_{\textsc{b}}}=\frac{1}{2}\pi$ (centre), and with ${\varepsilon}$-indicators for the slice ${\theta_{\textsc{a}}}=0,{\theta_{\textsc{b}}}=0$ (right), for the eigenstates $\ket{\psi_{4,k}}, 
 \,0 \leqslant k \leqslant 4$ in the BEC model.[]{data-label="fig:CorrPlotN4VaryOmega1"}](correlation_matrix_plot_4_bec_vary_omega1_lambda_quarter_mult.eps "fig:"){width="30.00000%"} ![Correlation of $\xi_{\textsc{svne}}$ with $\xi$-indicators (left), with ${\varepsilon}$-indicators for the slice ${\theta_{\textsc{a}}}=0,{\theta_{\textsc{b}}}=\frac{1}{2}\pi$ (centre), and with ${\varepsilon}$-indicators for the slice ${\theta_{\textsc{a}}}=0,{\theta_{\textsc{b}}}=0$ (right), for the eigenstates $\ket{\psi_{4,k}}, 
 \,0 \leqslant k \leqslant 4$ in the BEC model.[]{data-label="fig:CorrPlotN4VaryOmega1"}](correlation_matrix_plot_4_bec_vary_omega1_lambda_quarter_xp.eps "fig:"){width="30.00000%"} ![Correlation of $\xi_{\textsc{svne}}$ with $\xi$-indicators (left), with ${\varepsilon}$-indicators for the slice ${\theta_{\textsc{a}}}=0,{\theta_{\textsc{b}}}=\frac{1}{2}\pi$ (centre), and with ${\varepsilon}$-indicators for the slice ${\theta_{\textsc{a}}}=0,{\theta_{\textsc{b}}}=0$ (right), for the eigenstates $\ket{\psi_{4,k}}, 
 \,0 \leqslant k \leqslant 4$ in the BEC model.[]{data-label="fig:CorrPlotN4VaryOmega1"}](correlation_matrix_plot_4_bec_vary_omega1_lambda_quarter_xx.eps "fig:"){width="30.00000%"}

We now proceed to examine quantitatively the 