in recent experiments on generating and testing the extent of entanglement in CV systems, the variances of suitably chosen conjugate observables and the corresponding standard quantum limit alone are used  [@ExptCVentang]. We reiterate that these merely capture the extent of linear correlations between two states.

The second indicator (to be denoted by ${\varepsilon_{\small\textsc{bd}}}$) that we introduce and use is arrived at as follows. In probability theory, the mutual information [@ITCoverThomas] between two continuous random variables $X$ and $Y$ can be expressed in terms of the Kullback-Leibler divergence $D_{\textsc{kl}}$ [@kullback] between their joint probability density $p_{XY}(x,y)$ and the product of the corresponding marginal densities $p_{X}(x)= \int  p_{XY}(x,y) dy$ and $p_{Y}(y) = \int p_{XY}(x,y) dx$, as [@MI_KL_link] $$D_{\textsc{kl}}[p_{XY}\!:\!p_{X}p_{Y}] 
= \int \!dx \int\!dy \,p_{XY}(x,y)\,\log_{2} \,
\frac{p_{XY}(x,y)}{p_{X}(x) p_{Y}(y)},
\label{eqn:KLmutualinfo}$$ The quantity ${\varepsilon_{\small\textsc{tei}}}({\theta_{\textsc{a}}},{\theta_{\textsc{b}}})$ defined in Eq. is precisely the mutual information in the case of optical tomograms (which are continuous probability distributions): $${\varepsilon_{\small\textsc{tei}}}({\theta_{\textsc{a}}},{\theta_{\textsc{b}}})= 
D_{\textsc{kl}}
\big[w(X_{{\theta_{\textsc{a}}}},{\theta_{\textsc{a}}};X_{{\theta_{\textsc{b}}}},{\theta_{\textsc{b}}})\!:\! w_{\textsc{a}}(X_{{\theta_{\textsc{a}}}},\theta) w_{\textsc{b}}(X_{{\theta_{\textsc{b}}}},{\theta_{\textsc{b}}})\big]. 
\label{eqn:KL_MI_link}$$ A simpler alternative for our purposes is provided by the Bhattacharyya distance $D_{\textsc{b}}$ [@KL_BD_link] between $p_{XY}$ and $p_{X}p_{Y}$, defined as $$D_{\textsc{b}}[p_{XY}\!:\!p_{X}p_{Y}] =  
 -\log_{2}\,\Big\{\int \!dx\int \!dy \,\big[p_{xy}(x,y) 
p_{X}(x) p_{Y}(y)\big]^{1/2}\Big\}. 
\label{eqn:Bhattmutualinfo}$$ Using Jensen’s inequality, it is easily shown that $D_{\textsc{b}} \leqslant \frac{1}{2} D_{\textsc{kl}}$. $D_{\textsc{b}}$ thus gives us an approximate 