of the following forms$$\mathbf{G}=\left(
\begin{array}{cc}
g &  \\
& g\end{array}
\right) :=g\mathbf{I,~G}=\left(
\begin{array}{cc}
g &  \\
& -g\end{array}
\right) :=g\mathbf{Z}.$$ Here the parameter $g$ must satisfy $|g|\leq\mu-1$, so that $\mathbf{V}_{Aa}$ is both physical and separable [@twomodes]. Apart from the singular case $g=0$, this symmetric Gaussian state has always non-zero discord, i.e., $D(A|a)=D(a|A)>0$ [@VeriDISCO].

Mode $a$ is sent through the channel, where Eve performs a collective Gaussian attack, whose most general description can be found in Ref [colleGAUSS]{}. Assuming random permutations (so that quantum de Finetti applies), this is the most powerful attack against Gaussian protocols [RMP2]{}. One of the canonical forms of this attack is the so-called ‘entangling cloner’ attack [@RMP2], where Eve uses a beam splitter with transmissivity $\tau$ to mix the incoming mode $a$ with one mode $e$ of an EPR state $\rho_{eE^{\prime}}$ with CM $$\mathbf{V}_{eE^{\prime}}=\left(
\begin{array}{cc}
\omega\mathbf{I} & \sqrt{\omega^{2}-1}\mathbf{Z} \\
\sqrt{\omega^{2}-1}\mathbf{Z} & \omega\mathbf{I}\end{array}
\right) :=\mathbf{V}(\omega),   \label{Vomega}$$ where $\omega\geq1$. One output mode $B$ is sent to Bob, while the other output mode $E$ is stored in a quantum memory together with the retained mode $E^{\prime}$. Such memory will be coherently detected at the end of the protocol.

In order to extract two correlated (complex) variables, $X$ and $Y$, 