Prepare and Measure (PM) protocol such as GG02 where Alice sends coherent states to Bob who measures them, is to consider an equivalent Entanglement-Based (EB) protocol. In the latter, Alice prepares two-mode squeezed vacuum states of which she measures one mode with a heterodyne detection and sends the second mode to Bob. Interestingly, before Alice and Bob measure their respective modes, their share a bipartite state $\rho_{AB}$. In this paper, we will restrict our attention to collective attacks, meaning that at the end of the protocol, Alice and Bob share $n$ copies of that state, that is, $\rho_{AB}^{\otimes n}$.

In general, one cannot perform a perfect tomography of this state, simply because it lives in an infinite dimensional Hilbert space. In the case of protocols without postselection, this is not a problem since the secret key rate can be safely computed from the the Gaussian state with the same first two moments as $\rho_{AB}$ [@GC06; @NGA06]. This is remarkable because one only needs to compute the covariance matrix of the state instead of its whole density matrix.

Unfortunately, this approach fails in the case of protocols with postselection. Indeed, one would then need to compute the covariance matrix of the 