satisfy the first constraint. We impose the second constraint to ensure that the state we find is a faithful Gaussian state, such that its relative entropy and relative entropy variance to a separable Gaussian state can be easily evaluated using the formulas in and . As discussed above, the relative entropy of entanglement of the resource state should at least be equal to that of the Choi state, in order to simulate a channel. In order to ensure that we find a good upper bound on the secret-key-agreement capacity, we have imposed the third constraint on suboptimal relative entropy of entanglement. We find these states by numerically solving the above constraints with the aid of a computer program [^1], and we remark that finding an analytical solution in this case appears to be far more complicated than for the case from [@LMGA17], due to the fact that the suboptimal relative entropy of entanglement is a much more complicated function of the covariance matrix elements. In some cases, it is possible to find multiple solutions for the states that satisfy these constraints. For our purpose, any of these states can be chosen. We also note that the flexibility afforded by having 