This teleportation simulation argument with an infinitely-squeezed resource state is one of the core steps used to establish the bounds in , , , and .

Recently, an important development in the theory of the teleportation simulation of quantum Gaussian channels has taken place [@LMGA17]. In particular, the authors of [@LMGA17] have shown that all single-mode, phase-insensitive quantum Gaussian channels other than the pure-loss channel can be simulated via the action of teleportation on a finite-energy Gaussian resource state that has the same amount of entanglement as the Choi state of the channel. In [@LMGA17], the authors quantified the amount of entanglement in the resource state using an entanglement monotone [@H42007] called logarithmic negativity, which is the same entanglement measure considered in [@NFC09]. In our paper, we show how the main idea of their paper leads to strengthened bounds on the performance of secret-key-agreement protocols conducted over single-mode phase-insensitive bosonic Gaussian channels.

To describe the result of [@LMGA17] in more detail, let $X=\sqrt{\tau
}I_{2}$ and $Y=yI_{2}$ be the matrices representing the action of a single-mode phase-insensitive Gaussian channel on an input state, as in . In what follows and as in [@LMGA17], we exclusively consider the case when $\tau\geq0$. In 