of a general protocol that uses the channel $n$ times, with each use interleaved by local operations and classical communication (LOCC), can be bounded from above by the performance of a protocol with a much simpler form: the simplified protocol consists of a single round of LOCC acting on $n$ copies of $\omega_{AB}$ [@BDSW96; @NFC09; @Mul12]. This is called reduction by teleportation. Of course, a secret-key-agreement protocol is one particular kind of protocol of the above form, as considered in [@PLOB15; @WTB16], and so the general reduction method of [@BDSW96; @NFC09; @Mul12] applies.

For continuous-variable bosonic systems, the teleportation simulation of a single-mode bosonic Gaussian channels was considered in [@NFC09], and the simulation therein only simulates the channel exactly in the limit in which the resource state is the result of transmitting one share of an infinitely-squeezed, two-mode squeezed vacuum state [@S17] through the channel (this resource state is sometimes called the Choi state of the channel [@S17], and we use this terminology in what follows). Thus, when applying this argument to bound the rates of secret-key-agreement protocols as discussed above, one must take care with an appropriate limiting argument, as pointed out in [@N16] and handled already in [@WTB16]. 