a few channel uses and then use this parameter to calculate an asymptotic key rate (see the review in [@SBCDLP09] for discussions of such approaches).

Conclusion
==========

In this paper, we showed how to extend the teleportation simulation method of [@LMGA17] to the relative entropy of entanglement measure. By combining with prior results in [@WTB16] regarding non-asymptotic secret-key-agreement capacity, this extension leads to improved bounds on the non-asymptotic secret-key-agreement capacity of a thermal bosonic channel, in certain parameter regimes. Given that upper bounds on secret-key-agreement capacity have been advocated as a way to assess the performance of a quantum repeater, our results indicate that previous bounds from [@PLOB15; @WTB16] are too pessimistic, and it should be somewhat easier to demonstrate a working quantum repeater in the realistic regime of a finite number of channel uses.

We remark that our approach can be extended to quantum amplifier channels, but we did not discuss these channels in any detail because they appear to be most prominently physically relevant in exotic relativistic communication scenarios [@bradler2012quantum; @bradler2015black; @QW16]. Our approach also applies to single-mode additive-noise Gaussian channels.

Going forward from here, it would be interesting to generalize our results to multimode bosonic communication channels 