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Upper bounds on the secret-key-agreement capacity of a quantum channel serveas a way to assess the performance of practical quantum-key-distributionprotocols conducted over that channel. In particular, if a protocol employs aquantum repeater, achieving secret-key rates exceeding these upper bounds is awitness to having a working quantum repeater. In this paper, we extend a recentadvance [Liuzzo-Scorpo et al., arXiv:1705.03017] in the theory of theteleportation simulation of single-mode phase-insensitive Gaussian channelssuch that it now applies to the relative entropy of entanglement measure. As aconsequence of this extension, we find tighter upper bounds on thenon-asymptotic secret-key-agreement capacity of the lossy thermal bosonicchannel than were previously known. The lossy thermal bosonic channel serves asa more realistic model of communication than the pure-loss bosonic channel,because it can model the effects of eavesdropper tampering and imperfectdetectors. An implication of our result is that the previously known upperbounds on the secret-key-agreement capacity of the thermal channel are toopessimistic for the practical finite-size regime in which the channel is used afinite number of times, and so it should now be somewhat easier to witness aworking quantum repeater when using secret-key-agreement capacity upper boundsas a benchmark.

Upper bounds on secret key agreement over lossy thermal bosonic channels