Upper bounds on the secret-key-agreement capacity of a quantum channel serve
as a way to assess the performance of practical quantum-key-distribution
protocols conducted over that channel. In particular, if a protocol employs a
quantum repeater, achieving secret-key rates exceeding these upper bounds is a
witness to having a working quantum repeater. In this paper, we extend a recent
advance [Liuzzo-Scorpo et al., arXiv:1705.03017] in the theory of the
teleportation simulation of single-mode phase-insensitive Gaussian channels
such that it now applies to the relative entropy of entanglement measure. As a
consequence of this extension, we find tighter upper bounds on the
non-asymptotic secret-key-agreement capacity of the lossy thermal bosonic
channel than were previously known. The lossy thermal bosonic channel serves as
a more realistic model of communication than the pure-loss bosonic channel,
because it can model the effects of eavesdropper tampering and imperfect
detectors. An implication of our result is that the previously known upper
bounds on the secret-key-agreement capacity of the thermal channel are too
pessimistic for the practical finite-size regime in which the channel is used a
finite number of times, and so it should now be somewhat easier to witness a
working quantum repeater when using secret-key-agreement capacity upper bounds
as a benchmark.Comment: 16 pages, 1 figure, minor change
