  Entanglement distillation is an indispensable ingredient in extended quantum
communication networks. Distillation protocols are necessarily
non-deterministic and require advanced experimental techniques such as
noiseless amplification. Recently it was shown that the benefits of noiseless
amplification could be extracted by performing a post-selective filtering of
the measurement record to improve the performance of quantum key distribution.
We apply this protocol to entanglement degraded by transmission loss of up to
the equivalent of 100km of optical fibre. We measure an effective entangled
resource stronger than that achievable by even a maximally entangled resource
passively transmitted through the same channel. We also provide a
proof-of-principle demonstration of secret key extraction from an otherwise
insecure regime. The measurement-based noiseless linear amplifier offers two
advantages over its physical counterpart: ease of implementation and near
optimal probability of success. It should provide an effective and versatile
tool for a broad class of entanglement-based quantum communication protocols.
