  One of the main problems in quantum communications is how to achieve high
rates at long distances. Quantum repeaters, i.e., untrusted, intermediate relay
stations, are necessary to overcome the repeaterless bound which sets the
fundamental rate-distance limit of repeaterless communications. In this work,
we introduce a continuous-variable protocol which overcomes the repeaterless
bound and scales like the single-repeater bound using just one linear-optical
device called a "quantum scissor", combining the entanglement distillation and
entanglement swapping elements of previous repeater proposals into a single
step, thus, removing the need for quantum memories. Implementing a standard
continuous-variable quantum key distribution protocol using our repeater we
predict key rates which surpass the repeaterless bound. Our protocol works well
for non-ideal single-photon sources and non-ideal single-photon detectors, and
can tolerate some level of excess noise, making our protocol implementable with
existing technology. We show that our scheme can be extended to longer repeater
chains using quantum memories, using less physical resources than previous
schemes. Furthermore, for applications beyond key distribution, our scheme
generalises to higher order and distils more entanglement at the cost of a
reduced probability of success.
