  Quantum repeaters are indispensable for high-rate, long-distance quantum
communications. The vision of a future quantum internet strongly hinges on
realizing quantum repeaters in practice. Numerous repeaters have been proposed
for discrete-variable (DV) single-photon-based quantum communications.
Continuous variable (CV) encodings over the quadrature degrees of freedom of
the electromagnetic field mode offer an attractive alternative. For example, CV
transmission systems are easier to integrate with existing optical telecom
systems compared to their DV counterparts. Yet, repeaters for CV have remained
elusive. We present a novel quantum repeater scheme for CV entanglement
distribution over a lossy bosonic channel that beats the direct transmission
exponential rate-loss tradeoff. The scheme involves repeater nodes consisting
of a) two-mode squeezed vacuum (TMSV) CV entanglement sources, b) the quantum
scissors operation to perform nondeterministic noiseless linear amplification
of lossy TMSV states, c) a layer of switched, mode multiplexing inspired by
second-generation DV repeaters, which is the key ingredient apart from
probabilistic entanglement purification that makes DV repeaters work, and d) a
non-Gaussian entanglement swap operation. We report our exact results on the
rate-loss envelope achieved by the scheme.
