  In present-day quantum communications, one of the main problems is the lack
of a quantum repeater design that can simultaneously secure high rates and long
distances. Recent literature has established the end-to-end capacities that are
achievable by the most general protocols for quantum and private communication
within a quantum network, encompassing the case of a quantum repeater chain.
However, whether or not a physical design exists to approach such capacities
remains a challenging objective. Driven by this motivation, in this work, we
put forward a design for continuous-variable quantum repeaters and show that it
can actually achieve the feat. We also show that even in a noisy regime our
rates surpass the Pirandola-Laurenza-Ottaviani-Banchi (PLOB) bound. Our
repeater setup is developed upon using noiseless linear amplifiers, quantum
memories, and continuous-variable Bell measurements. We, furthermore, propose a
non-ideal model for continuous-variable quantum memories that we make use of in
our design. We then show that potential quantum communications rates would
deviate from the theoretical capacities, as one would expect, if the quantum
link is too noisy and/or low-quality quantum memories and amplifiers are
employed.
