  We consider a quantum relay which is used by two parties to perform several
continuous-variable protocols: Entanglement swapping, distillation, quantum
teleportation, and quantum key distribution. The theory of these protocols is
extended to a non-Markovian model of decoherence characterized by correlated
Gaussian noise. Even if bipartite entanglement is completely lost at the relay,
we show that the various protocols can progressively be reactivated by the
separable noise-correlations of the environment. In fact, above a critical
amount, these correlations are able to restore the distribution of
quadripartite entanglement, which can be localized into an exploitable
bipartite form by the action of the relay. Our findings are confirmed by a
proof-of-principle experiment and show the potential advantages of
non-Markovian effects in a quantum network architecture.
