Long-distance optical quantum channels are necessarily lossy, leading to errors in transmitted quantum information, entanglement degradation and, ultimately, poor protocol performance. Quantum states carrying information in the channel can be probabilistically amplified to compensate for loss, but are destroyed when amplification fails. Quantum correction of the channel itself is therefore required, but break-even performance—where arbitrary states can be better transmitted through a corrected channel than an uncorrected one—has so far remained out of reach. Here we perform distillation by heralded amplification to improve a noisy entanglement channel. We subsequently employ entanglement swapping to demonstrate that arbitrary quantum information transmission is unconditionally improved—i.e., without relying on postselection or post-processing of data—compared to the uncorrected channel. In this way, it represents realization of a genuine quantum relay. Our channel correction for single-mode quantum states will find use in quantum repeater, communication and metrology applications.