  High-quality long-distance entanglement is essential for both quantum
communication and scalable quantum networks. Entanglement purification is to
distill high-quality entanglement from low-quality entanglement in a noisy
environment and it plays a key role in quantum repeaters. The previous
significant entanglement purification experiments require two pairs of
low-quality entangled states and were demonstrated in table-top. Here we
propose and report a high-efficiency and long-distance entanglement
purification using only one pair of hyperentangled states. We also demonstrate
its practical application in entanglement-based quantum key distribution (QKD).
One pair of polarization spatial-mode hyperentanglement was distributed over 11
km multicore fiber (noisy channel). After purification, the fidelity of
polarization entanglement arises from 0.771 to 0.887 and the effective key rate
in entanglement-based QKD increases from 0 to 0.332. The values of
Clauser-Horne-Shimony-Holt (CHSH) inequality of polarization entanglement
arises from 1.829 to 2.128. Moreover, by using one pair of hyperentanglement
and deterministic controlled-NOT gate, the total purification efficiency can be
estimated as 6.6x10^3 times than the experiment using two pairs of entangled
states with spontaneous parametric down-conversion (SPDC) sources. Our results
offer the potential to be implemented as part of a full quantum repeater and
large scale quantum network.
