  We present a high-fidelity quantum teleportation experiment over a high-loss
free-space channel between two laboratories. We teleported six states of three
mutually unbiased bases and obtained an average state fidelity of 0.82(1), well
beyond the classical limit of 2/3. With the obtained data, we tomographically
reconstructed the process matrices of quantum teleportation. The free-space
channel attenuation of 31 dB corresponds to the estimated attenuation regime
for a down-link from a low-earth-orbit satellite to a ground station. We also
discussed various important technical issues for future experiments, including
the dark counts of single-photon detectors, coincidence-window width etc. Our
experiment tested the limit of performing quantum teleportation with
state-of-the-art resources. It is an important step towards future
satellite-based quantum teleportation and paves the way for establishing a
worldwide quantum communication network.
