  Quantum entanglement was termed "spooky action at a distance" in the
well-known paper by Einstein, Podolsky, and Rosen. Entanglement is expected to
be distributed over longer and longer distances in both practical applications
and fundamental research into the principles of nature. Here, we present a
proposal for distributing entangled photon pairs between the Earth and Moon
using a Lagrangian point at a distance of 1.28 light seconds. One of the most
fascinating features in this long-distance distribution of entanglement is that
we can perform Bell test with human supply the random measurement settings and
record the results while still maintaining space-like intervals. To realize a
proof-of-principle experiment, we develop an entangled photon source with 1 GHz
generation rate, about 2 orders of magnitude higher than previous results.
Violation of the Bell's inequality was observed under a total simulated loss of
103 dB with measurement settings chosen by two experimenters. This demonstrates
the feasibility of such long-distance Bell test over extremely high-loss
channels, paving the way for the ultimate test of the foundations of quantum
mechanics.
