  Remote state preparation (RSP) provides an indirect way of manipulating
quantum information based on the nonlocal effect of quantum measurement.
Although RSP has been demonstrated in recent years to remotely prepare
multi-photon states, quantum measurement on the same number of photons was
required, i.e., to prepare N-photon states via RSP, quantum measurement on the
other N-photons was required, hence significantly limiting practicality and
applicability of RSP. Here we report the first experimental demonstration of
remote preparation of three-photon entangled states by measuring only a
single-photon entangled with the three photons. We further generalize our
protocol to prepare multi-photon entangled states with arbitrary photon number
and purity via single-photon measurement. As our RSP scheme relies on the
nonlinearity induced by single-photon measurement, it enables quantum state
engineering of multi-photon entangled states beyond the linear optical limit.
Our results are expected to have significant impacts on quantum metrology and
quantum information processing.
