  In the last two decades, many quantum optics experiments have demonstrated
small-scale quantum information processing applications with several photons.
Beyond such proof-of-principle demonstrations, efficient preparation of large,
but definite, numbers of photons is of great importance for further scaling up
and speeding up photonic quantum information processing. Typical single-photon
generation techniques based on nonlinear parametric processes face challenges
of probabilistic generation. Here we demonstrate efficient synchronization of
photons from multiple nonlinear parametric heralded single-photon sources
(HSPSs), using quantum memories (QMs). Our low-loss optical memories greatly
enhance (~30x) the generation rate of coincidence photons from two independent
HSPSs, while maintaining high indistinguishability (95.7%) of the synchronized
photons. As an application, we perform the first demonstration of HSPS-based
measurement-device-independent quantum key distribution (MDI-QKD). The
synchronized HSPSs demonstrated here will pave the way toward efficient quantum
communication and larger scale optical quantum computing.
