  The time-reversed version of entanglement-based quantum key distribution
(QKD), called measurement-device-independent QKD (mdiQKD), was originally
introduced to close arbitrary security loopholes of measurement devices. Here
we show that the mdiQKD has another advantage which should be distinguished
from the entanglement-based QKD. In particular, an all-photonic adaptive Bell
measurement, based on the concept of quantum repeaters, can be installed solely
in the mdiQKD, which leads to a square root improvement in the key rate. This
Bell measurement also provides a similar improvement in the single-photon-based
entanglement generation of quantum repeaters.
