Measurement-device-independent quantum key distribution with all-photonic adaptive Bell measurement

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.