Measurement-device-independent quantum key distribution for Scarani-Acin-Ribordy-Gisin 04 protocol

The measurement-device-independent quantum key distribution (MDI QKD) was proposed to make BB84 completely free from any side-channel in detectors. Like in prepare & measure QKD, the use of other protocols in MDI setting would be advantageous in some practical situations. In this paper, we consider SARG04 protocol in MDI setting. The prepare & measure SARG04 is proven to be able to generate a key up to two-photon emission events. In MDI setting we show that the key generation is possible from the event with single or two-photon emission by a party and single-photon emission by the other party, but the two-photon emission event by both parties cannot contribute to the key generation. On the contrary to prepare & measure SARG04 protocol where the experimental setup is exactly the same as BB84, the measurement setup for SARG04 in MDI setting cannot be the same as that for BB84 since the measurement setup for BB84 in MDI setting induces too many bit errors. To overcome this problem, we propose two alternative experimental setups, and we simulate the resulting key rate. Our study highlights the requirements that MDI QKD poses on us regarding with the implementation of a variety of QKD protocols.