  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.
