  Two time-reversal quantum key distribution (QKD) schemes are the quantum
entanglement based device-independent (DI)-QKD and
measurement-device-independent (MDI)-QKD. The recently proposed twin field
(TF)-QKD, also known as phase-matching (PM)-QKD, has improved the key rate
bound from $O\left( \eta \right )$ to $O\left( \sqrt {\eta} \right )$ with
$\eta$ the channel transmittance. In fact, TF-QKD is a kind of MDI-QKD but
based on single-photon detection. In this paper, we propose a different PM-QKD
based on single-photon entanglement, referred to as single-photon
entanglement-based phase-matching (SEPM)-QKD, which can be viewed as a
time-reversed version of the TF-QKD. Detection loopholes of the standard Bell
test, which often occur in DI-QKD over long transmission distances, are not
present in this protocol because the measurement settings and key information
are the same quantity which is encoded in the local weak coherent state. We
give a security proof of SEPM-QKD and demonstrate in theory that it is secure
against all collective attacks and beam-splitting attacks. The simulation
results show that the key rate enjoys a bound of $O\left( \sqrt {\eta} \right
)$ with respect to the transmittance. SEPM-QKD not only helps us understand
TF-QKD more deeply, but also hints at a feasible approach to eliminate
detection loopholes in DI-QKD for long-distance communications.
