  The Quantum Key Distribution protocol can encode a single quantum state and
implements an information-theoretically secure key distribution protocol in
communication. In the actual QKD experimental system, there are usually two
encoding methods which are phase encoding and polarization encoding. Ma et
al.[Phase-Matching Quantum Key Distribution, Phys. Rev. X., 2018, 8(3)]
proposed the phase-matching QKD protocol, which has high transmission and it is
an extension of the measurement device independent QKD. This paper successfully
gives the polarization scheme of this PM-QKD protocol, the bases in the
polarization scheme are arbitrary, and eliminates detector side channel
attacks. Furthermore, we give the security analysis and simulation results of
the polarization scheme, and compare it with the BB84 protocol. The simulation
results show that our protocol is superior to the BB84 protocol in terms of
transmission distance under the fixed key rate.
