  We propose to adopt redundant space such as polarization mode in the
sending-or-not-sending Twin-Field quantum key distribution (TF-QKD) in the Fock
space. With the help of redundant space such as photon polarization, we can
post-select events according to the outcome of the observation to the
additional quantity. This compresses the bit-flip error rate in the
post-selected events of the SNS protocol. The calculation shows that the method
using redundant space can greatly improve the performance in practical TF-QKD,
especially when the total number of pulses is small.
