Sending-or-not-sending twin-field quantum key distribution with redundant space

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 postselect events according to the outcome of the observation to the additional quantity. This compresses the bit-flip error rate in the postselected 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.