Unconditional Security of Sending or Not Sending Twin-Field Quantum Key Distribution with Finite Pulses

For encrypted communication, the ``sending or not sending'' protocol of twin-field quantum key distribution has the advantages of proven unconditional security against any coherent attack, and fault tolerance to large misalignment error. The existing security proof is based on infinite key length, however. Here the authors consider the complete finite-key effects for this protocol under the universally composable framework. Numerical simulation shows that in practice this scheme can exceed a secure distance of 500 km for a typical, finite number of pulses, even with large misalignment error. The results of this work could be directly applied in experiment.