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

The sending-or-not-sending protocol of the twin-field quantum key distribution (TFQKD) has its advantage of unconditional security under any coherent attack and fault tolerance to a large misalignment error. Here, we consider the complete finite-key effects for the protocol and we calculate the secure key rate with a fixed security coefficient. The numerical simulation shows that the protocol with a typical finite number of pulses in practice can produce an unconditional secure final key under general attack, including all coherent attacks. It can exceed the secure distance of 500 km in a typical finite number of pulses in practice even with a large misalignment error.