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 (TF-QKD) has its advantage of unconditional security proof under any coherent attack and fault tolerance to large misalignment error. So far this is the only coherent-state based TF-QKD protocol that has considered finite-key effect, the statistical fluctuations. Here we consider the complete finite-key effects for the protocol and we show by numerical simulation that the protocol with typical finite number of pulses in practice can produce unconditional secure final key under general attack, including all coherent attacks. It can exceed the secure distance of 500 $km$ in typical finite number of pulses in practice even with a large misalignment error.

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