Unconditional security of sending or not sending twin-field quantum key distribution with finite pulses. (arXiv:1904.00192v3 [quant-ph] UPDATED)

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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