General theory of sending-or-not-sending twin-field quantum key distribution. (arXiv:1904.06331v1 [quant-ph])

The Sending-or-Not-Sending (SNS) 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 even
considered finite-key effect. Here we present a general theory that drastically
improves the performance of the SNS protocol. We use the refiened structure of
bit-flip error rate and error rejection through parity check with two-way
classical communications. This drastically improves the performance of the SNS
protocol for the twin-field quantum key distribution. In particular, given
misalignment error of $6\%$, our improved SNS protocol exceeds the linear scale
of key rate even when the dark count rate is as large as $10^{-6}$, and exceeds
a secure distance of 500km even the dark count rate is $10^{-8}$.

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