Sending-or-Not-Sending Twin-Field Quantum Key Distribution With Measurement Imperfections

Twin-field quantum key distribution (TF-QKD) protocol can drastically increase the secure transmission distance of quantum key distribution, changing the channel-loss dependence of key rate from
${O} (\eta)$
to
${O} (\sqrt {\eta })$
. To date, many revolutionary protocols have been invented to increase the practical performances of TF-QKD. However, most of them simply assume using symmetric detectors and ideal beam-splitters, which is inconsistent with the actual experiment. Here, we take experimental imperfections of the detection part in TF-QKD into account, for example, the two detectors own different detection efficiencies, different dark count rates, and the reflectivity of the beam-splitter is unbalanced. We employ the sending-or-not-sending twin-field quantum key distribution (SNS TF-QKD) protocol as an example, constructing a more systematic model to analyze its practical performance. Therefore, our work provides an useful reference for the practical implementation of TF-QKD.