  Quantum key distribution (QKD) can help two distant peers to share secret key
bits, whose security is guaranteed by the law of physics. In practice, the
secret key rate of a QKD protocol is always lowered with the increasing of
channel distance, which severely limits the applications of QKD. Recently,
twin-field (TF) QKD has been proposed and intensively studied, since it can
beat the rate-distance limit and greatly increase the achievable distance of
QKD. Remarkalebly, K. Maeda et. al. proposed a simple finite-key analysis for
TF-QKD based on operator dominance condition. Although they showed that their
method is sufficient to beat the rate-distance limit, their operator dominance
condition is not general, i.e. it can be only applied in three decoy states
scenarios, which implies that its key rate cannot be increased by introducing
more decoy states, and also cannot reach the asymptotic bound even in case of
preparing infinite decoy states and optical pulses. Here, to bridge this gap,
we propose an improved finite-key analysis of TF-QKD through devising new
operator dominance condition. We show that by adding the number of decoy
states, the secret key rate can be furtherly improved and approach the
asymptotic bound. Our theory can be directly used in TF-QKD experiment to
obtain higher secret key rate. Our results can be directly used in experiments
to obtain higher key rates.
