  Quantum key distribution (QKD) stands as a pioneering method for establishing
information-theoretically secure communication channels by utilizing the
principles of quantum mechanics. In the security proof of QKD, the phase error
rate serves as a critical indicator of information leakage and directly
influences the security of the shared key bits between communicating parties,
Alice and Bob. In estimating the upper bound of the phase error rate, phase
randomization and subsequent postselection mechanisms serve pivotal roles
across numerous QKD protocols. Here we make a precise phase error rate analysis
for QKD protocols with phase postselection, which helps us to accurately bound
the amount of information an eavesdropper may obtain. We further apply our
analysis in sending-or-not-sending twin-field quantum key distribution
(SNS-TFQKD) and mode-pairing quantum key distribution (MP-QKD). The simulation
results confirm that our precise phase error analysis can noticeably improve
the key rate performance especially over long distances in practice. Note that
our method does not require alterations to the existing experimental hardware
or protocol steps. It can be readily applied within current SNS-TF-QKD and
MP-QKD for higher key rate generation.
