  A two-pass fiber-optic quantum key distribution system with phase-encoded
photon states in synchronization mode has been investigated. The possibility of
applying the analytical expressions for the calculation of the correct
detection probability of the signal time window at synchronization has been
proved. A modernized algorithm of photon pulse detection, taking into account
the dead time of the single-photon avalanche photodiode was proposed. The
method of engineering an optical pulse detection process during the
synchronization in a quantum key distribution system has been offered.
