  Underwater quantum key distribution (QKD) has potential applications in
absolutely secure underwater communication. However, the performance of
underwater QKD is limited by the optical elements, background light, and dark
counts of the detector. In this paper, we propose a modified formula for the
quantum bit error rate (QBER), which takes into account the effect of detector
efficiency on the QBER caused by the background light. Then we calculate the
QBER of the polarization encoding BB84 protocol in Jerlov type seawater by
analyzing the effect of the background light and optical components in a more
realistic situation. Finally, we further analyze the final key rate and the
maximum secure communication distance in three propagation modes, i.e., upward,
downward and horizontal modes. We find that secure QKD can be performed in the
clearest Jerlov type seawater at a distance of hundreds of meters, even in the
worst downward propagation mode. Specifically, by optimizing the system
parameters, it is possible to securely transmit information with a rate of
67kbits/s at a distance of 100 m in the seawater channel with an attenuation
coefficient of 0.03/m at night. For practical underwater QKD, the performance
can also be improved by using decoy states. Our results are useful to long
distance underwater quantum communication.
