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Underwater quantum key distribution (QKD) has potential applications inabsolutely secure underwater communication. However, the performance ofunderwater QKD is limited by the optical elements, background light, and darkcounts of the detector. In this paper, we propose a modified formula for thequantum bit error rate (QBER), which takes into account the effect of detectorefficiency on the QBER caused by the background light. Then we calculate theQBER of the polarization encoding BB84 protocol in Jerlov type seawater byanalyzing the effect of the background light and optical components in a morerealistic situation. Finally, we further analyze the final key rate and themaximum secure communication distance in three propagation modes, i.e., upward,downward and horizontal modes. We find that secure QKD can be performed in theclearest Jerlov type seawater at a distance of hundreds of meters, even in theworst downward propagation mode. Specifically, by optimizing the systemparameters, it is possible to securely transmit information with a rate of67kbits/s at a distance of 100 m in the seawater channel with an attenuationcoefficient of 0.03/m at night. For practical underwater QKD, the performancecan also be improved by using decoy states. Our results are useful to longdistance underwater quantum communication.

Performance of Underwater Quantum Key Distribution with Polarization Encoding