Security of practical quantum key distribution with weak-randomness basis selection

Abstract

The security of the perfect quantum key distribution protocol can be guaranteed by applying the fundamental laws of quantum mechanics, but the practical quantum key distribution system may be attacked by utilizing imperfect state preparation and measurement devices. In this work, we analyze the security of the practical quantum key distribution system with weak-randomness basis selection, where the basis selection may be partly controlled by the eavesdropper due to the imperfect quantum devices. We propose the parameter $\ensuremath{\epsilon}$ to quantify the deviation value between the practical basis selection probability and the perfect basis selection probability, and the secret key rate of the practical quantum key distribution system is obtained under different $\ensuremath{\epsilon}$ values. By applying the practical experimental parameters, the analysis result demonstrates that the maximal transmission distance will be reduced from 142 to 139 km if $\ensuremath{\epsilon}\ensuremath{\le}0.1$, but no secret key can be generated in the case of $\ensuremath{\epsilon}\ensuremath{\ge}0.34$.