We investigate the secret key rates for the recently proposed intensity-modulated dual-threshold key distribution [T. Ikuta and K. Inoue, New J. Phys. 18 (2016)] under beam splitting attacks. We show that previous assumptions on an eavesdropper that performs hard decision measurements on the channel, overestimates the secret key rate. We discuss the impact of an eavesdropper that can measure full soft information and give the secret key rates under forward and reverse reconciliation. Further, we perform simulations for different system assumptions and show the optimal modulation depths for these systems. We also outline an attack on this protocol based on photon counting that prohibits secret key generation.
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