On a simple attack, limiting the range transmission of secret keys in a system of quantum cryptography based on coding in a sub-carrier frequency

In the paper by Gleim et al (2016 Opt. Express 24 2619), it was declared that the system of quantum cryptography, exploiting quantum key distribution (QKD) protocol BB84 with the additional reference state and encoding in a sub-carrier, is able to distribute secret keys at a distance of 210 km. The following shows that a simple attack realized with a beam splitter results in a loss of privacy of the keys over substantially smaller distances. It turns out that the actual length of the secret key transmission for the QKD system encoding in the sub-carrier frequency is ten times less than that declared in Gleim et al (2016 Opt. Express 24 2619). Therefore it is impossible to safely use the keys when distributed at a larger length of the communication channel than shown below. The maximum communication distance does not exceed 22 km, even in the most optimistic scenario.