## 4 Discussion  
Based on the quantum theory of electro-optical modulator and the quantim theory of open systems we developed a model that describes the influence of polarization divergence of a signal propagating through an OF on QBER for SCW QKD.  
It was shown that the polarization divergence can be viewed as two separate effects. The first one is due to birefringence and it can be compensated for by waveplates. However, there is also a second dichroism-related effect that cannot be compensated for in any way. It was explicitly demonstrated that QBER is dependent on \(\Delta\) that indicates dichroism. Fortunately, analysis reveals that dichroism-related contribution for QBER is rather weak. It should be stated that the development of this model was motivated mostly by the necessity of minimizing QBER for the purpose of the increase of the efficiency of SCW QKD protocol performance. Even a few percent of the considered contribution to QBER is worthy of concern.  
The simplest way of minimizing QBER resulting from polarization divergence is the utilization of electro-optical modulators whose modulation efficiency is not dependent on polarization of the optical signal. In addition, there is still birefringence that should be taken into account. Thus, it is necessary to compensate for this negative effect. It can be performed with the help of active [43] or passive [8] additional subsystems of compensation of polarization distortion. However, the additional optical parts of the scheme provide higher losses at the receivers (Bob) block and hence decrease the performance of the system.  
All things considered, the above work may be summarized by the fairly simple conclusion that utilization of polarization-independent schemes is necessary for the maintenance of sustainable SCW QKD system operation. Based on the results of our study, the authors may recommend utilizing electro-optical phase modulators whose modulation efficiency is not dependent on polarization of the modulated optical signal or additional subsystems of compensation of polarization distortion; however, the former is slightly preferable.  
Individual contributions are as follows: conceptualization, G.M.; methodology, A.G. and A.K.; software, A.G.; formal analysis, A.G., A.K. and G.M.; writing-original draft preparation, S.M. and A.G.; writing-review and editing, S.M. and A.G.; visualization, S.M. and A.G.; supervision, G.M.; project administration, A.K.; funding acquisition, A.G. and A.K. All authors have read and agreed to the published version of the manuscript.  
The work was done by Leading Research Center \"National Center of Quantum Internet\" of ITMO University during the implementation of the government support program, with the financial support of Ministry of Digital Development, Communications and Mass Media of the Russian Federation and RVC JSC; Grant Agreement ID: 000000007119P190002, agreement No. 006-20 dated 27.03.2020.  
The authors declare no conflict of interest.  
The following abbreviations are used in this manuscript:  
\begin{tabular}{l l} QKD & Quantum Key Distribution \\ SCW & Subcarrier Wave \\ OF & Optical Fiber \\ QBER & Quantum Bit Error Rate \\ \end{tabular}