## 1 Introduction  
Nowadays, the majority of quantum key distribution systems (QKD) are implemented by utilizing weak coherent states. Examples are point-to-point [1; 2] and twin-field systems with three parties [3; 4; 5; 6]. Further examples are systems based on phase modulated multi-frequency states known as subcarrier wave QKD (SCW QKD) [7; 8]. In addition, the state preparation approach utilized in SCW QKD can also be applied to a twin-field QKD system [9]. Different protocols can be implemented by using phase-modulated weak coherent states, including widely-used BB84-like protocol [10; 11] (four phase states equally distributed in the phase plane with phase difference between neighboring state as \(\pm\frac{\pi}{2}\)), and the B92 protocol [12] (two phase states with phase difference \(\pm\pi\)). The first SCW QKD setup has been proposed by the group of [PERSON] [13; 14]; it implements B92 protocol with phase modulation. Thereafter, the implementation of BB84-like protocol has been demonstrated for the SCW scheme by the same group using amplitude modulation [15]. The replacement of phase modulation by amplitude modulation was necessary for decoding all states at the receiver's side. In the last decade, the latter approach was expanded to the subcarrier multiplexing technique, which allows the authors of [16] to increase the key generation rate in several times. Another variation of the system was proposed in [17]. The authors show the possibility of implementing a strong reference technique by monitoring the intensity of the carrier wave. A version of the BB84-like protocol with phase modulation has recently been demonstrated by several authors of this work in [7; 8; 9; 18]. Proposed in the latter papers approach allows to decode only one state in each <<basis>> (the word basis only means two states with the phase difference \(\pm\pi\)). Moreover, recently it was shown that SCW QKD systems can utilize homo- or heterodyne detection schemes for continuous variable protocols [19]. Modulated multi-mode states are prepared by single frequency-mode coherent states, generated with laser beam, modulated by an electro-optical modulator. Detailed explanation of phase modulation's quantum regime is given in [20], and the structure of phase modulated states is shown in Equation (1). Briefly, information coding is made by choice of the modulation signal phase (made by the sender) and decoding is based on the fact that detection event should only be in case of matching second modulation signal. The second modulation process is similar to interference. Our study describes the process of second modulation in the case of modulation indices mismatch resulting from difference in the orientation of signal polarization at the fist and the second modulations (in general effective indices of modulation depend on polarization); divergence of the orientation of signal polarization is introduced by propagation through optical fiber (OF). It also should be noted that since the construction of the experimental setups for discrete variable and continuous variable SCW QKD systems are quite similar, except for the detection method. Proposed analysis is suitable for both discrete and continuous types of variables (where the second modulation takes place). The dielectric permittivity tensor in general is complex and anisotropic [21; 22; 23; 24]. The real and the imaginary parts of the tensor determine birefringence and dichroism in the OF respectively; both phenomena also depend on the signal frequency. Changes in dielectric permittivity tensor of the OF may be caused by inhomogenities and impurities in the structure of the fiber or by physical impact on OF (bends and torsions) or by external impacts (temperature fluctuations, vibrations, magnetic fields, etc.). The above-mentioned phenomena affect the polarization state of the signal.