# Continuous-Variable Quantum Key Distribution Robust Against Polarization-Dependent Loss
## 1 Introduction  
Quantum key distribution (QKD) is an important application of quantum technology [1; 2]. Continuous-variable (CV) QKD has been explored as an efficient approach to achieve quantum communication [3; 4]. It offers a prospect of higher detection efficiency and secret key rate compared with its discrete-variable (DV) counterpart, giving birth to extensive application perspectives [5; 6; 7; 8; 9]. Since the representative coherent protocol was proposed it has attracted attention and, hence, become one of the mainstream protocols [10; 11; 12; 13]. This protocol can be linked with the current optical fiber communication system, without the need of additional infrastructure construction and equipment configuration [14; 15; 16; 17].  
For the past years, CVQKD has developed towards long-haul and large-capacity transmission, and the channel multiplexing technology is an important approach for establishing practical quantum communication network [18]. In order to improve channel modulation capacity, the elegant technologies--e.g., the positive quadrature phase shift modulation (QPSK) and polarization-division-multiplexing (PDM)--are brought into focus [19]. The latter can double the transmission capacity by using two orthogonal polarizations of a wavelength channel without additional bandwidth resources. For a PDM-coherent optical system, it is important to ensure the orthogonality of two related channels as much as possible. Unfortunately, due to the influence of polarization-dependent loss (PDL) such as multiplexers, splitters, silicon photonics modulators, etc., it will be one of the challenging problems for the PDM-based CVQKD system [20]. The PDL is causedby the crystal dichroism in optical devices. It describes the maximum transmission difference of polarization states, which gives birth to orthogonal polarizations being attenuated in varying degrees. What is more, it will cause an imbalanced signal-to-noise ratio (SNR) between polarizations. However, it still remains an unresolved problem due to its nonunitary nature [21; 22; 23; 24]. An accumulated PDL can be observed after transmission [25]. It would cause increased signal distortion, and consequently obtain a higher error rate, worse secret key rate and transmission distance in the system.  
In order to mitigate the effect of PDL on the PDM-based system, a polarization-pairwise coding (PPC) scheme is proposed to enhance the practical performance. The PPC scheme shows the enhanced performance, which is compared with the Walsh-Hadamard transform that maximizes the coordinate diversity, and its decoder is much simpler than that of the Golden or Silver code [26; 27; 28]. Based on the PPC scheme, we can similarly achieve the PDL mitigation in the CVQKD system, where the CV-polarization is used for quantum communication.  
This paper is organized as follows. In Section 2, we suggest the four-state PDM-based CVQKD protocol with the discrete modulation. In Section 3, we show the influence of PDL on the system and demonstrate the need of mitigating it. In Section 4, we propose the PPC scheme for the system, and present details of coding procedure. In Section 5, we perform a specific proof-of-principle simulation of the proposed scheme in the system with security results. Finally the conclusions are drawn in Section 6.