## 1 Introduction  
Quantum key distribution (QKD) is an advanced cryptographic technology which can provide unconditionally secure shared keys for separated users based on the basic laws of quantum mechanics [1]. The first QKD protocol, i.e., BB84 protocol, was proposed by [PERSON] and [PERSON] in 1984, and its security was verified in 2000 [2]. Different kinds of QKD networks based on beam splitters, optical switches, trusted repeaters, etc., have been successfully built and demonstrated [3; 4; 5; 6; 7; 8]. Meanwhile, the improvement of quantum-signal transmission distance and key generation rate have promoted QKD to become practical. As the physical transport layer of communication systems, optical networks accommodate data for various applications such as cloud computing, internet services, and so on. The security of high-speed and large-capacity information transported in optical networks must be guaranteed. Several works have been dedicated to applying QKD technology to provide security solutions for optical networks [9; 10; 11; 12]. In order to avoid the mutual interference of quantum signals and classical signals, a physical dedicated fiber was used for QKD at the beginning. That means quantum signals as well as classical signals are transmitted in different single-mode fibers respectively. However, this led to a significant waste of fiber resources and resulted in a relatively high cost. To solve this problem, a multiplexing manner, i.e., quantum signals and classical signals multiplexed into the same fiber, was proposed. Existing studies show that by adopting wavelength division multiplexing (WDM) technology and implementing proper wavelength isolation as well as wavelength filtering, quantum signals and classic signals can coexist in the same fiber [13; 14; 15; 16; 17; 18]. Although the point-to-point quantum key distribution distance is limited, with the continuous expansion of the quantum key distribution network and the increasing number of users, quantum key distribution has been able to achieve long-distance encrypted communication [19; 20]. The point-to-point QKD system for secure data transmission in optical networks is illustrated in Figure 1a [21]. This is the basic theoretical model of the paper. [PERSON] and [PERSON] configure shared quantum keys for data encryption and decryption on a traditional data channel (TDCh) through a quantum-key channel (QKCh) and a measurable-basis channel (MBCh), which will hereinafter be referred to as key configuration process. QKCh transmits photonic signals with different polarization quantum states, while MBCh sends synchronized clock signals and exchanges measurable-basis information. MBCh and TDCh can be digitally multiplexed together and then share the same wavelengths. Considering MBCh needs to maintain synchronization with QKCh, we assign proprietary wavelengths to build MBCh. Proper wavelengths are reserved for constructing these three types of channels, and then they are multiplexed into the same fiber by WDM technology. By using a nearly optimal wavelength allocation technique, the background noise caused by Raman on the quantum channel can be minimized, thereby maximizing the key generation rate that the quantum channel can achieve [22]. Figure 1b shows an example of wavelengths allocation for different channels on the C-band. By using higher frequency for QKCh, it can reduce Raman scattering effects [23], and reserve a large guard-band (e.g., 200 GHz) between QKCh and other channels to weaken four-wave-mixing effects [16]. Several different solutions are proposed to transport quantum signals and classical signals together over a single fiber. Ref. [24] shows that the best transmission performance of quantum signals was achieved in the C-band. It suggested the QKCh can be located at the highest frequency in the C-band and should have a large guard band between TDCh and MBCh [18].