## 1 Introduction
Our work lays an important theoretical foundation for the practical dual-polarization division multiplexing (DPDM) LLO CV-QKD system. Figure 1: Schematic diagram of the previous pilot-assisted dual-polarization and time multiplexing scheme in the time domain. Pilot tones and quantum signals are placed in the proportion of 1:2. The GMCS quantum signal 1,3 (QSI,3) and pilot tone 1 (PT1)/pilot tone 3 (PT3) are modulated at vertical polarization. Signal 2,4 (QS2,4) and pilot tone 2 (PT2)/pilot tone 4 (PT4) are modulated at horizontal polarization. The Pilot Alternately Assisted Orthogonal Dual-Polarization CV-QKD Scheme Based on Multi-Dimensional Multiplexing Technology  
According to different arrangements of local oscillator (LO), there are two essential CV-QKD schemes, namely the transmitting LO (TLO) and local LO (LLO) CV-QKD [21; 22; 23; 24; 25]. Compared with the TLO scheme, in the LLO scheme, instead of transmitting local oscillator light in the optical fiber channel, the reference light named the pilot tone is transmitted for phase recovery and polarization compensation. As shown in Figure 1, in the previous polarization multiplexing scheme [15; 20], due to the fact that the pilot pulse has the same optical frequency as the quantum signal pulse, the photon leakage from the pilot pulse to the quantum signal is mainly isolated by the time division multiplexing technique. As a result, the degree of pulse isolation is only limited by the interval between the pilot pulse and quantum signal, which is related to the repetition frequency. To control the photon leakage, the repetition frequency and SKR are limited. For higher repetition frequency and SKR, a larger isolation degree between the pilot pulse and quantum signal is required. To further isolate the pilot pulse and the quantum light, the frequency multiplexing method is used in our scheme. As is shown in Figure 2b, the pilot tone is modulated by single-sideband modulation, which can increase the optical bandwidth efficiency and increase the isolation degree. Comparing with modulating the quantum signal, in the actual experiment, it is difficult to modulate the quantum signal with single-sideband modulation, and the quantum signal will become unstable. By the application of single-sideband modulation, the isolation degree between the pilot tone and the quantum signal is increased. Furthermore, by optimizing the pulse distribution of the quantum signal and pilot tone, the crosstalk can be further reduced. As shown in Figure 2a, the quantum signal  
Figure 2: (**a**) Schematic diagram of the pilot alternately assisted orthogonal scheme of dual polarization by the time and frequency multiplexing in the time domain. The GMCS quantum signals 1 (QS1) and 3 (QS3) together with PT1 are modulated at the vertical polarization. The quantum signal 2 (QS2) and 4 (QS4) together with the PT2 are modulated at the horizontal polarization. (**b**) Schematic diagram of the pilot alternately assisted orthogonal scheme of dual polarization by the time and frequency multiplexing in the frequency domain. The frequency of pilot tones, including PT1 and PT2, is shifted in the frequency domain by the single-sideband modulation. The center frequency of PT1 and PT2 is \(f_{A}+f_{m}\). and pilot tone are loaded in the two polarization directions. Without loss of generality, the proportion of 4:1 for signal and pilot pulse is set in this paper, as shown in Figure 2a. Here, the quantum signal is modulated as a Gaussian modulated coherent state (GMCS). Specifically, the quantum signals 1 (QS1) and 3 (QS3) together with PT1 are modulated at the vertical polarization. The GMCS quantum signals 2 (QS2) and 4 (QS4) together with the PT2 are modulated at the horizontal polarization. In previous works, we found that the crosstalk is mainly from PT1 and PT2, which constrained the repetition frequency and limited the SKR of the dual-polarization LLO CV-QKD system. To further optimize the isolation between quantum and pilot tone signals, frequency division multiplexing (FDM) technology is also used.