The co-fiber quantum-classical signal transmission technology is of great significance for the development of practical quantum secure communication networks. Quantum signals are interfered with the noise resulting from the nonlinear effects, such as Raman scattering (RS), four-wave mixing (FWM), and cross-phase modulation (XPM), of the classical signal in fiber channels. For the above reason, this paper constructs a simulation model for the secure key rate of a continuous-variable quantum key distribution (CVQKD) system based on co-fiber quantum-classical signal transmission. The paper focuses on analyzing the influences of the power of the classical light, channel spacing, and detection method on system noise and key rate. The results show that the FWM noise dominates the short-range transmission process, while the XPM noise is larger than both the RS noise and the FWM noise when the transmission range is longer than 10 km. The total system noise is positively correlated with the power of the classical light and inversely correlated with the spacing of wavelength division multiplexing channels. Under homodyne and heterodyne detection, the variations in the secure key rate with the transmission range exhibit a similar overall trend, although the homodyne detection method achieves a longer maximum transmission range. This paper can provide a reference for the optimal design of practical CVQKD systems based on co-fiber quantum-classical signal transmission.

Focusing on the CVQKD system, this paper builds a co-fiber quantum-classical signal transmission model integrating the RS, FWM, and XPM effects and simulates and analyzes the effects of the three nonlinear effects on system noise and key rate. The research status of co-fiber quantum-classical signal transmission and the focus of this paper are outlined; the simulation model is constructed, and the secure key rate of the CVQKD system, RS, FWM, XPM, and simulation parameter settings are presented; the properties of co-fiber quantum-classical signal transmission are expounded. This paper can provide theoretical support and a reference for co-fiber quantum-classical signal transmission of CVQKD systems in practical environments.

As shown in Fig. 2, the RS noise first increases and then decreases with the increase in the transmission range. The FWM noise exhibits an oscillating distribution as the range increases, and its maximum decreases gradually. The XPM noise increases with the range. When the transmission range is short, the FWM noise is dominant among the three noises. Otherwise, the XPM noise is larger than the RS noise and the FWM noise. In Fig. 3, the total system noise increases with the power of the classical light. As the transmission range increases, the maximum and minimum of the total noise gradually converge, and during long-range transmission, the total noise is approximately positively proportional to the power of the classical light. The differences in the maximum of the total noise under different power of the classical light are much larger in short-range transmission than in long-range transmission. Fig. 4 shows the variation in the total system noise with transmission distance under different channel spacings. The total noise decreases with the increase in channel frequency spacing, and with the increase in the range, the decreasing trend of the noise becomes obvious. The difference between the maximum and minimum of the total noise also decreases as the channel frequency spacing increases. Fig. 5 presents the change in the secure key rate of the CVQKD system with the transmission distance under different power of the classical light. The system's secure key rate gradually decreases with the increase in the transmission distance, and the secret key rate decreases rapidly when the transmission distance reaches a certain value, which is the longest transmission distance that the system can achieve under the corresponding condition. The secret key rate and the maximum transmission distance both decrease with the increase in the power of the classical light.

The RS noise first increases and then decreases with the increase in the transmission distance. The FWM noise is in an oscillating distribution as the range increases. The XPM noise is positively correlated with the transmission distance. When the transmission distance is short, the FWM noise dominates. In contrast, the XPM noise will be larger than both the RS noise and the FWM noise when the transmission distance is longer than 10 km. The total noise increases with the power of the classical light, and during long-range transmission, it is approximately positively proportional to the power of the classical light. Nevertheless, it decreases as the channel frequency spacing increases and decreases more rapidly as the distance increases. The system's secret key rate gradually decreases with the increase in the transmission distance. Large power of the classical light results in a lower secret key rate and a shorter maximum transmission distance that the system can achieve under the same distance. The secret key rate curves under different channel spacings are approximate during short-range transmission. As the transmission distance increases, the curves gradually separate, and the secret key rate and the maximum transmission distance both increase as the channel spacing increases. Under the two detection methods, the overall change trends of the secret key rate curves are close to each other. When the transmission distance is long, the homodyne detection can obtain a higher secret key rate, but the difference is not large. To sum up, the power of the classical light and channel spacing have a great influence on the noise and secret key rate of the system and should thus be selected properly in actual co-fiber classical-quantum signal transmission systems.