## 4 Bounds on Excess Noise
### Excess Noise Correction  
Obviously, if we can offset the excess noise caused by Trojan horse attacks, then this will not be discovered by [PERSON] and [PERSON]. Previous studies have shown that [PERSON] can estimate the deviation of emitted noise by inserting pulses of different wavelengths. The coupling ratio of fiber BS is closely related to the wavelength of input light: at the specified central wavelength, the fused biconical taper fiber BS has good working characteristics. However, if it deviates from the central wavelength, the BS ratio will periodically vary with the input wavelength. In the practical homodyne detection CV-QKD system, the transmittance of BS is controlled by preparing photons of different wavelengths. Then,  
Figure 6: Total excess noise induced by Trojan horse attacks with various input powers in homodyne detection. Figure 7: Noise induced by Trojan horse attacks with various input powers in homodyne detection. by selecting the appropriate light intensity, the excessive noise added by the Trojan horse attack can be corrected. In our CV-QKD system, [PERSON]'s laser source is divided into two coherent signal beams: a strongly attenuated quantum signal and a strong LO. The \(x\) and \(p\) quadratures of the coherent state are modulated according to the modulation variance \(V_{A}\) by using a 5 GS/s digital-to-analog converter. The signal light and LO light are modulated in phase and amplitude, using time and polarization multiplexing, and then they are sent together into standard telecommunication fiber. Polarization multiplexing is achieved by using Faraday mirrors(FM) and polarizing beam splitters(PBS). On the receiving side, [PERSON] randomly measures the \(x\) or \(p\) quadrature of these states by using the LO in the homodyne detector of the 1 GHz bandwidth shot-noise limit of the quantum signal pulse interference. The security of the system depends on the estimation of light transmittance and excess noise during the parameter estimation process. This CV-QKD system has certain loopholes: the proportional relationship between the shot noise measured by the detector and the light intensity of the LO is pre-determined by [PERSON]. Using the relationship between the two, [PERSON] can estimate the size of shot noise \(N_{0}\) by detecting the light intensity of LOs, and take it as a unit to measure the excess noise (see in Figure 8). [PERSON] intercepts the signal light and LO light sent by [PERSON], and uses heterodyne detection to simultaneously obtain the information of the \(X\) and \(P\) variables of the signal state, denoted as \(X_{E}\) and \(P_{E}\). Applying the measurement results, [PERSON] prepares the coherent state \(\mid\alpha_{E}=\sqrt{T}(X_{E}+iP_{E}))\) with the same polarization as the original signal state. Prepare the LO with amplitude \(\alpha_{LO}\), the polarization is the same as the original. [PERSON] compresses and delays the width of the pulses to delay [PERSON]'s measurement time, reducing the measurement result to \(\mu(\mu<1)\) times the peak value. Prepare two additional light pulses, denoted \(s\) and \(lo\). Polarization of pulse \(s\) is the same as the original signal state, polarization of pulse \(lo\) is the same as the original LO. Finally, [PERSON] places the prepared four pulses within the same original pulse width time, and sends them to [PERSON] through the non-attenuation channel. In the latest CV-QKD system, an amplitude modulator (AM) is added to the signal path. [PERSON] randomly applies an AM with attenuation ratios \(r_{1}\approx 0\) and \(r_{2}\approx 1\) to measure the real-time emission noise level. In this paper, we set \(r_{1}\) and \(r_{2}\) to 0.001 and 1, respectively. The input light wavelength and transmittance of the fused biconical taper BS have the following relationship:  
\[T=F^{2}\text{sin}^{2}(\frac{C\lambda^{5/2}w}{F})=\text{sin}^{2}(AX)\equiv T( \lambda), \tag{16}\]  
Figure 8: Schematic diagram of CV-QKD with excess noise correction.