## 2 PnP QKD Decoy System with Amplification Structure  
The proposed structure was implemented as shown in Figure 1. The main flow of the pulse is as follows:  
1. [PERSON] generates a strong laser pulse (1550.92 nm) with a gain-switched laser. Then, the pulse passes through the asymmetric Mach-Zehnder interferometer and is divided into a time-bin pulse \(|f\rangle+|s\rangle\) and transmitted to [PERSON]. Now, in our scheme, \(|f\rangle\) has horizontal polarization, while \(|s\rangle\) has vertical polarization. 2. After passing through the QC, some part of the strong pulse that reaches [PERSON] branches to \(\circled{\circ}\). The rest goes to an attenuator (Att_1) forward-directed circulator (Cir), storage line (SL), bandpass filter, and OA. 3. The OA amplifies the intensity of the pulse. Noise from the OA is reduced by a bandpass filter. Subsequently arriving at the phase modulator (PM), which is used for phase encoding and randomization, the pulse is then attenuated at Att_2, reflected from the Faraday mirror (FM), and proceeded backward to OA. Then, it is amplified once again in OA. 4. The pulse proceeds in reverse order of 2. At this point, most of the pulse power is delivered in the circulator's forward direction, 2. The only rest weak power of the pulse is transmitted to att_1, and it is fine-tuned to a single-photon level at [PERSON]'s output. 5. The single-photon level pulse passes through the QC and reaches [PERSON]'s PM. Decoding starts through this PM. After passing [PERSON]'s asymmetric Mach-Zehnder interferometer, it reaches the beam splitter (BS) and interferes. The results of the interference can be known from the measurement results of the single-photon detectors (SPDs). 6. A pulse that splits from the BS of [PERSON] reaches photo diode_1 (PD_1). This pulse enables the timing control of [PERSON]'s device. Moreover, measuring the intensity of the pulse may help to adjust the intensity of [PERSON]'s initial laser pulse. 7. This is the forward flow of the circulator. It is connected to PD_2, and the output pulse can be monitored through PD_2. The intensity of each pulse for the decoy-state protocol can be controlled by driving the OA component. In this case, the control of the OA is achieved with simple open-loop control without complicated feedback control. In addition, the OA control timing is easily adjusted using the time detected by PD_1. The ideal OA gives the desired amplification regardless of the characteristics of the input pulses. However, in reality, a semiconductor optical amplifier (SOA) has a few technical issues that need to be addressed. These are from a device imperfection. First, the pulse intensity to reach an OA must be less than \(-25\) dBm. If this is not the case due to an output pulse saturation problem on the typical OA, the amplification rate drops abruptly. It is difficult to control the intensity without distorting the pulse if the pulse is amplified in the range where gain drops abruptly (input intensity \(>-25\) dBm). By adjusting the intensity of [PERSON]'s initial transmission pulse, or the attenuation rate of Att_1, a pulse less than \(-25\) dBm is input to the OA. Second, as shown in Figure 2, OA still has a polarization dependence characteristic. A single-mode fiber, which is often used as a QC, does not maintain pulse polarization. Therefore, the pulse transmitted from [PERSON] to [PERSON] becomes randomly polarized. Typically, amplifying the pulse with random polarization causes pulse distortion because the amplifier's gain in the vertical and horizontal components is different. To solve the polarization issue, we installed FM and Att_2 and used the double amplification method. FM reflects the phase of the pulse orthogonally, and Att_2 makes the pulse become less than \(-25\) dBm. A pulse with randomly polarization is expressed as the vertical and horizontal components as follows:  
\[\text{Pulse}=A|V\rangle+B|H\rangle,\ |A|^{2}+|B|^{2}=1 \tag{1}\]  
where \(A\) and \(B\) are the intensities of each component.