## 2 PnP QKD Decoy System with Amplification Structure
When this pulse was amplified at the initial OA, the vertical and horizontal components were amplified at amplification rates of \(G_{V}\) and \(G_{H}\), respectively. \[\text{Pulse}=(A\times G_{V})|V\rangle+(B\times G_{H})|H\rangle. \tag{2}\]  
Figure 1: PnP QKD architecture with decoy system. The overall structure is similar to the original PnP QKD, but an optical amplifier (OA), band pass filters (BPFs), a circulator, and an attenuator have been added for generating decoy pulses in Alice. An initial pulse is generated in Bob’s laser diode and then passed through an asymmetric Mach–Zehnder interferometer to generate a time-bin pulse. At this time, to create a similar intensity of pulses of \(|f\rangle\) and \(|s\rangle\), the phase modulator in Bob is placed behind the polarization beam splitter. Amplification-based decoy states are generated at OA using double amplification method. The circulator in Alice is used to monitor the output signal, and it plays a role in large attenuation of the pulse passing in the reverse direction of the circulator, as well. After that, the pulse is precisely attenuated to a single-photon level by the attenuator of Att_1 and transmitted to Bob. (FM: Faraday mirror (NFRM-15, General photonics), PM: phase modulator (PM-055, Eospace), BPF: Bandpass filter (of003, Fiberpia), OA: optical amplifier (SOA1117P, Thorlabs), SL: storage line, Cir: circulator (FPCR-155, Haphitt), BS: beam splitter (FPCL-1550, Haphitt), PD: photodiode (TPA-4 NN3, Teradian), Att: attenuator (bc, Fiberpia), QC: quantum channel (single-mode fiber), PBS: polarization beam splitter (PBS-1550, AC photonics), DL: delay line (polarization-maintaining fiber), SPD: single-photon detector (SPD_a_M2, Aurea), LD: laser diode (FRL 15 DCWA-A81-19330, Fitel [1550.92 nm]). The amplified pulse was reflected from FM, and the polarization changed orthogonally. \[\text{Pulse}=(A\times G_{V})|H\rangle+(B\times G_{H})|V\rangle. \tag{3}\]  
If the pulse was amplified in OA again,  
\[\text{Pulse}=(A\times G_{V}\times G_{H})|H\rangle+(B\times G_{H}\times G_{V})|V\rangle. \tag{4}\]  
The results of Equation (4) show that both the H and V components are amplified at the same amplification rate, \(G_{V}\times G_{H}\). When amplified using the proposed structure, no pulse distortion occurred. As long as the output of the OA is not saturated, the double amplification method works well. Third, the pulse reaching OA must be larger than \(-50\) dBm. During operation, the OA generates noise by itself to the level of \(-30\) dBm. Considering the gain (approximately 20 dBm), the intensity of the input pulse must be greater than \(-50\) dBm to distinguish pulse from noise. Thus, three technical issues that may arise due to the characteristics of the OA itself can be resolved successfully. However, there is still one more technical difficulty when implementing attenuation. Because the pulse is amplified at OA in the proposed structure, much more attenuation is needed to make a single-photon-level pulse. If large attenuation is implemented with a typical passive attenuator for lowering the intensity to the single-photon level, it attenuates the input pulse of Alice as well; therefore, the intensity of the pulse at OA may drop below \(-50\) dBm. On the other hand, unlike the general PnP QKD, our proposed structure uses a circulator as the main attenuator. In the pulse path of 2 in Figure 1, the input pulse is not attenuated, and only the output pulse in the pulse path of 4 is significantly attenuated (around 40 dBm). With the aid of Att_1, an accurate attenuation rate for generating single-photon-level pulses is precisely adjusted. In addition, the OA output pulse proceeding in the forward direction of the circulator (2) can be easily measured with a general photodiode. This makes it easy to monitor the output pulse, which was difficult in the conventional PnP-type structure, and by using it, it can also defend efficiently against [PERSON]'s Trojan horse attack [22, 23]. Figure 2: Gain of OA according to polarization and optical input power.