## 3 Method and Results  
An experiment was conducted to verify the feasibility of the structure described in Figure 1. First, the characteristics of the OA to be used were experimentally verified. We used an SOA of SOA1117P (Thorlabs) as an OA. For supplying an input current of 400 mA to the SOA, an SOA driver of SOA-std (Aerodiode) was used. After that, we set the laser of FRL 15 DCWA-A81-19330 (Fitel) to have vertical polarization, and it was inputted to the OA while changing the power. The amplified output pulse from the OA was measured with an optical power meter of PM100D (Thorlabs). Afterward, the same experiment was repeated by setting the laser to horizontal polarization. Next, the double amplification method was experimentally verified. Experiments were performed with laser pulses that had a pulse width of 3 ns. The pulses input to the OA were time-bin pulses \(|f\rangle\) and \(|s\rangle\). \(|f\rangle\) is a pulse that passes through a short path (BS-PBS) among the divided pulses in BS, and \(|s\rangle\) is that which passes through a long path (BS-delay line (DL)-PBS) in [PERSON]'s system, as shown in Figure 1. The time interval between time-bin pulses \(|f\rangle\) and \(|s\rangle\) is 100 ns. In PD_1 of TPA-4 NN3 (Teradian), the original time-bin pulses \(|f\rangle\) and \(|s\rangle\) are measured. We measured the output value of the PD using an oscilloscope of RTM 3K (Rohde and Schwarz). At this time, intensity of \(|s\rangle\) is subtly smaller than \(|f\rangle\) owing to the insertion loss of DL. In PD_2, \(|f\rangle\) and \(|s\rangle\) of the amplified pulse are measured. When there is no difference in amplification rate due to polarization, the intensity ratio of \(|f\rangle\) and \(|s\rangle\) of the original pulse and the amplified pulse becomes the same. It is important to confirm that the amplification rate of the OA is reproducibly constant. For verifying reproducibility, we measured 10,000 times. Next, an experiment was conducted to adjust the intensity of the pulse by controlling the OA input current. We adjusted the OA input current from 350 to 450 mA and verified whether we could produce a pulse (signal (average photon number: 0.5), decoy (average photon number: 0.1), vacuum pulse) of the desired intensity. The interference visibility of the MZ interferometer formed by [PERSON] and [PERSON] was measured using an amplified pulse. Except for the vacuum state, it was measured using the signal and decoy pulses. The interference visibility can be obtained from the result of a pair of SPD of SPD_A_M2 (Aurea) measurements of [PERSON] according to the change in the input pulse of [PERSON]'s PM of PM-055-12 (Eospace). Finally, we measured the key generation rate and QBER. Except for the QC, we implemented an experimental setup, as shown in Figure 1. QC was replaced with a passive attenuator (5 dB), which has the same attenuation rate as QC (25 km, single-mode fiber, 0.2 dB/km (1550 nm)). As in the previous experiment, the width of the generated laser pulse was 3 ns, and the interval between \(|f\rangle\) and \(|s\rangle\) was 100 ns. A single-photon was detected with an SPD using gate mode. The detector had a gate width of 4 ns and a detection efficiency of 15%. The OA was controlled through a simple open-loop control to generate signal pulses and decoy pulses. We conducted static modulation for signal and decoy pulse intensities. The measurement results of the change in the OA's amplification rate according to the input pulse intensity and polarization are shown in Figure 2. As mentioned earlier, OA's gain drops abruptly when the pulse power input is higher than \(-\)25 dBm. Additionally, the amplification gain is different depending on the polarization. The double amplification method experiment results are shown in Figure 3. The results show that the original pulses have an intensity ratio of 1:0.82 and the amplification pulses have an intensity ratio of 1:0.82. The results show that the double amplification method amplifies pulse intensity regardless of its polarization.