## 3 Experimental Results  
We performed experiments in a laboratory and in the field. The experimental setup for the laboratory test is shown in Figure 2. A 1550 nm distributed feedback (DFB) laser was used for generating continuous-wave (CW) light. The MZM used in the experiment was an AZ-0S5-10-PFU-PFU (EOSpace Inc., USA) model, which utilizes a Z-cut LiNbO\({}_{3}\) crystal optimized for a wavelength of 1550 nm and has a bandwidth of up to 10 GHz. A refrigerant spray was used to abruptly reduce the temperature of the MZM. The control method was implemented on a STM32 Nucleo-144 board with a STM32F413 ZH microcontroller unit (MCU). We set \(N=4\), considering the accumulation time and random bit consumption for the diagnostic signals. The desired bias point was set to the null point, and an adjustment interval of \(1^{\circ}\) was used to calculate \(p_{Ti}\left(\theta_{drift}^{T}\right)\) in Equation (3). A 16-bit digital-to-analog converter and a 12-bit analog-to-digital converter built on the STM32 board were used to generate the diagnostic signals and to measure the output of the photodiode (PD). We measured the output intensities of the MZM, which was spray-cooled using a refrigerant (SF-1013), with and without the proposed control method. As shown in Figure 2b, the output stability depended on whether the proposed method was employed or not. The output intensity with the bias control (red solid line) remained at the desired null point, whereas the intensity without the bias control (black solid line) fluctuated. Figure 2c shows the direct-current (DC) bias voltage (blue solid line) used to compensate for the phase drifts, which were estimated using the MZM output intensities of the four diagnostic signals, as shown in Figure 2d. The phase drift (Step 4 in Section 2) was estimated from the output voltage of the PD instead of the photon counts of the SPD because CW light was used in the laboratory test. The fluctuation near 3.5 min in Figure 2c was attributed to an MZM \(V_{2\pi}\) of approximately 7 V.  
In the field test, we applied the control method to a real testbed, namely, a 1 \(\times\) 3 QKD network system installed in a secure communication system of a smart factory in South Korea. The field deployment of the QKD network system and its corresponding experimental setup are shown in Figure 3. The control system was implemented using a personal computer and an FPGA board equipped with multiple 16-bit digital-to-analog converters, instead of the STM32 board used in the laboratory test. Although different hardware platforms were used, parameters such as \(N\), the step interval and the desired setpoint had similar values in both tests. Each transmitter (Alice) had an individual control system and performed the steps described in Section 2 at the respective time slots allocated via time-division multiplexing. We set the count accumulation time of the diagnostic pulses to approximately 5 min because there were no significant phase drifts during a 5 min window (in the facility's communication room); this means that the bias drift was compensated every 5 min. As mentioned, the optimal accumulation time depends on the QKD system parameters, such as temperature, channel loss, detection efficiency and pulse intensity. The field test results are shown in Figure 4. We measured the extinction ratios (ERs) of the MZMs and QKD performance parameters, such as sifted key rates and quantum bit error rates (QBERs), over 4-5 days. Figure 4a,b show the sifted key rates and QBERs of the 1 \(\times\) 3 QKD network, respectively. Figure 4c shows the ERs of the MZMs. During the test period, all the ERs were maintained over 20 dB, and satisfactory QKD performances were achieved. There was no significant difference in the stabilities despite the different counts owing to the different channel losses. These results indicate that the proposed method could maintain MZM stability in an actual network environment.