## 4 Conclusions  
We proposed and experimentally demonstrated an efficient MZM bias control method for QKD systems. The proposed method is cost-effective and simplifies the transmitter. This is because it can be implemented using a software modification for bias drift estimation without any additional hardware. This is a crucial advantage of the proposed method, particularly in a QKD network system comprising many users. Unlike the PID control method that converges to the desired setpoint by gradually minimizing errors, the proposed method immediately compensates for the phase drift estimated through the diagnostic pulses. Thus, based on our own experience, it can attain the setpoint faster than the  
Figure 4: Experimental results of the field test: (**a**) Sifted key rates; (**b**) Quantum bit error rates (QBERs); (**c**) Extinction ratios (ERs) of the MZMs. The red, black and blue solid lines are the results of Alice 1-3, respectively. Figure 3: Field deployment and experimental setup of the 1 \(\times\) 3 quantum key distribution (QKD) network system: (**a**) Field deployment in a smart factory in South Korea. Map data: Google, © 2022 Maxar Technologies, TerraMetrics. The insets show the equipment for the transmitter (Alice) and receiver (Bob); (**b**) Experimental setup. Time- and wavelength-division multiplexing were used to establish the 1 \(\times\) 3 network. The lengths (in km) and losses (in dB) of the quantum channels were indicated. The abbreviations are defined as follows: tunable laser driver (TLD); circulator (CIR); beam splitter (BS); single-photon detector (SPD); phase modulator (PM); delay line (DL); polarization beam splitter (PBS); dense wavelength division multiplexer (DWDM); p-i-n photodiode (PINPD); variable optical attenuator (VOA); storage line (SL); and Faraday rotator mirror (FM). conventional PID control method. In addition, the proposed method can be implemented on a parallel processor, such as an FPGA. Finally, there is no significant decrease in the key rate, as only the time slots allocated to the existing decoy pulses are used for diagnostic pulses. We demonstrated the implementation feasibility of the proposed method in a laboratory test and in a field test in a \(1\times 3\) QKD network testbed, which was installed in the security facility of a smart factory in South Korea. In the experimental results, we showed that the proposed method could handle temperature changes and maintained the ERs over 20 dB (bit error rate \(\leq\)1%) for several days, even in an actual network environment. Although the measured ERs did not meet the maximum performance that was provided by the manufacturer (i.e., 30 dB), they were sufficient for application in the QKD system (considering that a maximum error of only 1% was attributed to the 20 dB ER). Furthermore, they can be further improved by optimizing the compensation period, diagnostic pulse proportion and \(N\). As mentioned, the optimal control period strongly depends on the implementation environment. Additionally, it has a trade-off relation with the key generation rate. Thus, to optimize the QKD performance, future researchers should take this into account. As we perceived that the real-time stabilities of the ERs, sifted key rates and QBERs sufficiently showed the feasibility of the proposed method, we did not calculate the secret key rate indicating the overall QKD performance in this study. However, we assume that it is not significantly different from that of the conventional decoy-state BB84 QKDs. This is because our method can be implemented by consuming only the time slots of existing decoy pulses. Based on our experimental results, we believe the proposed method can provide an efficient way to implement an MZM bias control in QKD systems. In the future, we will improve control performance via parameter optimization. In addition, although the current method in this study corresponds to only single MZM bias control, we will develop an advanced one for multiple MZMs for a wide range of applications, such as coherent optical communications.