# Practical Real-Time Phase Drift Compensation Scheme for Quantum Communication Systems
## 3 Experiment and Results  
We perform our scheme on an FSMI-based quantum communication system, as schematically shown in Figure 2. A fiber laser produces 1550 nm photon pulses with a width of 50 ps and a repetition frequency of 1.25 GHz; an intensity modulator attenuates the optical pulses to \(\mu=0.6\) photons per pulse combined with an attenuator. Benefiting from the sophisticated design of the FSMI, the polarization disturbance in the system need not be considered. The delay of the interferometers is 400 ps and both interferometers are equipped with a phase modulator on their long arms. The phase modulator has three drive voltage interfaces, two of which are RF interfaces for random phase modulation with a repetition frequency of 1.25 GHz and one is a direct current (DC) bias interface for phase compensation. A 12-bit digital-to-analog converter (DAC) is employed for phase tracking, allowing for a total range of 12V and providing a precision of 2.93 mV. The coded pulses are then sent to [PERSON] over a 50 km fiber channel. After transmission, the photons pass through [PERSON]'s FSMI and finally detected by two InGaAs single photon detectors (SPDs), whose average detection efficiency, dark count rate, and afterpulse probability are 20 %, \(1\times 10^{-6}\), and 1.4 %, respectively. It should be noted that, before transmission, we obtain the initialization parameters and \(e_{0}=1.59\) % (shown as Figure 3) through a scanning process. Figure 1: The main flowchart of the real-time phase drift compensation scheme. Calc, the calculation module to calculate the incremental driving voltage \(\Delta V_{i}\) using the initial parameters and \(e_{i}\); P, I, and D respectively represent the proportional, integral, and derivative components; \(\sum\) sum of the three components. To better simulate the complex field environments, a hot air fan is used to blow the interferometer for about half an hour, followed by a subsequent cooling treatment. Figure 4 depicts the experimental results obtained from running the system for 1 h. The results demonstrate a high overall stability of the system, with an average QBER value of 1.69% and a standard deviation of 0.0813%. However, a noticeable difference is still observed compared to the previously measured value \(e_{0}\). Considering the rapid velocity of phase shift, in order to mitigate this discrepancy, we increase the frequency of feedback compensation from 1 s to 0.1 s per iteration. Figure 5 illustrates the test results under similar experimental conditions as before, showing a distinct decrease in QBER. The average value and standard deviation reached 1.62% and 0.0687%, respectively. Moreover, the standard deviation decreased to 0.0425% when performing statistical calculations at a rate of every 1 s. This result validates the effectiveness of improving the feedback speed in enhancing  
Figure 3: QBER verse Driving Voltage of the phase modulator. Figure 2: Schematic of the experimental setup. IM, intensity modulator; FSMI, asymmetric Faraday–Sagnac–Michelson interferometer; BS, beam splitter; FM, Faraday mirror; PBS, polarization beam splitter; FR, Faraday rotator; PM, phase modulator; ATT, attenuator; CIR, circulator; SPD, single-photon detector. The yellow lines represent polarization-maintaining fibers (PMFs), and the blue ones are single-mode fibers (SMFs). the overall system performance. It should be noted that both sets of experimental results exhibit noticeable periodic fluctuations in QBER, primarily occurring during full-cycle voltage adjustments due to limited driving voltage. This is mainly attributed to insufficient modulation bandwidth of the modulation electrode and its temperature-dependent half-wave voltage drift. The limited modulation bandwidth results in a longer time required for the modulator to reach the target value. During this period, the optical pulses passing through the modulator are subjected to inaccurate modulation. Additionally, the inaccuracy in the half-wave voltage directly leads to errors in the modulation voltage.