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Abstract
We have developed a simple time-bin phase encoding quantum key distribution system, using the optical injection locking technique. This setup incorporates both the merits of simplicity and stability in encoding, and immunity to channel disturbance. We have demonstrated the field implementation of quantum key distribution over long-distance deployed aerial fiber automatically. During the 70-day field test, we achieved approximately a 1.0 kbps secure key rate with stable performance. Our work takes an important step toward widespread implementation of QKD systems in diverse and complex real-life scenarios.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
In today’s information age, various demands of data transmission arise every day, with growing requirements of the bandwidth [1]. Optical fiber, due to its ultra-high bandwidth and ultra-low loss, is a suitable candidate as the medium for data transmission. Optical fiber communication has become the foundation of modern communication, and most data are transmitted through optical fiber networks. However, the security of optical fiber communication is becoming increasingly prominent due to the threat posed by quantum computing [2,3] to asymmetric-key cryptosystems [4]. To combat these threats, it is urgent to find new secure communication methods. One promising solution is quantum key distribution (QKD) [4–6], which shares secure keys between separated parties by transmitting quantum states in the physical layer. When combined with the symmetric encryption approach, information-theoretically secure communication can be achieved [5,6]. Since the first QKD protocol proposed in 1984 (BB84) [7], QKD has achieved considerable developments both theoretically and experimentally [4–6,8]. In particular, the decoy-state scheme has been proposed [10–12] to resist photon-number-splitting (PNS) attack [13] assuring the security of weak coherent photon sources, and the measurement-device-independent (MDI) QKD [14] as well as the twin-field (TF) QKD [15] were proposed to resist all detection-side attacks. Experimental research into QKD has been extensively conducted both in the laboratory [16–19] and in deployed networks [20–24], and its effective distance has extended to 421 km using point-to-point fiber link [25], 1000km using the TF QKD [26,27], and 1200 km using free-space link [28]. The achievable secure key rate has exceeded 100Mbps [29]. QKD has now entered the large-scale application stage [9], being employed in backbone QKD networks [30–32] and metropolitan QKD networks [33,34]. Chip-based integrated QKD systems have also been reported [35,36].
In optical fiber communication networks, besides the buried and ducted fiber, aerial fiber is also widely used [37]. Aerial fiber is a preferred choice in suburban and rural aeras, where it is difficult to lay buried fiber or ducted fiber cables. In particular, aerial fiber cables are widely deployed in the power supply network, known as the Optical Fiber Composite Overhead Ground Wire (OPGW) [38,39]. However, unlike the buried and ducted fiber, aerial fiber is more susceptible to external conditions such as natural climate and human factors [40,41], making it challenging for long-distance quantum key distribution in this fast-changing scenario.
In this work, we propose a time-bin phase encoding setup for quantum key distribution based on optical injection locking (OIL) [42]. Unlike the traditional approach, this new setup is modulator-free and does not require an intensity modulator or phase modulator for quantum state encoding. As a result, it offers intrinsic stability, simplicity, and practical security advantages. Furthermore, it is immune to channel disturbance and has a low insertion loss of time-bin basis decoding, making it ideal for stable and high-speed secure key generation. We develop compact terminals for a quantum key distribution system based on this setup and conduct experiments over an aerial fiber link deployed in Urumqi City, Xinjiang Province, China. Our scheme can be used also for establish QKD network between different countries [32].
2. Experimental setup
The field experiment in an aerial fiber scenario was implemented in Urumqi City, Xinjiang Province, China. The transmitter Alice is placed at the node of Xinjiang Astronomical Observatory (N43$^{\circ }$51’56.29", E87$^{\circ }$34’18.71"). The receiver Bob is placed at Nanshan Observation Stationare (N43$^{\circ }$28’42.16", E87$^{\circ }$11’11.62"). The link of the field test is shown in Fig. 1. It features a fiber length of 87.28 km and an overall attenuation of 23.27 dB, including 60.95-km-long aerial fiber and 26.33-km-long buried fiber, separated in the Cangfanggou telecom business hall (N43$^{\circ }$45’51.05", E87$^{\circ }$35’16.34"). This region is special in the geographical and climatic conditions, and there are often strong winds which affect the deployment environment of aerial fiber.
Fig. 1. Plan view showing the experimental site in the field test of QKD over the deployed aerial fiber link. The fiber length is 87.28 km for the whole link, with the overall loss of 23.27 dB. LD: laser diode, BS: beam splitter, ISO: isolator, PM: phase modulator, FDL: fiber delay line, CIR: circulator, VOA: variable optical attenuator, FBG: fiber Bragg grating, DWDM: dense wavelength-division multiplexer, FM: Faraday Mirror, APD: avalanche photodiode.
At the transmitter, the time-phase encoding scheme is realized based on the OIL technique. The pulses from the master laser #0 pass through the AMZI in a reverse manner to lock both master lasers #1 and #2. Thus, these master lasers can share the same original global phase, as well as the same wavelength to avoid any potential information leakage through wavelength difference [43]. Then, the pulses of master lasers #1 and #2 are inputted to the same AMZI through the first BS from two different ports with an intrinsic $\pi /2$ phase difference. After passing through the AMZI, the pulse of master laser #1 (#2) splits into two equal parts with a phase difference of $\Delta (\Delta + \pi )$, where $\Delta$ is determined by the path length of the AMZI. The AMZI has a 1.6 ns time delay between its two arms. Subsequently, the two equal parts of master laser #1 (#2) are injected into the slave laser via a circulator or a BS to lock the slave laser.
The master and slave lasers are triggered at 312.5 MHz and 625 MHz respectively, thereby giving an effective system repetition rate of 312.5 MHz because two time-bins are required for a single qubit state. To prepare the states in the phase basis, two successive electrical signals of the slave laser in one system period should be above the lasing threshold, and master laser #1 (#2) outputs a seed pulse to modulate the $|{X_0}\rangle (|{X_1}\rangle )$ state. Since the phase difference of the two pulse parts of master laser #1 differs from that of master laser #2 by $\pi$, the two successive pulses of the slave laser locked by two pulse parts of master laser #1 can maintain a phase difference of $\pi$ from that locked by master laser #2. To prepare states on a time-bin basis, two successive electrical signals of the slave laser should be above and below the lasing threshold, respectively, for the $|{Z_0}\rangle$ state, and vice versa for the $|{Z_1}\rangle$ state. In this situation, either master laser #1 or #2 is required to output a seed pulse to lock the slave laser. As seen, this scheme takes advantage of the phase difference between the two arms of AMZI to modulate $|{X_0}\rangle$ and $|{X_1}\rangle$, thereby avoiding the use of phase modulators or high-performance driving electrics. Furthermore, it utilizes gain switching of the pulse laser instead of IM to modulate $|{Z_0}\rangle$ and $|{Z_1}\rangle$, and thus have the merit of stable encoding of the time-bin basis.
A Sagnac-based IM (Sag-IM) [44–46] is used to realize the decoy state modulation [10–12] and normalize the average photon numbers in the two bases. Intrinsic intensity stability is maintained due to the inherent common-path interference mechanism in the Sagnac interferometer. Then a 99:1 BS and one PIN detector are adopted to monitor the signal intensity for feedback. An isolator and a fiber Bragg grating (FBG) filter with a circulator are used to prevent against any injected attacking light [47]. Another PIN detector is connected to the circulator and actively detects injected attacking light [47].
At the receiver, a BS is used for measurement basis choice with an asymmetric splitting ratio of 70%:30% for the Z:X basis. For the Z basis, the BS output port is directly connected to an InGaAs/InP avalanche photodiode (APD0), and the detection of the former or latter time position in one period will be decoded for bit 0 or 1. For the X basis, the other BS output port is connected to a Michelson interferometer followed by APD1 and APD2, whereupon the detection of APD1 or APD2 is decoded to bit 0 or 1. Here we used the Michelson interferometer [48] instead of AMZI because it allows polarization-independent interference without polarization stabilization. This greatly simplifies the complexity of the receiver by removing the electric polarization controller and polarization beam splitter components. Furthermore, it reduces the insertion loss and thus increases the secure key rate. Details of the setup can be found in Appendix A1.
3. Results and discussion
The system ran continuously and automatically for more than two months without any human intervention. Active phase tracking and feedback method is adopted to reduce the QBER in the X basis. Details can be found in Appendix A2. The measured secure key rate and QBER are shown in sections of a) and b), respectively, of Fig. 2. The QBER of the Z basis in signal state was about 1.25%, and maintained quite stable throughout the whole test period. The QBER of X basis can be maintained at approximately 3% with the help of the feedback scheme. Throughout the whole test period, the average secure key rate was 945.77 bps and the standard deviation was 13.43%. Details of data post-processing are presented in Appendix A3. We speculate that the fluctuation of the secure key rate (and QBER in the X basis), in the later part (from 40th day to 70th day) is likely due to the count rate fluctuation caused by the detection efficiency changes of APD1 and APD2, especially the relative effciency changes. This, in turn, results in an increase in voltage error on the FPS after phase feedback. We would like to leave the solution of this problem for future work.
Fig. 2. Measured secure key rate and QBER over 70 days between 2022.01.18 and 2022.03.28 during the field test. The overall loss of the quantum link is 23.27 dB.
We compare our result with few attempts of quantum key distribution over aerial fiber from previous works [49,50], as shown in Table 1. First, in terms of the total distance of the quantum link, we have achieved the long-distance transmission in a field-installation environment by utilizing an 87-km mixed link comprising both aerial and buried fibers. If only considering the length of the aerial fiber, it is approximately 61km in our experiment, slightly shorter than Ref. [50]. Second, we have achieved the largest link loss by more than 8 dB. Furthermore, our system features the highest secure key rate among all field tests of aerial fiber links. Due to the differences in attenuation, it is inconvenient to directly compare the secure key rate. We therefore normalize the secure key rate to that of the 10 dB transmission loss. These results demonstrate that the secure key rate in our experiments is improved more than 175% compared with those reported in previous experiments.
Table 1. Comparison of our results with previous work.
Apart from our scheme, several other approaches may also help to settle the problem of quantum key distribution through aerial fiber link, such as adopting the reference-frame-independent (RFI) QKD protocol [51], and using a BB84 phase-coding scheme [5]. The RFI QKD protocol exploits six states (eigenstates of the X/Y/Z bases) to eliminate the requirement of reference frame alignment between the transmitter and receiver, thereby rendering the QKD system more adaptive to changing environments. The RFI QKD protocol requires more quantum states for encoding and decoding than the original BB84 protocol, which is more complex and less efficient. Moreover, the RFI QKD is limited to retrieve slow perturbations. BB84 phase-encoding systems are intrinsically immune to channel disturbance because relative phase between successive pulses is not disturbed by the environment, making them more adaptable to changing environments. Regrettably, their performance is limited due to the high insertion loss introduced by the phase modulator (PM) for decoding. Thus, all these approaches have obvious drawbacks compared to our solution.
4. Conclusion
In summary, we have developed a novel time-bin phase encoding setup that utilizes both the OIL technique and intrinsic phase difference between two AMZI input ports. This modulator-free setup provides inherent stability and simplicity in quantum state encoding, and is immune to channel disturbance. We successfully implemented quantum key distribution over a hybrid 87-km-long deployed aerial fiber link, with an overall loss of up to 23.27 dB. During the 70-day continuous operation in the field test, we achieved a secure key rate of approximately 1.0 kbps and a quantum bit error rate below 1.3%. Our work demonstrates high performance and stability of quantum key distribution over long aerial fiber link, paving the way for widespread implementation and diverse applications of QKD systems in complex real-life scenarios.
Appendix
A1. Experiment details of the setup
Up till now, there are various kinds of time-bin phase-encoding schemes [35,52–55]. Traditional time-bin phase-encoding setups require an asymmetric Mach-Zehnder interferometer (AMZI) to split pulses into two time-bins. Subsequently, an intensity modulator (IM) is employed to encode the time-bin basis (Z basis), and a PM is employed to encode the phase basis (X basis) [52]. This setup requires two modulators, and the IM operates at twice the system frequency and needs to be stabilized, rendering the encoding setup either complex or unstable. To avoid the use of modulators, several other schemes are proposed. One kind of setup utilizes the OIL technique [35,53] to directly modulate the phase and intensity on phase and time-bin bases. Encoding on the time-bin basis can be intrinsically stable since it is carried out by gain switching of pulse lasers instead of using IM. However, encoding on the phase basis requires high-performance driving electrics to modulate a wide electronic pulse on the master laser, capable of covering two successive time-bins. Additionally, the difference in the electronic pulse between the first and the second time-bins, especially the chirp, could cause a wavelength difference between the two time-bins, opening a potential loophole in terms of practical security. Another kind of setups also utilizes the OIL technique [54], and the difference is that to modulate the phase basis, it ultilizes a phase modulator instead of a wide electronic pulse modulation on the master laser. Besides, a fully passive time-bin phase encoding scheme is recently proposed [55], with an asymmetric interferometer and a post-selection module to avoid active modulation. But an optical switch operating at high speed is needed to break the interference of adjacent time bins.
In this paper, we propose a new time-phase encoding scheme based on the OIL technique. This approach is modulator-free for the preparation of quantum states. The complete QKD system based on this scheme is shown in Fig. 1. The status of the electrical driving signals of these lasers corresponding to four quantum states is shown in Fig. 3.
Fig. 3. Status of electrical driving signals of lasers (three master lasers and one slave laser) corresponding to four quantum states.
At the transmitter, three master lasers and one slave laser operate in a two-stage cascade injection-locked mode to make the spectra of all output signals consistent. The measured spectra are shown in Fig. 4. It is clear that the center wavelengths of the $0$ pulse and the $\pi$ pulse are essentially the same when the master laser #0 is turned on (both are the same as the center wavelength of the master laser #0), while the $0$ pulse and the $\pi$ pulse deviate by approximately 0.1 nm when the master laser #0 is turned off.
Fig. 4. Spectrum of the 0 pulse and the $\pi$ pulse. When master laser #0 is on, both master lasers #1 and #2 with different initial wavelengths are locked to master laser #0 and share the same wavelength, and thus the 0 pulses and the $\pi$ pulse can also share the same wavelength.
The lasers ensure a temperature control accuracy of 0.01$^{\circ }$C. Even in the case of a temperature control drift reaching 10 times the accuracy (i.e., 0.1$^{\circ }$C), supplementary tests have shown that the central wavelength variation after injection locking does not exceed 0.1 pm [56]. It is because the wavelength and phase of the generated slave laser emission is fully determined by the injected master laser #0 [57]. In this scenario, the phase difference caused by the wavelength deviation of master laser #1 and #2 does not exceed $< 0.125 rad$, resulting in an impact of $<0.2{\% }$ on the error rate of the X basis. Therefore, our approach ensures the stability of the X basis encoding.
In terms of time-domain characteristics, we measured the pulse waveforms of $|{Z_0}\rangle$, $|{X_0}\rangle$ and $|{X_1}\rangle$ from different bases, as shown in Fig. 5. These pulse waveforms indicate no significant differences, with only minor variations observed at the falling edges due to the limited tunable accuracy of the master laser in the time domain. This minor deviation can be further optimized by fine-tuning the driving signals for the master lasers. We will consider this optimization of our system and further comprehensive research on the quantum security aspects in future work.
The decoy state method is considered to resist the photon-number splitting attack, implemented by the Sag-IM modulator. Here, we use a vacuum + weak decoy state scheme [58], and the photon numbers are set to $\mu =0.33$, $\nu =0.1$, and $\omega \ll 0.001$ for the signal, decoy, and vacuum state, respectively. Two Micro-Electro-Mechanical System variable optical attenuator (MEMS VOA) are employed for suitable attenuation to this photon number level. A true random number generator sets the probabilities of sending a signal or a decoy and vacuum state to $P_\mu =1/2$, $P_\nu =3/8$, and $P_\omega =1/8$ respectively. For the signal state (decoy state), the basis probabilities are set to $P_z = 7/8$ and $P_x = 1/8$ ($P_z = 2/8$ and $P_x = 6/8$). Here the true random number generator is a high-speed multi-channel physical random number generator [59].
At the receiver, the optical module of a BS for basis choice and an asymmetric Michelson interferometer with a fiber phase shifter (FPS) [60] inside for phase demodulation are designed. The followed three detectors used at the receiver are operated at a gate frequency of 1.25 GHz, a detection efficiency of approximately 15%, and a dark count rate below 800 Hz. When using a time window of 600 ps and a system period of 3.2 ns, the effective dark count rate can be reduced to below 150 Hz.
With the scheme of the high-speed QKD transmitter and receiver, we develop a compact QKD system for real-time operation, including automatic feedback system (detailed in Appendix A2) and complete data sifting module fulfilling error correction and privacy amplification (detailed in Appendix A3). Standard 1G Ethernet interfaces are used for classical communication between the transmitter and receiver.
A2. Phase shift tracking and feedback
For a continuous operation of this system, we should maintain the stability of the QBER of X basis which shifts over time, mainly due to the slow phase shift of the unbalanced interferometer, i.e., the AMZI in the transmitter and the Michelson interferometer in the receiver. Hence, we propose a real-time feedback scheme as shown in Fig. 6, which adopts the feedback frame of the large pulse intensity, time-multiplexed with the quantum frame by 20% time consumption. This feedback frame is modulated with a fixed 0 phase, and detected by the same APDs (APD1 and APD2) to obtain its real-time visibility. Compared with the calibrated maximum visibility (as a target) in the calibration procedure before continuous operation, it is then possible to calculate phase shift for compensating the voltage of the FPS [60] within the Michelson interferometer in the receiver. One MEMS VOA in the transmitter is used switch the pulse intensity between the feedback frame and the quantum frame. An appropriate voltage on the VOA of the feedback frame is set to ensure that the detector obtains a count rate of about one order lower than its saturation count rate to reduce the effects of its saturation count rate and dark count rate.
Fig. 6. Feedback scheme using feedback frame time-multiplexed with the quantum frame by 20% time consumption.
A3. Data post-processing
Here we present details of data post-processing using an FPGA implementation for real-time secure key extraction. After the pulses are registered at Bob’s detectors, key sifting and basis sifting are executed, followed by error correction using Winnow algorithm and an error verification using CRC-64. Here we set the initial segment length to be 15 (we note that this parameter can be optimized to be 31 to improve the error correction efficiency), and thus the error correction efficiency is resulted to be about 1.7 when the overall QBER is around 1.3%. Afterwards, when the corrected key had been accumulated to be approximately 500 kbits, privacy amplification is performed to eliminate information leakage to Eve including that during the error correction and the error verification. A Toeplitz matrix is constructed to extract secure keys from the corrected keys by a compression ratio, i.e., the ratio of the estimated secure key length to the corrected key length after error verification. The secure key length $L$ is calculated by the following formula according to the theory of decoy state QKD [61–63]:
Here, subscripts $\mu, \nu$ denote the average photon numbers per signal in the signal and decoy states, respectively, $H_2(x)$ is the binary entropy function given by $H_2(x) = -x\log _2x -(1-x)\log _2(1-x)$, and $leak_{EC}$ is the information leakage during the error correction process.$M_{1zz}^L (M_{1xx}^L)$ is the lower bound of the single photon number of the Z (X) basis after basis sift in signal state, $e_{1zz}^{pU} (e_{1xx}^{pU})$ is the upper bound of the single photon phase error rate of the Z (X) basis after basis sift in signal state. Here we added details about the parameter estimation. $M_{1zz}^L$ is calculated using the following formula (similar for $M_{1xx}^L$):
where $F_L(x,N)=x(1-\delta /\sqrt (N)$, $F_U(x,N)=x(1+\delta /\sqrt (N)$ are the lower and upper bounds, respectively, when considering statistical fluctuations with $\delta = 6.5$ corresponding to a failure probability of $\varepsilon =10^{-9}$ [62], $p_{bz}(p_{bx})$ is the probability of Z/X measurement basis choice, and $N_{\mu z}(N_{\mu x})$ is the count corresponding to the Z (X) basis sent in the signal state.We here follow the method developed in [61–63] to estimate the lower bound of gain $Q_{1zz}^L$ (similar for $Q_{1xx}^L$) according to the following formula:
We also use the method developed in [61–63] to estimate the upper bound of phase error rate $e_{1zz}^{pU}$ (similar for $e_{1xx}^{pU}$ ) according to the following formula:
A4. Lab experiment
We verified the performance of the QKD system via lab experiment before we deployed the terminals in the field test. The overall efficiency of the test link is set to 25 dB to assume an extreme condition, which was composite of 90-km-long fiber pools and attenuators. The quantum bit error rate (QBER) was measured to be approximately 1.2% for the Z basis and 2.9% for the X basis. After experimentally measuring the relevant parameters, we calculated the final key length $L$. The relevant parameters are listed in Table 2 for a accumulate time of $t_{accu}=105$ s to accumulate approximately 500 kbits (the block size used in our experiment). The final key rate $R= L/t_{accu}$ is 1.1 kbps.
Table 2. Measured and derived specifications based on decoy states.
Funding
Major Scientific and Technological Special Project of Anhui Province (202103a13010004); Key R & D Plan of Shandong Province (2020CXGC010105); Major Scientific and Technological Special Project of Hefei City (2021DX007); China Postdoctoral Science Foundation (2021M700315).
Acknowledgments
We thank Prof. Teng-Yun Chen, Prof. Sheng-Kai Liao and Prof. Feihu Xu for helpful discussions. We thank colleagues at QuantumCTek, especially Lian-Jun Jiang, Guo-Qing Liu, Ze-Xu Zhang, Liang Zhu, and Zhao-Jie Diao for experimental assistance. We also thank Enago for its linguistic assistance during the preparation of this paper.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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