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Abstract
The commercialization of quantum key distribution (QKD), which enables secure communication even in the era of quantum computers, has acquired significant interest. In particular, plug-and-play (PnP) QKD has garnered considerable attention owing to its advantage in system stabilization. However, a PnP QKD system has limitations on miniaturization owing to a bulky storage line (SL) of tens of kilometers. And, the secure key rate is relatively low because Bob transmits the signal pulses only at the dedicated time slots to circumvent backscattering noise. This study proposes a new method that can eliminate the SL by realizing an optical pulse train generator based on an optical cavity structure. Our method allows Alice to generate optical pulse trains herself by duplicating Bob’s seed pulse and excludes the need for Bob’s strong signal pulses that trigger backscattering noise as much as the conventional PnP QKD. Accordingly, our method can naturally overcome the miniaturization limitation and the slow secure key rate, as the storage line is no longer necessary. We conducted a proof-of-concept experiment using our method and achieved a key generation rate of 1.6×10−3 count/pulse and quantum bit error rate ≤ 5%.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Quantum key distribution (QKD) allows two distant users (Alice and Bob) to share a secure key. QKD guarantees unconditional security via the laws of quantum physics [1]. Since its first proposal in 1984 [2], it has become the most rapidly developed quantum technology, as its first commercial products appeared in the 2000s [3]. For expanding a market, the technologies have been consistently developed such as QKD network, long distance, higher secure key rate, miniaturization, long term stable operation, and so on [4–8]. Furthermore, verifications via several testbeds have been conducted [9–16].
Owing to the fragile characteristic of quantum signals, precise controls are required to achieve system stability and long-term operations against environmental changes. The plug-and-play (PnP) QKD proposed in 1997 is an innovative structure, which was first commercialized by minimizing control systems [17]. In particular, because both laser and detectors that require accurate control are installed in the receiver (Bob), it is easy to control them systematically. In addition, the simplified transmitter (Alice) without laser provides a significant advantage in the 1 × N QKD network configuration [8,18].
However, the PnP architecture exhibits the following limitations. First, there is a constraint on miniaturizing Alice, which requires a bulky storage line (SL) with several tens of kilometers to prevent backscattering noise inducing quantum bit errors. Second, the feasible key rate is lower than the one-way QKD system because Bob should send the signals in the form of pulse trains, rather than continuous pulses.
In this study, we theoretically propose and experimentally demonstrate a new structure that can address these limitations using an optical pulse train generator (OPTG). The proposed method allows Alice to duplicate pulses by splitting and amplifying a seed pulse from Bob. Therefore, Alice does not need the SL to prevent the backscattering noise, as Bob does not need to send bright pulse trains. Consequently, it enables both miniaturization of Alice’s configuration and improvement of the key rate. In Section 2, we comprehensively explain the OPTG. In Section 3, we present the results obtained from experiments. Finally, in Section 4, we summarize the study and conclude the paper.
2. Proposed PnP QKD architecture with an optical pulse train generator
We propose a new architecture of Alice in which she has OPTG generating pulse trains by herself, as illustrated in Fig. 1. Because Alice can reproduce pulse trains using the seed pulse of Bob, the proposed architecture can eliminate the SL unlike conventional PnP's. Therefore, miniaturization and higher key rates can be achieved as explained below.
Fig. 1. PnP QKD system where Alice’s SL is substituted by an OPTG. (FM: Faraday mirror, PM: phase modulator, BPF: Bandpass filter, SOA: semiconductor optical amplifier, BS: beam splitter, PD: photodiode, VOA: variable optical attenuator, QC: quantum channel, PBS: polarization beam splitter, DL: delay line, CIR: circulator, SPD: single photon detector, LD: laser diode)
2.1 System architecture
The OPTG that creates pulse trains may be implemented using a ring resonator [19]. But we implement OPTG through optical cavities as shown in Fig. 1 because Alice must have a single port for input and output. Alice based on the proposed OPTG is realized with two Faraday mirrors (FMs), beam splitters (BS), semiconductor photo amplifiers (SOA), photodiodes (PDs), band pass filters (BPF), and phase modulator (PM) elements. The PD is adopted for time synchronization and detecting the Trojan-horse attack [20,21]. The SOA compensates for system loss when the seed pulse makes a round trip between the FMs. It makes the signals have consistent intensity by maintaining the amplification factor. In addition, the BPFs allow the SOA to amplify not the noise but the light with solely the signal wavelength [22].
The OTPG operates in the order of the arrows in Fig. 1:
- 1. Bob sends a time-bin pulse comprising one fast pulse and one slow pulse to Alice via the quantum channel (QC)
- 2. The time-bin pulse from Bob is divided into two parts by the BS of Alice. One is transmitted to the PD to generate a synchronization signal while the other is transmitted to the optical cavity to be adopted as the OPTG seed signal.
- 3. The seed signal is amplified by the SOA. BPFs (0.8nm bandwidth) almost eliminate noise with wavelengths that differ from that of the signal (1550.1nm). Then, the amplified signal is transmitted to the FM via the PM.
- 4. The signal is orthogonally reflected by FM and returns to the BS through the BPFs and SOA. Then, it is divided into two parts by the BS again. One is transmitted to the optical cavity as the OPTG seed signal while the other is transmitted to Bob via the QC.
- 5. The OPTG seed signal is orthogonally reflected by the second FM and again divided into two parts, which are transmitted to the PD and optical cavity, respectively. Then, Alice can generate her own pulses by repeating Steps 3–5.
The QKD pulse generation rate of the system using OPTG is determined by several parameters as shown in Fig. 2. Theoretically, the pulse generation rate of the QKD system, i.e., ${f_{QKD\; pulse}},$ is determined as follows:
Because the value of QC is determined by the distance between Alice and Bob, the pulse generation rate differs depending on the values of ${f_{\textrm{Alice}\_\textrm{OPTG}}}$ and ${T_{\textrm{OPTG}}}$. In an ideal case where ${T_{\textrm{OPTG}}}$ is significantly longer than ${T_{\textrm{QC}}}$, in other words, if the OPTG can continue to generate signals with only one seed signal, ${f_{\textrm{QKD}\; \textrm{pulse}}}$ is defined as follows:
In the above case, excluding the quantum channel transmission time, (i.e., $\textrm{ }{T_{\textrm{QC}}}$) it can be seen that the signal generation rate of one-way QKD becomes equal. In other words, it is theoretically feasible that the signal can be transmitted at the same speed as the one-way QKD if there is an infinitely long ${T_{\textrm{OPTG}}}$, i.e., ${T_{\textrm{OPTG}}} = \infty $ . In the case of ${T_{\textrm{OPTG}}} = 1\textrm{ }ms$, the signal generation rate is improved up to 80% of the one-way QKD architecture, as illustrated in Fig. 3.
Meanwhile, the signal generation rate of the general PnP QKD is expressed as:
With a 25-km QC, a 15-km SL, and ${f_{\textrm{pulse}}} = 10\textrm{MHz}$, ${f_{\textrm{QKD pulse}\_\textrm{general}}}$ is approximately 2.7 MHz. Hence, as illustrated in Fig. 3, the generation rate of our method with a ${T_{\textrm{OPTG}}}$ (>100 us) can be higher than that of the general PnP QKD system with a 15-km SL.
2.2 Implementation of OPTG
In this sub-section, we describe technical considerations when the OPTG is implemented in practice. In the proposed optical cavity structure (using two FMs), without the SOA, the signal would be attenuated according to the attenuation factor of the BS. Assuming an ideal splitting ratio of 50:50 BS and no insertion loss of the remaining optical devices employed for the OPTG, the intensity of the N-th output signal of the OPTG is attenuated by ${2^{ - 2N}}$. Therefore, the SOA is required to generate signals with a consistent intensity by compensating for such attenuation.
Unlike an ideal optical amplifier, a gain in the SOA depends on the intensity and polarization of the input, as illustrated in Fig. 4. In addition, because most QCs of actual QKD systems deployed in commercial fibers comprise single-mode fibers [23,24], we cannot ensure the input polarization. Hence, the following points should be considered.
First, we should adjust the intensity of the signal below the specific level. As illustrated in Fig. 4, the gain depends on the input power and the dependence becomes significant when the input power is higher than -20 dBm. Therefore, to prevent distortion, the input power should be lower than -20 dBm.
Second, the propagation losses of the following two paths must be identical.
Two paths, except PM and BS, are symmetric. Hence, we should compensate for the difference between the PM and BS. Because the losses of the PM and BS (50:50) are approximately 2 dB and 3.5 dB, respectively, we employ a BS (70:30) as a substitute of the BS (50:50).
Third, the gain and loss should be equal. If the gain is greater (lower) than the loss, the signal would gradually increase (decrease) as it reciprocates. Hence, the gain of the SOA is set to 10.6 dB to compensate for the round-trip attenuation of 10.6 dB induced by the BPF (3.3 dB), BS (2 dB), and PM (2 dB). In addition, as described above, the gain of the randomly polarized input is distorted because of the polarization dependency. Hence, we adopt the FMs, which reflect the input polarization state to the orthogonally polarized state, to compensate for the polarization dependency [18,25]. The gain distortion between two polarization states before reflection is naturally compensated after reflection.
2.3 Phase encoding
As illustrated in Fig. 5(a), the phase of the seed pulse is also copied to the new pulse generated by the OPTG. This should be considered when Alice encodes the relative phase between the time-bin pulses comprising the fast and slow pulses. Two methods can be adapted to address this issue. First, Alice can compensate for the previous modulation of the fast (slow) pulse [25] by equally modulating the slow (fast) pulse as the previous modulation. For example, as illustrated in Fig. 5(b), Alice compensates for the phase, $\pi $ of the fast pulse, by modulating the phase of the slow pulse as $\pi $. Second, Alice can modulate the difference between the previous and new target values, as illustrated in Fig. 5(c). When Alice attempts to modulate the five signals by 0, $\pi $, $\pi $, $\frac{{3\pi }}{2}$, and 0, respectively Alice actually modulates the five pulses by 0, $\pi ({\pi - 0} )$, 0($\pi - \pi )$, $\frac{\pi }{2}$($\frac{{3\pi }}{2} - \; \pi )$, and $\frac{\pi }{2}$($0 - \; \frac{{3\pi }}{2})$, respectively. To adopt Fig. 5(c) method, a bipolar digital-to-analog converter should be included to prevent phase decoherence triggered by accumulated modulations. In this study, we adopt the first method to simplify the experiment and prevent phase decoherence.
Fig. 5. Phase difference of OPTG signal by phase modulation. a) Subsequent signal phase differences by phase modulation. b) Compensation of subsequent signal phase differences by phase modulation. c) Integration of modulated phase value.
2.4 Security analysis
Our proposed architecture is based on a conventional PnP QKD. The difference is that Alice generates a pulse train after receiving an initial time-bin signal pulse from Bob. Therefore, it is needed to address analyzing the security of generating pulse train by Alice.
There are three representative quantum attacks that may occur at Alice in PnP QKD. It is required to check if these may exist when generating a pulse train or not. The first is the Trojan horse attack [20]. In QKD, all the pulses in the channel are assumed to be able to be fully controlled by Eve (an eavesdropper). Eve may send to Alice by adding an additional high-intensity pulse to the pulse Bob originally sent in PnP QKD. If Alice receives this larger intensity of the pulses, she transmits not single-photon but multi-photon level pulses through a quantum channel. This results in a photon number splitting (PNS) attack. The proposed architecture can prevent this attack easily by using the PD. The PD in the proposed architecture can monitor the intensity of every pulse. Not only an initial time-bin pulse input to Alice but also Alice’s output pulses can be measured. If Eve sends a larger intensity pulse, Alice can notice the attack by measuring the intensity with a PD just like a conventional PnP QKD does. Also, even if Alice fails to detect it, Eve can’t have any information through the PNS attack [26] because the output pulses are adjusted to the intensity of the single-photon level using an electrical feedback system (not shown in Figure 1) that can consistently monitor the intensity of the output pulses and attenuates them accordingly.
Next, we will consider the phase-remapping attack [27]. If Eve changes the arrival time of the pulses, then the pulses pass through the PM at different times. This causes the different phase modulation from Alice's intended to be modulated. The phase-remapping process allows Eve to launch the intercept-and-resend attack. Our proposed architecture controls each device in Alice at proper timing that is based on the time at which the initial pulse is measured in the PD. Therefore, the phase-remapping attack can be prevented. In addition, there may be a threat of different phase-remapping attack using different wavelength pulse, but this is also easily defended by BPF in Figure 1.
Finally, we will discuss the nonrandom-phase attack [28]. The proposed architecture is a method of generating a pulse train through the received pulse from Bob. Therefore, the first pulse and subsequent pulses may have the same phase. In our architecture, a PM can be used for phase randomization of each pulse. We can add a phase randomization signal to the encoding signal when driving the PM [29]. In conclusion, the nonrandom-phase attack is easily prevented, as well.
3. Experimental result
We conducted experiments to demonstrate the proposed PnP QKD system. First, we tested the OPTG, which is the core of the structure we proposed. We measured the output intensity of the OPTG to verify that the OPTG appropriately generates new pulses using the seed pulse from Bob. Subsequently, we tested whether PM is operating normally through interference visibility measurement. Then, before driving the real QKD system, we measured the interference results of phase modulations based on the BB84 protocol (Alice: 0, $\frac{\pi }{2}$, $\pi $, $\frac{{3\pi }}{2}$, Bob: 0, $\frac{\pi }{2}$). Finally, we measured the QKD system performance of our architecture.
In the first experiment, we implemented Alice (Fig. 1) and measured the output intensity of the OPTG. As illustrated in Fig. 6, the normalized intensities of 10 pulses generated by the SOA varied by a magnitude of ± 10% of the average intensity. Furthermore, the variation can be reduced up to ± 4% without the first pulse. This result shows successful pulse train signal generation based on the seed signal, measured by Bob's APDs. And as mentioned in Section 2, because a portion of generated signals is transmitted to Alice's PD, in addition to performing synchronizations, we can employ the PD to measure the intensity difference. This allows for easy control of Alice's output signal by controlling the VOA. In addition, we can also easily detect the signals Eve(eavesdropper) sends to Alice (for Trojan horse attacks).
Subsequently, we measured the interference visibility of the OPTG output pulses to check phase encoding ability. The phase encoding method in Fig. 5(b) was used. Fig. 7 presents the experimental results of the first and tenth pulses. It is demonstrated that the time-bin signal generated by the OPTG can interfere normally in Bob’s Mach–Zehnder interferometer. In addition, the results of the first and tenth pulses are found to be similar. These indicate that the initial relative phase generated by Bob’s Mach–Zehnder interferometer is maintained in the case of the reproduction of the OPTG.
Before we conduct the QKD protocol, we measured the interference for the BB84 protocol where Alice and Bob modulate the phase with 0, $\frac{\pi }{2}$, $\pi $, $\frac{{3\pi }}{2}$ and, 0, $\frac{\pi }{2}$, respectively. As illustrated in Fig. 8, we obtained the desired interference results with errors less than 5% for all the 10 signals generated by the OPTG. These results verify that the OPTG can be adopted to implement the PnP QKD system.
Fig. 8. Alice PM 0, $\frac{{\boldsymbol \pi }}{2}$, ${\boldsymbol \pi }$, $\frac{{3{\boldsymbol \pi }}}{2}$ modulation and Bob PM 0, $\frac{{\boldsymbol \pi }}{2}$ modulation results. a) Result of APD_1; b) Result of APD_2
Finally, as illustrated in Fig. 9, we measured the QKD performance parameters, such as the key rate and quantum bit error rate (QBER), using the OPTG. The interval of the time-bin pulses is 50ns and $1/{f_{\textrm{Alice}\_\textrm{OPTG}}}$ is 172ns. ${T_{\textrm{OPTG}}}$ is set to 1.72 us to generate 10 signals. The length of QC is 25 km, T_QC is 125 us at this time. The optimized ${f_{\textrm{Bob}}}$ is 1/251.72 MHz, but the experiment was performed at 1 kHz for a proof-of-principle experiment. Finally, in the proposed PnP QKD using the OPTG, signals are generated at 10 kHz. APD detection efficiencies of 15% and a mean photon number of 0.2 were adopted for the experiment. A slight difference exists in the key rate according to the intensity differences presented in Fig. 6. The key rate of the fourth pulse is the largest (1.7×10−3 count/pulse). In addition, the overall averaged key rate is 1.6×10−3 count/pulse. Meanwhile, QBER results evidently differ according to the generation order. The QBER of the tenth pulse is the highest owing to the noise accumulated from the first pulse generation. However, the errors in these results (< 5%) are sufficiently low to ensure the security of the generated keys [20,21].
4. Conclusion
We proposed a new PnP QKD architecture that can improve the secure key rate and be compactly implemented while maintaining the advantages of the conventional PnP QKD. Using the OPTG, Alice can generate pulse trains and implement the system without SL. As a result, unlike traditional PnP QKD, it can be miniaturized. We experimentally demonstrated the feasibility of addressing this limitation by measuring the QKD performance of our architecture. In the experiments, we demonstrated that the OPTG can generate ten signals from Bob’s seed pulse. Then, we measured the interference visibilities of the pulses. Finally, we performed the BB84 protocol and obtained an average key rate and a QBER of 1.6×10−3 count/pulse and < 5%, respectively.
The proposed architecture without bulky SL enables the miniaturization of PnP QKDs, such as a chip-based PnP QKD. In addition, if the proposed PnP QKD architecture is implemented on a chip, a higher secret key rate can be achieved due to ${f_{\textrm{Alice}\_\textrm{OPTG}}}$ being inversely proportional to the round-trip time of the optical cavity (length between two FMs). Based on these results, we believe that our proposed scheme will be a prevalent scheme in the PnP QKD system.
Funding
Korea Institute of Science and Technology (2E31531); Institute for Information and Communications Technology Promotion (2020-0-00947, 2020-0-00972); National Research Foundation of Korea (2019M3E4A1079777, 2021M1A2A2043892).
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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