⇦Chinese Physics Letters, 2020, Vol. 37, No. 11, Article code 110301 A Fully Symmetrical Quantum Key Distribution System Capable of Preparing and Measuring Quantum States Tianqi Dou (窦天琦), Jipeng Wang (王吉鹏), Zhenhua Li (李振华), Wenxiu Qu (屈文秀), Shunyu Yang (杨舜禹), Zhongqi Sun (孙钟齐), Fen Zhou (周芬), Yanxin Han (韩雁鑫), Yuqing Huang (黄雨晴), and Haiqiang Ma (马海强)* Affiliations School of Science and State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876, China Received 17 July 2020; accepted 17 September 2020; published online 8 November 2020 Supported by the Fundamental Research Funds for the Central Universities (Grant No. 2019XD-A02), and the State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications (Grant No. IPO2019ZT06).
*Corresponding author. Email: hqma@bupt.edu.cn Citation Text: Dou T Q, Wang J P, Li Z H, Qu W X and Yang S Y et al. 2020 Chin. Phys. Lett. 37 110301    Abstract We propose a fully symmetrical QKD system that enables quantum states to be prepared and measured simultaneously without compromising system performance. Over a 25.6 km fiber channel, we demonstrate point-to-point QKD operations with asymmetric Mach–Zehnder interferometer modules. Two interference visibilities of above 99% indicate that the proposed system has excellent stability. Consequently, the scheme not only improves the feasibility of distributing secret keys, but also enables QKD closer to more practical applications. DOI:10.1088/0256-307X/37/11/110301 PACS:03.67.Dd, 03.67.Hk, 03.67.-a © 2020 Chinese Physics Society Article Text Quantum key distribution (QKD) provides an information-theoretic secure communication method to share secret keys between two remote parties (commonly denoted as Alice and Bob) and its unconditional security is guaranteed by the principles of quantum mechanics.[1] Since the first QKD protocol,[2] i.e., the BB84 protocol, was proposed by Bennett and Brassard, theoretical and experimental research on QKD has become increasingly prosperous.[3–9] However, the actual implementation of the QKD system is imperfect because it is difficult to meet the requirements of the ideal QKD protocol. Hence, it is vulnerable to security loopholes in practical QKD systems. Fortunately, Hwang proposed a decoy-state method[10] to resist the photon number splitting (PNS) attack[11,12] on a weak coherent state source. Similarly, Lo et al. put forward a measurement-device-independent QKD (MDI-QKD) protocol that is immune to all attacks on measurement devices.[13,14] In addition, the reference frame of most QKD systems needs to be rigorously calibrated during transmission owing to its unknown and slow variances introduced by environment, which increases the complexity of communication. Therefore, Laing et al. presented a reference frame independent QKD (RFI-QKD) protocol to generate secure keys without the alignment of the reference frame.[15] In consequence, the protocols mentioned above greatly improve the feasibility and practicality of QKD systems. Generally, the polarization or phase of a photon is used as a carrier for coding in an optical fiber QKD system.[14] Further, the phase coding is widely used on account of its better stability and easier compensation in long-distance optical fiber communication.[16] So far, QKD has become a commercial technology for the wide-scale deployment of quantum networks. Significant efforts have been made to enhance the key rate,[17,18] transmission distance[19–21] and practicality[22] of QKD systems and the key rate of 6.5 b/s of ultralow-loss optical fiber over 405 km has been realized.[19] Moreover, the twin-field QKD (TF-QKD) protocol is proposed to overcome repeaterless secret key capacity.[23] The achieved secure key rate over a 509 km ultralow-loss optical fiber is higher than that of a traditional QKD protocol using perfect repeaterless QKD devices.[24] In addition, most current communication systems comprise bulk optics and thus it is not beneficial for the large-scale deployment of QKD technology. Therefore, chip-based components have been developed to facilitate system implement integration[25] and miniaturization to enhance system performance, obtaining the secure key rate of 400 kb/s in a standard 100 km single-mode fiber channel.[26] Despite intense efforts having been performed, existing QKD systems have not yet implemented that both parties can prepare and measure quantum states in a single set of QKD system. The current implementations are primarily categorized into the following three types. The first is where the sender prepares the quantum states and the receiver measures the received quantum states. The second is where the sender prepares the quantum states and measures them after returning back, while the other party only encodes the quantum states. The final type is where both parties prepare the quantum states, respectively, and send them to an untrusted third party who performs measurement. Note that it is not easy to realize the requirement that both parties prepare and measure quantum states in a single set of QKD communication system. Therefore, in most current systems, if an optical apparatus (i.e., an encoding device) of one party is broken, the entire system will not work properly. In this work, we present a fully symmetrical QKD system based on asymmetric Mach–Zehnder interferometer (AMZI) modules. In this system, both parties are capable of preparing and measuring quantum states without compromising system performance. This means that the entire key rate can be up to double the original realization. The system also shows high feasibility and practicality against devices that may be damaged. Consequently, this scheme offers a novel solution for practical applications of quantum communication. As a proof-of-principle experiment, our scheme is implemented using a phase-encoding BB84 QKD protocol with the decoy-state method and experimental results demonstrate its excellent stability, obtaining the interference visibilities exceeding 99% over one hour. The proposed implementation can be applied to many QKD protocols. In this work, we take the most mature and well-known protocol, i.e., the BB84 protocol, as an example. The sender Alice, prepares one of four phase shifts $(0, \pi/2, \pi,3\pi/2)$ with equal probabilities to perform encoding. Phase shifts 0 and $\pi$ encode bits 0 and 1, respectively, in the $Z$ basis and phase shifts $\pi/2$ and $3\pi/2$ encode bits 0 and 1 in the $X$ basis. Then, the encoded pulse is sent to Bob via the quantum channel. Bob randomly chooses the $X$ or $Z$ basis to decode the phase information and generate the raw key.
cpl-37-11-110301-fig1.png
Fig. 1. Schematic of the experimental setup. LD: laser diode; IM: intensity modulator; PC: polarization controller; ATT: attenuator; Cir/CIR: circulator; BS: beam splitter; PM: phase modulator; FR: Faraday rotator; DL: delay line; PBS: polarization beam splitter; SC: Sagnac configuration; EPC: electronic polarization controller; QC: quantum channel; SPD: single photon detector. The difference between the CIR and Cir is that the former makes pulses enter from port 3 and exit at port 1, while the latter cannot. In other words, for the CIR, pulses entering from one port will exit at the subsequent port in a clockwise direction.
The experimental setup is depicted in Fig. 1. Both parties have identical and symmetrical optical devices. The devices of two separate parties can each be controlled by a field programmable gate array and synchronized via an optical service channel based on small form-factor pluggable transceivers. Here, the specific processes of the scheme are illustrated in an example where Alice prepares quantum states and Bob measures them. Likewise, the steps in which Bob prepares quantum states and Alice measures them are similar. Alice possesses a phase-randomized distributed feedback pulsed laser at 1550 nm (ID Quantique, ID300) with a 1 MHz repetition rate. An intensity modulator (IM) is used to prepare signal or decoy states. A polarization controller (PC) is used to modulate the initial $45^{\circ}$ polarized pulses. After attenuated by an attenuator (ATT) to the single-photon level, pulses pass through a circulator (Cir) and are encoded with bit and basis information using an AMZI module. The AMZI module comprises a beam splitter (BS), a polarization beam splitter (PBS), an electronic polarization controller (EPC), two circulators (CIRs), two delay lines (DLs) and two Sagnac configurations (SCs). During the encoding of Alice's AMZI module, the pulses pass through the BS where they are temporally separated into two paths. A one-meter DL allows ample separation between shorter and longer arm pulses, considering the pulse duration is approximately 300 ps. The longer arm pulses are modulated by the SC, and the shorter arm pulses pass through the CIR in a clockwise direction. The SC is used to modulate the phase information, the details of which can be found in Ref. [22]. These pulses are then recombined into a single path via the PBS. Note that the polarization of these pulses will not be changed when the pulses pass through the EPC of Alice's AMZI module. Then, these pulses are transmitted through the same optical path via a 25.6 km single-mode fiber. The PBS of the AMZI module makes only one pulse response in the detection window, avoiding the unnecessary waste of photons, thereby improving the efficiency of the entire system. Similarly, in the decoding process, the polarization of pulses is changed by the EPC of Bob's AMZI module. It is used to compensate for the polarization drifts of shorter and longer arm pulses sent by Alice and change the polarization direction of these pulses so that they are both rotated by $90^{\circ}$. Through the two AMZI modules, the pulses from the longer (shorter) path are directed into the shorter (longer) path of Bob's AMZI module. After that, the pulses entered into the longer arm are modulated by the SC of Bob's AMZI module, and the other pulses go directly through the CIR. Hence, the phase information of pulses sent from Alice is decoded. The length difference between the longer and shorter arms of the two AMZI modules are matched. Finally, interference occurs when two pulses reach the BS, and results can be detected by two single-photon detectors (SPDs) in Geiger mode. The proposed system includes the following characteristics and advantages: (a) An important feature of the proposed scheme is that both parties have identical and symmetrical implementations, which is beneficial to the integration and encoding of QKD systems. (b) Both parties can not only prepare quantum states but also measure quantum states, and even prepare and measure them at the same time. This enables the key rate to become twice that of the original realization, thus significantly increasing the feasibility and practicality of the systems. (c) In most current QKD systems, the sender and receiver are distinguishable because they can only prepare or measure quantum states. Correspondingly, in the QKD system integration process, the two sets of integrated equipment of preparing and measuring quantum states are also distinguished. However, in our solution, both parties have identical and symmetrical implementations without distinction, hence they have the same integrated equipment. This is suitable for the mass production of QKD systems and further has reference significance for large-scale deployment of chip-based QKD systems. (d) Compared with constructing two sets of QKD implementations to realize the preparation and measurement of quantum states, our solution only requires a single set of QKD implementation to achieve this requirement, observably reducing the complexity of system construction. (e) Finally, our system is a one-way communication system in which the encoding and decoding of both parties are independent of each other. This means that it is unnecessary to consider the impact of coding problems caused by the timing sequence. Concurrently, it is beneficial to increase the repetition rate to improve the performance of the entire system. We perform a fully symmetrical QKD system over a 25.6 km fiber channel by employing the decoy-state BB84 protocol in the asymptotic regime. In order to compare the performance of the system in two opposite directions, the loss of encoding devices for both parties are modulated to be approximately the same. This protocol is implemented with the “weak + vacuum” decoy-state method,[27,28] in which signal pulses ($\mu$) of 0.54 photons per pulse and decoy pulses ($\nu$) of 0.07 photons per pulse are sent. The detection efficiency of the detector (ID Quantique, ID210) is 15%, the loss in the fiber channel is 0.22 dB/km, and the dark count is $2\times10^{-6}$ per gate. The key rate $R$ is calculated by $$\begin{alignat}{1} &R=qQ_\mu[-fH_2(E_\mu)+\varDelta_1[1-H_2(e_1)]],~~ \tag {1} \end{alignat} $$ $$\begin{alignat}{1} &\varDelta_{1} =\frac{\mu^{2} {e}^{-\mu}}{\mu v-v^{2}}\Big(\frac{Q_{v}}{Q_{\mu}} {e}^{v}-\frac{v^{2}}{\mu^{2}} {e}^{\mu}-\frac{\mu^{2}-v^{2}}{\mu^{2}} \frac{Y_{0}}{Q_{\mu}}\Big),~~ \tag {2} \end{alignat} $$ $$\begin{alignat}{1} &e_{1} = \frac{E_{v} Q_{v} {e}^{v}-e_{0} Y_{0}}{\varDelta_{1}} \frac{\mu {e}^{-\mu}}{v Q_{\mu}} ,~~ \tag {3} \end{alignat} $$ where $q$ depends on the protocol (i.e., $q$ = 1/2 for the original BB84 protocol in the proposed scheme and $q \approx 1$ for the efficient BB84 protocol[29]), $Q_\mu$ and $Q_\nu$ are the gains of the signal and decoy states, $E_\mu$ and $E_\nu$ are the quantum bit error rates of the signal and decoy states, $f$ refers to the error correction efficiency, which is set to 1.16, $H_2(e)=-e\log_2{(e)}-(1-e)\log_2{(1-e)}$ represents the binary Shannon entropy function, $\varDelta_1$ implies the yield of single-photon states, $Y_0$ is the yield of vacuum states, $e_1$ denotes the error rate of single-photon states, and $e_0$ is the error rate of vacuum states. In Fig. 2(b), the colored surface illustrates the theoretical key rates at different transmission distances and the key rate corresponding to a transmission distance of 25.6 km is $1.2 \times 10^{-3}$ bit/pulse. The mean of the experimental key rate is $9.52\times10^{-4}$ bit/pulse during one-way communication of Alice preparing quantum states and Bob measuring them as shown in Fig. 2(a). Similarly, in the reverse communication process, where Bob prepares quantum states and Alice measures them, the mean of the experimental key rate is $9.66\times10^{-4}$ bit/pulse as shown in Fig. 2(c). From the above results, we can see that the experimental data is slightly lower than the theoretical data, which is caused by phase drifts or imperfections of the experimental devices. The slight difference between the two experimental results is due to the fact that the loss of encoding devices and the efficiency of detectors are not entirely the same. To experimentally quantify the long-term stability of the proposed system, the interference visibility is characterized by $$ V = \frac{I_{\max} - I_{{\min}}}{I_{\max} + I_{{\min}}} ,~~ \tag {4} $$ where $I_{\max}$ and $I_{{\min}}$ are the maximum and minimum counts of the SPD, respectively. As shown in Fig. 3, we obtain two interference visibilities of 99.01% and 99.08% within one hour, and the internally embedded submaps are the histogram of corresponding interference visibility distribution.
cpl-37-11-110301-fig2.png
Fig. 2. The theoretical and experimental key rates of the proposed scheme. The colored surface indicated in (b) represents the theoretical key rate changes with different transmission distances, while the black line indicates the key rate at a 25.6 km optical transmission distance. The black solid lines in (a) and (c) are the experimental key rates at a 25.6 km fiber distance over an hour; (a) represents the key rate where Alice prepares the quantum states and Bob measures the received quantum states, while (c) indicates the key rate for the reverse communication, where Bob prepares the quantum states and Alice measures them.
Taking the above-mentioned results, the proposed system has excellent stability and can be applied for practical applications. In order to ensure the stability of the actual experimental system, we can use a fiber stretcher or tunable optical delay to ensure that the arm length difference of the AMZI modules of both parties are matched. By integrating all the optical components, this scheme can accelerate the practical process of QKD networks.
cpl-37-11-110301-fig3.png
Fig. 3. Measured interference visibilities within an hour. The internal subgraphs are the histogram of corresponding interference visibility distribution. (a) The interference visibility of the communication with Alice preparing quantum states and Bob measuring them. (b) The interference visibility of the reverse communication.
Even if both parties communicate at the same time, the coding problems caused by the time sequence need not be considered. The reason for this is that the devices of both parties for preparing and measuring quantum states (the SCs) are different. Specifically, both parties adopt the SCs of the longer arm of the AMZI modules to encode or decode phase information. The SCs of the shorter arm are used in the opposite communication. In this way, a conflict between preparation and measurement will not occur. Accordingly, the coding problems that may be caused by the time sequence are solved. In this sense, it is essential to simplify system complexity. It is worth noting that the proposed method relies on the symmetrical nature of the roles of Alice and Bob. That is, one of the two parties prepares quantum states while the other measures them. Therefore, the proposed scheme has not only adopted the BB84 protocol, but also could be used in the SARG04 protocol. In order to improve system performance, a biased basis choice with the decoy-state QKD protocol can also be used in the entire system.[30] Additionally, our apparatuses can also be applied to other protocols such as the recently proposed RFI-QKD protocol. The difference is that the time-bin encoding is adopted for the RFI-QKD protocol. Additional variable optical attenuators are required to prepare the initial quantum states, so we should employ time division multiplexing method, which requires precise modulation of the time difference between the preparation and measurement of two parties, such that Bob's pulses arrive at Alice's station during the interval between pulses generated by Alice. Although the complexity of the initial modulation of the system is to some extent increased, the more widely available protocols are of great significance to the entire QKD communication system. Meanwhile, considering that if both parties all need to measure quantum states, some components such as two SPDs are added in our system, which will increase system cost. However, the characteristic that both parties can prepare and measure quantum states is valuable for promoting the practical process of QKD systems. In summary, we have proposed a fully symmetrical QKD system capable of preparing and measuring quantum states simultaneously. The proposed AMZI module enables both parties to have identical and symmetrical optical devices, which greatly reduces the complexity of the experimental system and improves its practicality and feasibility. Two interference visibilities of above 99% indicate the long-term stability of our system. The secure key rates exceeding 9.5 ${\times10^{-4}}$ bits/pulse are obtained as a function of time over one hour for a fiber distance of 25.6 km during two opposite communications. The above results show that the proposed system can double the key rate. Our scheme offers a viable method to improve the practicality of QKD technology. In future work, we will focus on improving key rates, for instance, combining with wavelength division multiplexing technology. References Quantum cryptographyQuantum cryptography: Public key distribution and coin tossingSecure quantum key distributionFocus on Quantum Cryptography: Theory and PracticeSimple and high-speed polarization-based QKDFinite-Key Analysis for a Practical High-Dimensional Quantum Key Distribution System Based on Time-Phase StatesSpace-to-Ground Quantum Key Distribution Using a Small-Sized Payload on Tiangong-2 Space LabExperimental Point-to-Multipoint Plug-and-Play Measurement-Device-Independent Quantum Key Distribution NetworkFour-State Modulation in Middle of a Quantum Channel for Continuous-Variable Quantum Key Distribution Protocol with Noiseless Linear Amplifier *Quantum Key Distribution with High Loss: Toward Global Secure CommunicationQuantum cryptography with coherent statesLimitations on Practical Quantum CryptographyMeasurement-Device-Independent Quantum Key DistributionExperimental demonstration of polarization encoding quantum key distribution system based on intrinsically stable polarization-modulated unitsReference-frame-independent quantum key distributionQuantum key distribution based on phase encoding in long-distance communication fiberOvercoming the rate–distance limit of quantum key distribution without quantum repeatersQuantum key distribution using in-line highly birefringent interferometersSecure Quantum Key Distribution over 421 km of Optical FiberProvably secure and practical quantum key distribution over 307 km of optical fibreLong-distance quantum key distribution secure against coherent attacksPractical gigahertz quantum key distribution robust against channel disturbanceFundamental limits of repeaterless quantum communicationsSending-or-Not-Sending with Independent Lasers: Secure Twin-Field Quantum Key Distribution over 509 kmChip-based quantum key distributionA modulator-free quantum key distribution transmitter chipDecoy State Quantum Key DistributionPractical decoy state for quantum key distributionEfficient Quantum Key Distribution Scheme and a Proof of Its Unconditional SecurityDecoy-state quantum key distribution with biased basis choice
[1] Gisin N, Ribordy G, Tittel W and Zbinden H 2002 Rev. Mod. Phys. 74 145
[2] Bennett C H and Brassard G 2020 Theor. Comput. Sci. 560 7
[3] Lo H K, Curty M and Tamaki K 2014 Nat. Photon. 8 595
[4] Lütkenhaus N and Shields A J 2009 New J. Phys. 11 045005
[5] Grünenfelder F, Boaron A, Rusca D, Martin A and Zbinden H 2018 Appl. Phys. Lett. 112 051108
[6] Gan Y H, Wang Y, Bao W S, He R S et al. 2019 Chin. Phys. Lett. 36 040301
[7] Liao S K, Lin J, Ren J G, Liu W Y et al. 2017 Chin. Phys. Lett. 34 090302
[8] Tang G Z, Sun S H and Li C Y 2019 Chin. Phys. Lett. 36 070301
[9] Mao Y, Liu Q, Guo Y, Zhang H and Zhou J 2019 Chin. Phys. Lett. 36 100302
[10] Hwang W Y 2003 Phys. Rev. Lett. 91 057901
[11] Huttner B, Imoto N, Gisin N and Mor T 1995 Phys. Rev. A 51 1863
[12] Brassard G, Lütkenhaus N, Mor T and Sanders B C 2000 Phys. Rev. Lett. 85 1330
[13] Lo H K, Curty M and Qi B 2012 Phys. Rev. Lett. 108 130503
[14] Wang J D, Qin X J, Jiang Y Z, Wang X J et al. 2016 Opt. Express 24 8302
[15] Laing A, Scarani V, Rarity J G and O'Brien J L 2010 Phys. Rev. A 82 012304
[16] Sun S H, Ma H Q, Han J J, Liang L M and Li C Z 2010 Opt. Lett. 35 1203
[17] Lucamarini M, Yuan Z L, Dynes J F and Shields A J 2018 Nature 557 400
[18] Martinez A, Fröhlich B, Dynes J F, Sharpe A W et al. 2018 Appl. Phys. Lett. 113 031107
[19] Boaron A, Boso G, Rusca D, Vulliez C et al. 2018 Phys. Rev. Lett. 121 190502
[20] Korzh B, Lim C C W, Houlmann R, Gisin N et al. 2015 Nat. Photon. 9 163
[21] Fröhlich B, Lucamarini M, Dynes J F, Comandar L C et al. 2017 Optica 4 163
[22] Wang S, Chen W, Yin Z Q, He D Y et al. 2018 Opt. Lett. 43 2030
[23] Pirandola S, Laurenza R, Ottaviani C and Banchi L 2017 Nat. Commun. 8 15043
[24] Chen J P, Zhang C, Liu Y, Jiang C et al. 2020 Phys. Rev. Lett. 124 070501
[25] Sibson P, Erven C, Godfrey M, Miki S et al. 2017 Nat. Commun. 8 13984
[26] Paraı̈so T K, De Marco I, Roger T, Marangon D G et al. 2019 npj Quantum Inf. 5 42
[27] Lo H K, Ma X F and Chen K 2005 Phys. Rev. Lett. 94 230504
[28] Ma X F, Qi B, Zhao Y and Lo H K 2005 Phys. Rev. A 72 012326
[29] Lo H K, Chau H F and Ardehali M 2005 J. Cryptology 18 133
[30] Wei Z C, Wang W L, Zhang Z, Gao M et al. 2013 Sci. Rep. 3 2453