Integrated photonics provides a route to both miniaturization of quantum key distribution (QKD) devices and enhancing their performance. A key element for achieving discrete-variable QKD is a single-photon detector. It is highly desirable to integrate detectors onto a photonic chip to enable the realization of practical and scalable quantum networks. We realize a heterogeneously integrated, superconducting silicon-photonic chip. Harnessing the unique high-speed feature of our optical waveguide-integrated superconducting detector, we perform the first optimal Bell-state measurement (BSM) of time-bin encoded qubits generated from two independent lasers. The optimal BSM enables an increased key rate of measurement-device-independent QKD (MDI-QKD), which is immune to all attacks against the detection system and hence provides the basis for a QKD network with untrusted relays. Together with the time-multiplexed technique, we have enhanced the sifted key rate by almost one order of magnitude. With a 125-MHz clock rate, we obtain a secure key rate of 6.166 kbps over 24.0 dB loss, which is comparable to the state-of-the-art MDI-QKD experimental results with a GHz clock rate. Combined with integrated QKD transmitters, a scalable, chip-based, and cost-effective QKD network should become realizable in the near future. |
1.IntroductionQuantum key distribution (QKD) employs the laws of quantum physics to provide information-theoretical security for key exchange.1–5 Despite the substantial progress in the past 35 years, practical implementations of QKD still deviate from ideal descriptions in security proofs, mainly due to potential side-channel attacks. For instance, a series of loopholes have been identified due to the imperfections of measurement devices.6–9 Inspired by the time-reversed entanglement-based QKD, measurement-device-independent QKD (MDI-QKD), which removes all detector side attacks, has been proposed.10,11 Instead of relying on the trusted nodes of traditional QKD protocols, MDI-QKD requires only a central node (Charlie) to perform a Bell-state measurement (BSM). The correlations between the two senders (Alice and Bob) can be obtained from the BSM results. Importantly, even if Charlie is not trusted, one can still guarantee the security of the MDI-QKD as long as Charlie can project his two photons onto Bell states. The outstanding features of MDI-QKD invite global experimental efforts, which are mainly based on bulk/fiber components.12–20 Despite the additional BSM by Charlie, the key rate17 and the communication distance18 of MDI-QKD can be comparable with those of traditional QKD. Furthermore, the star-like topology of the MDI-QKD quantum network is naturally suited for the metropolitan network with multiple users.21–23 Recently, the generalization of the MDI protocol to multipartite schemes has been investigated.24–26 It has been shown that the performance of the multipartite schemes can be advantageous to iterative use of independent bipartite protocols.26 From the perspectives of hardware, recent developments involve particular integrated photonic devices for QKD, including on-chip encoders based on silicon modulators,27–31 on-chip transmitters including lasers, photodiodes, modulators based on indium phosphide,32,33 and decoders based on silicon oxynitride34 and silicon dioxide,35 as well as integrated silicon-photonic chips for continuous-variable (CV) QKD.36,37 The notion of MDI has also been extended to CV protocols38 and can be applied for multipartite metropolitan networks with a considerable rate.39 Most of the components used in QKD, including lasers, modulators, and passive components [such as beam splitters (BSs) and attenuators] are widely used in classical optical communication systems and are not specifically designed for QKD. In addition, single-photon detectors are indispensable for discrete-variable QKD systems, because the senders’ pulses have to have a mean photon number of <1 to guarantee communication security. So far, a single-photon detector integrated chip platform has not been employed in an MDI-QKD system. In this work, we report the realization of a heterogeneously integrated, superconducting silicon-photonic chip, and its application for MDI-QKD. 2.Schematic of a Time-Multiplexed MDI-QKDWe use time-bin qubits to encode bit information, which are well suited for fiber-based quantum communication due to their immunity to random polarization rotations in fibers. The conceptual scheme of our experiment is shown in Fig. 1(a). Alice and Bob encode keys with time-bin qubits using modulated weak coherent pulse sets. In Pauli -basis, the time-bins are encoded as the early and the late for bit values of 0 and 1, respectively. The temporal separation between and is . In Pauli -basis, the keys are encoded as the coherent superposition states between and : and , representing bit values of 0 and 1, respectively. The -basis code is used for key exchange, and the -basis code is for error detection. These encoded time-bin qubits are then sent to Charlie, who performs the BSM on the incoming time-bin qubits using a BS and two single-photon detectors ( and ).10,11 Using linear optical elements, the success probability of BSM is bounded by 50%.40 For projective measurements, optimal BSM corresponds to distinguish two out of four Bell states. Although time-bin qubits are well suited for fiber-based quantum communication, optimal BSM for time-bin qubits has yet to be realized. The bottleneck so far has been the lack of high-speed single-photon detectors.33,41,42 The BSM scheme for time-bin qubits is shown in the inset of Fig. 1(a). The coincidence counts between two different detectors at different time bins correspond to coincidence counts between ( detects a photon at an early bin, red) and ( detects a photon at a late bin, red), or coincidence counts between and . Such coincidence detection projects two photons onto , which is the common scenario realized in most of the time-bin BSM schemes.14,33,42 In order to achieve optimal BSM, we also need to detect by measuring the coincidence counts of one detector at different time bins, corresponding to the coincidence detection between and , or and . This particular BSM requires high-speed single-photon detection, able to detect consecutive photons separated by . The unique design of the waveguide-integrated superconducting nanowire single-photon detector (SNSPD) provides a short recovery time () for single-photon detection, enabling us to perform time-bin-encoded optimal BSM between two independent lasers for the first time. Note that if we only use one set of time-bin qubits, the system repetition rate will be limited to . In order to maximize the channel efficiency, we use time-multiplexed encoding to insert independent sets of bins ( and ) between the and bins of and . Therefore, the system repetition rate will be greatly increased to , where is the time difference between and . By harnessing the optimal BSM and time-multiplexing, the key rate generation is enhanced by an order of magnitude compared to the system without using these two techniques. Consequently, our key rate is comparable to the state-of-the-art MDI-QKD experimental results with a GHz clock rate, as detailed later. 3.Integrated Relay Server for MDI-QKD Based on Superconducting Silicon PhotonicsOur heterogeneously integrated, superconducting silicon-photonic platform provides a server architecture for realizing a multiple-user trust-node-free quantum network with a fully connected bipartite-graph topology. As shown in Fig. 1(b), modulated weak coherent pulses are prepared by Alices () and Bobs () and are sent to the routers. Two routers select the pair of the communicating Alice and Bob and send their pulses to an untrusted relay server controlled by Charlie. At Charlie’s station, a chip with multiple low-dead-time,43 low-timing-jitter,44 and high-efficiency detectors in conjunction with low-loss silicon photonics45 is used to realize the BSM. This configuration allows any user at Alice’s side to communicate with any user at Bob’s side and hence to realize a fully connected bipartite quantum network. The schematic of our experimental setup is shown in Fig. 2(a). Alice (Bob) chops the CW laser operated at about 1536.47 nm into the desired pulse sequences. The pulse is about 370 ps wide and separated by 12 ns at a rate of 41.7 MHz rate (1/24 ns). -basis (-basis) states are generated by chopping the laser into or (and) states with intensity modulators (IMs). The average photon numbers per pulse in the two bases are about the same. The resulting pulses are sent into a phase modulator (PM) with (without) -phase shift for the generation of () states. The electrical signals applied to the modulators are generated by an arbitrary waveform generator [not shown in Fig. 2(a)]. An additional 50:50 BS combined with a power sensor (PS) is employed to monitor the long-term stability of laser power in each encoder. One of the most important requirements of MDI-QKD is to obtain high-quality two-photon Hong–Ou–Mandel (HOM) interference on the integrated relay server. To achieve that, it is necessary for Alice and Bob to generate indistinguishable weak-coherent pulses. The interfering pulses have to be indistinguishable in all degrees of freedom (DOFs), including spectrum, time, and polarization. For the spectrum DOF, Alice’s and Bob’s unmodulated pulses pass through polarization beam splitters (PBSs), with one of the outputs connected with a 50:50 BS for frequency beating. From the beating signal, we feedback onto one of the lasers and regulate the frequency difference of these two lasers to be within 10 MHz (see Supplementary Material for details). For the polarization DOF, two electrical polarization controllers (EPCs) are used to optimize the polarization of both pulses before they are coupled into Charlie’s chip. For the temporal DOF, we adjust the relative electrical delay between Alice’s and Bob’s IMs to ensure that their pulses arrive at the chip simultaneously. Attenuators are used to adjust the average photon number per pulse and simulate the loss of the communication channels. These pulses are then sent to Charlie’s relay server chip, which is mounted on a nanopositioner in a closed-cycle cryostat with a base temperature of 2.1 K. We show the U-shape waveguide-integrated SNSPD in Fig. 2(b) in which the superconducting nanowire (80-nm-wide, -long) is highlighted in red and the silicon optical waveguide (500 nm-wide) is shown in blue. Figure 2(c) shows the scanning electron microscope image of the photonic-crystal grating coupler,46,47 which couples light from the fiber array to the chip. We obtain coupling loss from the reference device, which is at the right side of the main device.48 The grating coupler with a back-reflected mirror offers a coupling loss of at a wavelength of 1536 nm. The main device has two identical grating couplers, coupling Alice’s and Bob’s pulses from fiber to chip. Silicon optical waveguides guide the pulses to a multi-mode interference (MMI) coupler, which acts as a 50:50 BS. At the output of the MMI, two waveguide-integrated SNSPDs work simultaneously for detecting photons. Both SNSPDs are biased with constant voltage sources and connected with electronic readout circuitries. In Fig. 2(d), we show the electrical signals of waveguide-integrated SNSPDs with different nanowire lengths. The decay time of SNSPD is directly proportional to the kinetic inductance of the nanowire. Shorter detectors exhibit lower kinetic inductance and therefore have shorter decay times, resulting in faster detector recovery.49 However, for traditional normal-incidence SNSPDs, the shorter nanowire length leads to lower detection efficiency, because it is necessary to fabricate large-area meander nanowire to match the optical modes from fibers to obtain high detection efficiency. Therefore, it is hard to simultaneously obtain low dead time and high detection efficiency with the traditional design. In our work, we use the evanescent coupling between the optical waveguide and superconducting nanowire to circumvent this trade-off. Therefore, we are able to obtain low dead time as well as high on-chip detection efficiency. To further quantitatively characterize the efficiency of our SNSPDs for projecting two photons onto , we measure the normalized coincidence counts of one detector consecutively detecting both early and late time bins as a function of the time separation between them. The experimental results are shown in Fig. 2(e). The detection probability is significantly decreased when the time separation is smaller than the dead time and is fully recovered for separation larger than 12 ns. Based on these results, the dead time of the SNSPD we use in our QKD system is about 3.4 ns for the 1/e-delay time, and we set the time separation between and to be 12 ns. This short time separation not only allows high-speed detection but also greatly simplifies frequency stabilization of the light source (LS). For a traditional normal-incidence SNSPD that limits 75 ns time-bin separation,50 a 185-kHz frequency difference between two lasers can result in a 5-deg phase error, which is technologically challenging and not practical. By contrast, for our waveguide-integrated SNSPD, the frequency-stabilization requirement is only 1.2 MHz for achieving the same phase error, which is significantly more feasible in practice. 4.Optimal Bell-State Measurement for Time-Bin QubitsIn Figs. 3(a) and 3(b), we show the two-photon coincidence counts with optimal BSM as a function of the relative electronic delays between Alice’s and Bob’s pulse sequence in which Charlie projects the two photons sent by Alice and Bob onto and , respectively. The dependence of the coincidence counts on the delay is a result of BSM, showing the coherent two-photon superposition. Due to the symmetry of and , when Alice and Bob send the same states in -basis, or , we obtain the destructive/constructive interference patterns for the BSM results of , as shown by the blue dots in Figs. 3(a) and 3(b). When Alice and Bob send the orthogonal states in -basis, or , we obtain the inverse results, as shown by the red dots in Figs. 3(a) and 3(b). [The logic of coincidence detection for and is shown in the inset of Fig. 1(a).] We obtain secure keys from the -basis measurements and verify the reliability of the QKD system in -basis.18 To quantify the performance of the system, we analyze the quantum bit error rate (QBER). For instance, Alice and Bob exchange their keys conditionally on Charlie obtaining from his BSM, when Alice and Bob send the same/orthogonal states. For -basis, the probability of Charlie obtaining a coincidence at two subsequent time bins with time separation is . We then obtain the QBER in -basis () based on51 In addition, the phase difference of two subsequent time bins induced by frequency difference is where is the speed of light and () and () are the laser’s frequency and wavelength of Alice (Bob), respectively.can be written as where is the visibility and is the coincidence window.As for -basis, always have the same formula for . In Figs. 3(c) and 3(d), we show the measured and (blue) as functions of time delays between Alice and Bob, which show the minimum close to 0.25 at the zero time delay. For -basis, the measured (red) are close to zero, showing the high quality of our system. In Figs. 3(e) and 3(f), we vary the relative central wavelength between Alice’s and Bob’s lasers. Also, we show the results for and as functions of the relative wavelength, respectively. The experimental data (blue dots) agree well with the theoretical prediction (blue curves). 5.Enhancing Key Rate with Time-MultiplexingAlthough the full-recovery time of the detector determines the time-bin separation to be 12 ns, we can harness the time-multiplexed technique by inserting more pairs of time-bin pulses to enhance the key rate. This is particularly useful in high-loss communication applications. As shown in the insets of Fig. 4(a), we insert up to five bins within 12 ns with an equal temporal separation of 2 ns. By combining this time-multiplexed technique and optimal BSM, we enhance the sifted key rate by almost an order of magnitude. At the same time, these two techniques have little impact on and , as shown in Fig. 4(b). We demonstrate a complete MDI-QKD system including decoy states and phase randomization for guaranteeing the security13–20,52,53 with our heterogeneously integrated, superconducting silicon-photonic platform. We use a four-intensity encoding protocol52 with three intensities (, , ) in the -basis for decoy-state analysis and one intensity () in the -basis for key generation. Finite-key effects are considered in the secure-key-rate analysis with a failure probability of .54 For statistical fluctuations, we use the joint constraints where the same observables are combined and treated together52 (see Supplementary Material for details). In this part of the experiment, we evenly insert two more pairs of time-bin qubits within 12 ns separation. Therefore, the effective clock rate of our system is tripled to 125 MHz (1/8 ns). The secure key rates for different losses are shown in Fig. 5. With the 125 MHz clock rate, we obtain the key rate of 6.166 kbps at the loss of 24.0 dB. This loss includes chip insertion loss . The actual transmission loss is about 19.5 dB, which corresponds to 98 km standard fiber. To the best of our knowledge, this is the highest secure key rate obtained experimentally with transmission loss in MDI-QKD, which is highly relevant in the context of a metropolitan quantum network without detector vulnerabilities. Furthermore, we obtain the secure key rates of 170 and 34 bps with total losses of about 35.0 and 44.0 dB. We emphasize that our secure key rates with the 125 MHz clocked system are very close to the best MDI-QKD experiments with a GHz clock rate.31,56 In contrast with the GHz clock rate MDI-QKD experiments, our system does not require the complicated injection locking technique, which significantly reduces the complexity of the transmitter (see Table S1 in the Supplementary Material for detailed comparison). 6.ConclusionWe have demonstrated the first integrated relay server for MDI-QKD with a heterogeneous superconducting silicon-photonic chip. The excellent optical and electronic performance of this chip not only facilitates the experimental high-visibility HOM interference and low QBER, but also allows us to perform optimal BSM for time-bin qubits for the first time. Our work shows that integrated quantum-photonic chips provide not only a route to miniaturization but also significantly enhance the system performance more than traditional platforms. Our chip-based relay server can also be employed in twin-field QKD (TF-QKD),57 which can overcome the rate-distance limit of QKD without quantum repeaters. TF-QKD is indispensable in long-distance intercity communication links. Moreover, the chip-based relay server with the MDI-QKD protocol presented in this work could be an ideal solution for a scalable trust-node-free metropolitan quantum network. Using more advanced waveguide-integrated SNSPDs,45 one can further improve the integrated server with a high detection efficiency, low timing jitter, and high repetition rate. Combined with photonic-chip transmitters,31,33 a fully chip-based, scalable, and high-key-rate MDI-QKD metropolitan quantum network should be realized in the near future. AcknowledgmentsWe would like to thank R. Chen and A. Miller for helpful discussions. This research was supported by the National Key Research and Development Program of China (Nos. 2017YFA0303704, 2019YFA0308700, and 2017YFA0304002), the National Natural Science Foundation of China (Nos. 11690032, 11321063, and 12033002), the NSFC-BRICS (No. 61961146001), the Leading-Edge Technology Program of Jiangsu Natural Science Foundation (No. BK20192001), and the Fundamental Research Funds for the Central Universities. ReferencesH.-K. Lo and H. F. Chau,
“Unconditional security of quantum key distribution over arbitrarily long distances,”
Science, 283
(5410), 2050
–2056
(1999). https://doi.org/10.1126/science.283.5410.2050 SCIEAS 0036-8075 Google Scholar
N. Gisin et al.,
“Quantum cryptography,”
Rev. Mod. Phys., 74
(1), 145
–195
(2002). https://doi.org/10.1103/RevModPhys.74.145 RMPHAT 0034-6861 Google Scholar
V. Scarani et al.,
“The security of practical quantum key distribution,”
Rev. Mod. Phys., 81
(3), 1301
–1350
(2009). https://doi.org/10.1103/RevModPhys.81.1301 RMPHAT 0034-6861 Google Scholar
F. Xu et al.,
“Secure quantum key distribution with realistic devices,”
Rev. Mod. Phys., 92
(2), 025002
(2020). https://doi.org/10.1103/RevModPhys.92.025002 RMPHAT 0034-6861 Google Scholar
S. Pirandola et al.,
“Advances in quantum cryptography,”
Adv. Opt. Photonics, 12
(4), 1012
–1236
(2020). https://doi.org/10.1364/AOP.361502 AOPAC7 1943-8206 Google Scholar
V. Makarov, A. Anisimov and J. Skaar,
“Effects of detector efficiency mismatch on security of quantum cryptosystems,”
Phys. Rev. A, 74
(2), 022313
(2006). https://doi.org/10.1103/PhysRevA.74.022313 Google Scholar
Y. Zhao et al.,
“Quantum hacking: experimental demonstration of time-shift attack against practical quantum-key-distribution systems,”
Phys. Rev. A, 78
(4), 042333
(2008). https://doi.org/10.1103/PhysRevA.78.042333 Google Scholar
L. Lydersen et al.,
“Hacking commercial quantum cryptography systems by tailored bright illumination,”
Nat. Photonics, 4
(10), 686
–689
(2010). https://doi.org/10.1038/nphoton.2010.214 NPAHBY 1749-4885 Google Scholar
M. Elezov et al.,
“Countermeasure against bright-light attack on superconducting nanowire single-photon detector in quantum key distribution,”
Opt. Express, 27
(21), 30979
–30988
(2019). https://doi.org/10.1364/OE.27.030979 OPEXFF 1094-4087 Google Scholar
S. L. Braunstein and S. Pirandola,
“Side-channel-free quantum key distribution,”
Phys. Rev. Lett., 108
(13), 130502
(2012). https://doi.org/10.1103/PhysRevLett.108.130502 PRLTAO 0031-9007 Google Scholar
H.-K. Lo, M. Curty and B. Qi,
“Measurement-device-independent quantum key distribution,”
Phys. Rev. Lett., 108
(13), 130503
(2012). https://doi.org/10.1103/PhysRevLett.108.130503 PRLTAO 0031-9007 Google Scholar
A. Rubenok et al.,
“Real-world two-photon interference and proof-of-principle quantum key distribution immune to detector attacks,”
Phys. Rev. Lett., 111
(13), 130501
(2013). https://doi.org/10.1103/PhysRevLett.111.130501 PRLTAO 0031-9007 Google Scholar
Y. Liu et al.,
“Experimental measurement-device-independent quantum key distribution,”
Phys. Rev. Lett., 111
(13), 130502
(2013). https://doi.org/10.1103/PhysRevLett.111.130502 PRLTAO 0031-9007 Google Scholar
Y.-L. Tang et al.,
“Measurement-device-independent quantum key distribution over 200 km,”
Phys. Rev. Lett., 113
(19), 190501
(2014). https://doi.org/10.1103/PhysRevLett.113.190501 PRLTAO 0031-9007 Google Scholar
Z. Tang et al.,
“Experimental demonstration of polarization encoding measurement-device-independent quantum key distribution,”
Phys. Rev. Lett., 112
(19), 190503
(2014). https://doi.org/10.1103/PhysRevLett.112.190503 PRLTAO 0031-9007 Google Scholar
C. Wang et al.,
“Phase-reference-free experiment of measurement-device-independent quantum key distribution,”
Phys. Rev. Lett., 115
(16), 160502
(2015). https://doi.org/10.1103/PhysRevLett.115.160502 PRLTAO 0031-9007 Google Scholar
L. Comandar et al.,
“Quantum key distribution without detector vulnerabilities using optically seeded lasers,”
Nat. Photonics, 10
(5), 312
–315
(2016). https://doi.org/10.1038/nphoton.2016.50 NPAHBY 1749-4885 Google Scholar
H.-L. Yin et al.,
“Measurement-device-independent quantum key distribution over a 404 km optical fiber,”
Phys. Rev. Lett., 117
(19), 190501
(2016). https://doi.org/10.1103/PhysRevLett.117.190501 PRLTAO 0031-9007 Google Scholar
C. Wang et al.,
“Measurement-device-independent quantum key distribution robust against environmental disturbances,”
Optica, 4
(9), 1016
–1023
(2017). https://doi.org/10.1364/OPTICA.4.001016 Google Scholar
H. Liu et al.,
“Experimental demonstration of high-rate measurement-device-independent quantum key distribution over asymmetric channels,”
Phys. Rev. Lett., 122
(16), 160501
(2019). https://doi.org/10.1103/PhysRevLett.122.160501 PRLTAO 0031-9007 Google Scholar
B. Fröhlich et al.,
“A quantum access network,”
Nature, 501
(7465), 69
–72
(2013). https://doi.org/10.1038/nature12493 Google Scholar
R. J. Hughes et al.,
“Network-centric quantum communications with application to critical infrastructure protection,”
(2013). Google Scholar
Y.-L. Tang et al.,
“Measurement-device-independent quantum key distribution over untrustful metropolitan network,”
Phys. Rev. X, 6
(1), 011024
(2016). https://doi.org/10.1103/PhysRevX.6.011024 PRXHAE 2160-3308 Google Scholar
Y. Fu et al.,
“Long-distance measurement-device-independent multiparty quantum communication,”
Phys. Rev. Lett., 114
(9), 090501
(2015). https://doi.org/10.1103/PhysRevLett.114.090501 PRLTAO 0031-9007 Google Scholar
C. Zhu, F. Xu and C. Pei,
“W-state analyzer and multi-party measurement-device-independent quantum key distribution,”
Sci. Rep., 5
(1), 17449
(2015). https://doi.org/10.1038/srep17449 SRCEC3 2045-2322 Google Scholar
F. Grasselli, H. Kampermann and D. Bruß,
“Conference key agreement with single-photon interference,”
New J. Phys., 21
(12), 123002
(2019). https://doi.org/10.1088/1367-2630/ab573e NJOPFM 1367-2630 Google Scholar
Y. Ding et al.,
“High-dimensional quantum key distribution based on multicore fiber using silicon photonic integrated circuits,”
npj Quantum Inf., 3
(1), 25
(2017). https://doi.org/10.1038/s41534-017-0026-2 Google Scholar
D. Bunandar et al.,
“Metropolitan quantum key distribution with silicon photonics,”
Phys. Rev. X, 8
(2), 021009
(2018). https://doi.org/10.1103/PhysRevX.8.021009 PRXHAE 2160-3308 Google Scholar
C. Ma et al.,
“Silicon photonic transmitter for polarization-encoded quantum key distribution,”
Optica, 3
(11), 1274
–1278
(2016). https://doi.org/10.1364/OPTICA.3.001274 Google Scholar
P. Sibson et al.,
“Integrated silicon photonics for high-speed quantum key distribution,”
Optica, 4
(2), 172
–177
(2017). https://doi.org/10.1364/OPTICA.4.000172 Google Scholar
K. Wei et al.,
“High-speed measurement-device-independent quantum key distribution with integrated silicon photonics,”
Phys. Rev. X, 10
(3), 031030
(2020). https://doi.org/10.1103/PhysRevX.10.031030 PRXHAE 2160-3308 Google Scholar
C. Agnesi et al.,
“Hong–Ou–Mandel interference between independent III–V on silicon waveguide integrated lasers,”
Opt. Lett., 44
(2), 271
–274
(2019). https://doi.org/10.1364/OL.44.000271 OPLEDP 0146-9592 Google Scholar
H. Semenenko et al.,
“Chip-based measurement-device-independent quantum key distribution,”
Optica, 7
(3), 238
–242
(2020). https://doi.org/10.1364/OPTICA.379679 Google Scholar
P. Sibson et al.,
“Chip-based quantum key distribution,”
Nat. Commun., 8
(1), 13984
(2017). https://doi.org/10.1038/ncomms13984 NCAOBW 2041-1723 Google Scholar
C.-Y. Wang et al.,
“Integrated measurement server for measurement-device-independent quantum key distribution network,”
Opt. Express, 27
(5), 5982
–5989
(2019). https://doi.org/10.1364/OE.27.005982 OPEXFF 1094-4087 Google Scholar
G. Zhang et al.,
“An integrated silicon photonic chip platform for continuous-variable quantum key distribution,”
Nat. Photonics, 13
(12), 839
–842
(2019). https://doi.org/10.1038/s41566-019-0504-5 NPAHBY 1749-4885 Google Scholar
J. F. Tasker et al.,
“Silicon photonics interfaced with integrated electronics for 9 GHz measurement of squeezed light,”
Nat. Photonics, 15
(1), 11
–15
(2021). https://doi.org/10.1038/s41566-020-00715-5 NPAHBY 1749-4885 Google Scholar
S. Pirandola et al.,
“High-rate measurement-device-independent quantum cryptography,”
Nat. Photonics, 9
(6), 397
–402
(2015). https://doi.org/10.1038/nphoton.2015.83 NPAHBY 1749-4885 Google Scholar
C. Ottaviani et al.,
“Modular network for high-rate quantum conferencing,”
Commun. Phys., 2
(1), 118
(2019). https://doi.org/10.1038/s42005-019-0209-6 Google Scholar
J. Calsamiglia and N. Lütkenhaus,
“Maximum efficiency of a linear-optical Bell-state analyzer,”
Appl. Phys. B, 72
(1), 67
–71
(2001). https://doi.org/10.1007/s003400000484 Google Scholar
J. A. W. van Houwelingen et al.,
“Quantum teleportation with a three-Bell-state analyzer,”
Phys. Rev. Lett., 96
(13), 130502
(2006). https://doi.org/10.1103/PhysRevLett.96.130502 PRLTAO 0031-9007 Google Scholar
F. Samara et al.,
“Entanglement swapping between independent and asynchronous integrated photon-pair sources,”
Quantum Sci. Technol., 6 045024
(2021). Google Scholar
W. H. Pernice et al.,
“High-speed and high-efficiency travelling wave single-photon detectors embedded in nanophotonic circuits,”
Nat. Commun., 3
(1), 1325
(2012). https://doi.org/10.1038/ncomms2307 NCAOBW 2041-1723 Google Scholar
B. Korzh et al.,
“Demonstration of sub-3 ps temporal resolution with a superconducting nanowire single-photon detector,”
Nat. Photonics, 14
(4), 250
–255
(2020). https://doi.org/10.1038/s41566-020-0589-x NPAHBY 1749-4885 Google Scholar
S. Ferrari, C. Schuck and W. Pernice,
“Waveguide-integrated superconducting nanowire single-photon detectors,”
Nanophotonics, 7
(11), 1725
–1758
(2018). https://doi.org/10.1515/nanoph-2018-0059 Google Scholar
Y. Ding et al.,
“Fully etched apodized grating coupler on the SOI platform with −0.58 dB coupling efficiency,”
Opt. Lett., 39
(18), 5348
–5350
(2014). https://doi.org/10.1364/OL.39.005348 OPLEDP 0146-9592 Google Scholar
Y. Luo et al.,
“Low-loss two-dimensional silicon photonic grating coupler with a backside metal mirror,”
Opt. Lett., 43
(3), 474
–477
(2018). https://doi.org/10.1364/OL.43.000474 OPLEDP 0146-9592 Google Scholar
A. Gaggero et al.,
“Amplitude-multiplexed readout of single photon detectors based on superconducting nanowires,”
Optica, 6
(6), 823
–828
(2019). https://doi.org/10.1364/OPTICA.6.000823 Google Scholar
A. J. Kerman et al.,
“Kinetic-inductance-limited reset time of superconducting nanowire photon counters,”
Appl. Phys. Lett., 88
(11), 111116
(2006). https://doi.org/10.1063/1.2183810 APPLAB 0003-6951 Google Scholar
R. Valivarthi et al.,
“Efficient Bell state analyzer for time-bin qubits with fast-recovery WSi superconducting single photon detectors,”
Opt. Express, 22
(20), 24497
–24506
(2014). https://doi.org/10.1364/OE.22.024497 OPEXFF 1094-4087 Google Scholar
J. Jin et al.,
“Two-photon interference of weak coherent laser pulses recalled from separate solid-state quantum memories,”
Nat. Commun., 4
(1), 2386
(2013). https://doi.org/10.1038/ncomms3386 NCAOBW 2041-1723 Google Scholar
Y.-H. Zhou, Z.-W. Yu and X.-B. Wang,
“Making the decoy-state measurement-device-independent quantum key distribution practically useful,”
Phys. Rev. A, 93
(4), 042324
(2016). https://doi.org/10.1103/PhysRevA.93.042324 Google Scholar
Z. Zhang et al.,
“Improved key-rate bounds for practical decoy-state quantum-key-distribution systems,”
Phys. Rev. A, 95
(1), 012333
(2017). https://doi.org/10.1103/PhysRevA.95.012333 Google Scholar
M. Curty et al.,
“Finite-key analysis for measurement-device-independent quantum key distribution,”
Nat. Commun., 5
(1), 3732
(2014). https://doi.org/10.1038/ncomms4732 NCAOBW 2041-1723 Google Scholar
S. Pirandola et al.,
“Fundamental limits of repeaterless quantum communications,”
Nat. Commun., 8
(1), 15043
(2017). https://doi.org/10.1038/ncomms15043 NCAOBW 2041-1723 Google Scholar
R. I. Woodward et al.,
“Gigahertz measurement-device-independent quantum key distribution using directly modulated lasers,”
npj Quantum Inf., 7
(1), 58
(2021). https://doi.org/10.1038/s41534-021-00394-2 Google Scholar
M. Lucamarini et al.,
“Overcoming the rate–distance limit of quantum key distribution without quantum repeaters,”
Nature, 557
(7705), 400
–403
(2018). https://doi.org/10.1038/s41586-018-0066-6 Google Scholar
BiographyXiaodong Zheng is a PhD student working under the supervision of Xiao-Song Ma at the School of Physics of Nanjing University (NJU). Currently, he is working on superconducting nanowire single-photon detection and quantum key distribution. Peiyu Zhang received her MS degree from NJU in 2020. Currently, she is working on optical communication. Renyou Ge received his PhD from Sun Yat-sen University in 2021. Currently, he is working on integrated optical devices. Liangliang Lu received his BS degree from Guangzhou University in 2009 and his PhD from NJU in 2015. He worked as a researcher at the School of Physics of NJU from 2017 to 2020 and joined the School of Physical Science and Technology at Nanjing Normal University in November 2020. His research area is integrated photonic quantum information processing, including quantum simulation, quantum key distribution, and nonlinear optics. Guanglong He is a PhD student working under the supervision of Labao Zhang at the School of Electronic Science and Engineering of NJU. Currently, he is working on superconducting nanowire single-photon detectors. Qi Chen is a PhD student working under the supervision of Labao Zhang at the School of Electronic Science and Engineering of NJU. Currently, he is working on superconducting nanowire single-photon detectors. Fangchao Qu received his MS degree from NJU in 2020. Currently, he is working on integrated circuits. Labao Zhang received his PhD from NJU, Nanjing, China, in 2010. He is currently a professor at NJU. His current research interests include the phenomena and the physics of nanostructured superconductors. Xinlun Cai received his PhD in electrical and electronics engineering from the University of Bristol, Bristol, UK, in 2012. He is currently a professor at the School of Electronics and Information Technology, Sun Yat-sen University, Guangzhou, China. His research is mainly focused on optical communication and photonic integrated devices. Yanqing Lu received his BS and PhD degrees from NJU, Nanjing, China, in 1991 and 1996, respectively. He has 5 years of experience in the U.S. and China telecom industries. He designed and developed a serial of liquid-crystal-based fiber-optic devices with his colleagues, which include variable optical attenuators, variable Mux/Demux, and DWDM wavelength blockers. He is currently a Changjiang distinguished professor at NJU. His research interests include liquid crystal photonics, nonlinear optics, and quantum optics. Shining Zhu is a professor at the School of Physics and a principal investigator at the National Laboratory of Solid State Microstructures, NJU, Nanjing, China. He is an academician of the Chinese Academy of Sciences (CAS) and a fellow of Optical Society of America, Chinese Optical Society, and American Physical Society, respectively. His research interests include microstructured functional materials, nonlinear optics, laser physics, quantum communication, and integrated quantum optics. Peiheng Wu received his PhD in physics from NJU, Nanjing, China, in 1961. He has been a professor at NJU, since 1985 and an academician at the CAS, Beijing, China, since 2005. From January 2001 to July 2001, he was a professor with RIEC, Tohoku University, Sendai, Japan. His research interests include superconducting electronics, high-frequency techniques, and their applications. Xiao-Song Ma received his BS degree from NJU in 2003 and his PhD from the University of Vienna in 2010. He worked as a postdoc fellow at the University of Vienna and Yale University from 2010 to 2015. He joined the School of Physics at NJU as a professor in 2015. His research interests include quantum communication, quantum network, quantum simulation and computation, solid-state quantum memory, and integrated photonic quantum technologies. |