Integrated measurement server for measurement-device-independent quantum key distribution network

Ci-Yu Wang; Jun Gao; Zhi-Qiang Jiao; Lu-Feng Qiao; Ruo-Jing Ren; Zhen Feng; Yuan Chen; Zeng-Quan Yan; Yao Wang; Hao Tang; Xian-Min Jin

doi:10.1364/OE.27.005982

Optics Express
Vol. 27,
Issue 5,
pp. 5982-5989
(2019)
•https://doi.org/10.1364/OE.27.005982

Integrated measurement server for measurement-device-independent quantum key distribution network

Ci-Yu Wang, Jun Gao, Zhi-Qiang Jiao, Lu-Feng Qiao, Ruo-Jing Ren, Zhen Feng, Yuan Chen, Zeng-Quan Yan, Yao Wang, Hao Tang, and Xian-Min Jin

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Ci-Yu Wang, Jun Gao, Zhi-Qiang Jiao, Lu-Feng Qiao, Ruo-Jing Ren, Zhen Feng, Yuan Chen, Zeng-Quan Yan, Yao Wang, Hao Tang, and Xian-Min Jin, "Integrated measurement server for measurement-device-independent quantum key distribution network," Opt. Express 27, 5982-5989 (2019)

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About this Article
History
- Original Manuscript: October 25, 2018
- Revised Manuscript: December 25, 2018
- Manuscript Accepted: December 26, 2018
- Published: February 20, 2019

Abstract

Quantum key distribution (QKD), harnessing quantum physics and optoelectronics, may promise unconditionally secure information exchange in theory. Recently, theoretical and experimental advances in measurement-device-independent (MDI)-QKD have successfully closed the physical back door in detection terminals. However, the issues of scalability, stability, cost and loss prevent QKD systems from widespread application in practice. Here, we propose and experimentally demonstrate a solution to build a star-topology quantum access network with an integrated server. By using femtosecond laser direct writing techniques, we construct integrated circuits for all the elements of Bell state analyzer together and are able to integrate 10 such analyzer structures on a single photonic chip. The measured high-visibility Bell state analysis suggests the integrated server as a promising platform for the practical application of MDI-QKD network.

Living in a new era of ‘Internet Of Everything’, the ability to build a secure communication network is essential more than ever. Since the emergence of QKD [1] – an indispensable part of quantum communication, many proof-of-principle demonstrations of quantum internet [2–8] have been done in increasingly complex systems. Experiments have boomed in bulk components implementations [9–12], leaving connecting multiple users an expensive as well as a massive construction project. Integrated quantum device, featuring its cheap, compact, stable and flexible performance, becomes a revolutionary solution to establish quantum communication links.

Much efforts have been put forward on versatile integrated QKD platforms [13–15]. Chip-based client [16–22] has been developed to investigate the practical possibilities for miniaturization of the quantum communication terminal. Recently, Bunandar et al. [23] achieved a 43-km-long link with silicon integrated devices, paving the way for one-way long-distance and high-speed chip-based QKD.

However, these point-to-point schemes have been threatened by many attacks through physical loopholes in detection terminals. MDI-QKD [24–28] introduces an independent untrusted third party (Charlie) to announce the measurement results, and the end users (Alice and Bob) only need to encode and send their photons (Fig. 1(a)). It is immune to all attacks on detection and has a high tolerance of finite basis-dependent flaws.

Fig. 1 Schematic of integrated server for MDI-QKD a. Overview of MDI-QKD protocol. Two clients (Alice and Bob) encode their photons in BB84 bases by polarization modulator (Pol-M) and send them to an untrusted relay Charlie to conduct Bell state analysis. Intensity modulators (IM) are used to generate decoy states. The Bell state analyzer is composed of one 50/50 beam splitter (BS) and a polarization beam splitter(PBS) on each of its output ports for projection. b. Fully connected star-topology network requiring N channels. c. Fully connected mesh-topology network requiring $C_{N}^{2} = N (N - 1) / 2$ channels. d. Integrated server for proof-of-principle test. Two single photons from Alice and Bob are employed to qualify on-chip Bell state analyzer. Signals from off-chip avalanche photodiode detectors (APD) are processed by a field-programmable gate array (FPGA).

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In this letter, we demonstrate a solution to build a star-topology quantum access network with an integrated server. The star topology is found perfectly matching the features of MDI-QKD scheme. However, the server needs plenty of Bell state analyzers for simultaneously supporting QKD among many pairs of clients, which can be well solved by constructing integrated circuits for all the elements of Bell state analyzer and assembling an array of such integrated analyzers on single photonic chip in server.

In star topology (Fig. 1(b)) [29–32], all clients only need to build one quantum channel with the server, where an all-optical router can switch and connect any two clients on an integrated Bell state analyzer. The keys are not touched in the routing process. Furthermore, this solution is very resource-efficient for multi-user networks. The star network needs N quantum channels to fully connect any two clients, which is far below the requirement of mesh network (Fig. 1(c)), $C_{N}^{2} = N (N - 1) / 2$ quantum channels, constructed with point-to-point schemes.

We employ femtosecond laser direct writing [33] to realize all the elements of Bell state analyzer (Fig. 1(d)), since the written chip can uniquely be single-mode-fiber compatible for low insertion loss, and can be fabricated in a single-step, mask-free and cost-effective way. By controlling the nonlinear absorption of writing laser, we are able to tune the mode profile and birefringence of the waveguide for polarization manipulating integrated devices [34–40]. The waveguides used in this work are fabricated in boro-silicate glass via femtosecond laser direct writing. Waveguides are formed by laser-induced permanent refractive index change, locating at 170 μm under the substrate surface by focusing femtosecond laser (wavelength 513nm, repetition rate 1 MHz, pulse energy 210 nJ, writing speed 20 mm/s) through a 50 × objective (numerical aperture 0.55). Profiting from the mode control capacity of femtosecond laser direct writing, the written chip can be linked to a standard V-groove fiber array packaging with facet coupling as low as 1dB.

Figure 2(a) shows the detailed design of the Bell state analyzer. The special configuration of polarization insensitve coupler (PIC) is found not very sensitive to fabrication parameters in terms of splitting ratio. The simulation results with commercially available softwares (RSoft BeamPROP and CAD suite) are shown in Figs. 2(b) and 2(c). Polarization insensitiveness is made possible by geometrically controlling interaction length with different coupling width to compensate the birefringence-induced difference of coupling coefficients between horizontal (H) and vertical (V) polarized light [41,42]. Table 1 shows the characterization of typical PIC. Several such devices are measured. The output splitting ratios are found around 50% with a fluctuation less than 2%, which confirms the high repeatability performance of this type of structure.

Table 1. 50/50 PIC performance. Output splitting ratios under different input conditions.

View Table

According to coupling mode theory, photons transferring from one waveguide (bar) to the other (cross) follows a sinusoidal law as shown in Fig. 2(d). Therefore, power transmission and reflection coefficients are defined in analogy to bulk beam splitter as:

Transmission = \frac{P_{cross}}{P_{cross} + P_{bar}}

Reflection = \frac{P_{bar}}{P_{cross} + P_{bar}}

where P_cross and P_bar are the output powers on the two arms [41]. Slight difference in coupling coefficients for H and V polarized light leads to different oscillation periods, and finally an opposite output behaves as a polarization directional coupler (PDC). Two waveguides are prototyped with a fixed coupling width 8 μm, small enough but not overlapped, to ensure that the two propagating modes become coupled during evanescent field overlap.

Fig. 2 Design of integrated elements of on-chip Bell state analyzer. a. Top view geometry of integrated analyzer consisting of one polarization insensitive coupler (PIC) and two identical polarization directional couplers (PDC). r: radius of fabrication circular arc. CL: coupling length. CW: coupling width. b. Contour map of index simulation of PIC with designed two crossings. c. Power distribution in waveguides with a Gaussian beam injected from In1. d. Measured transmission of couplers by scanning coupling lengths when coupling width is fixed at 8μm, for horizontal-(red square) and vertical-(blue circle) polarization input light. Solid lines are the best-fitting curves according to coupling mode theory. Dashed line marks the right coupling length for realizing a PDC.

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The main task of MDI-QKD is to conduct Bell state analysis, thus we first use a probe laser to characterize our integrated analyzer. The results obtained by injecting photons from In1 and In2 are presented with hatched and colored histograms respectively, and are piled together to clearly reveal their uniformity for different inputs and for different wavelengths of light at 780 nm (Fig. 3(a)) and 786 nm (Fig. 3(b)).

Fig. 3 Characterized polarization performance of on-chip Bell state analyzer. a. Measured polarization projection with a probe laser at 780 nm. b. Measured polarization projection with a probe laser at 786 nm. c. and d. Measured projection coincidence counts per 100 seconds with heralded single photon at 780 nm injected from In1 and In2.

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To test the performance of polarization projection on two PDCs, we prepare four typical input states for BB84 protocol bases, polarized at 0° (H), 90° (V), 45° (D) and 135° (A). The normalized projection results agree with the expected relative ratio for H/V and A/D bases (red dashed lines). More importantly, the average polarization extinction ratio for H/V bases is about 20:1, which can well identify |ψ⁺〉 out of |ϕ^±〉 for Bell state analysis.

However, the response and noise level of detection system for laser and single photons are different. Thus, we repeat the experiment with input states of heralded single photons. We generate photon pairs via Type-II spontaneous parametric down-conversion by pumping a beta-barium borate (BBO) crystal with a Ti:sapphire laser. Heralding efficiency of conditionally detecting one single photon by the other one is over 25%. Apparently, the detection and coupling efficiencies for different outputs can not be identical in practice, which may modify the projection results. As we can see, the projection coincidence counts per 100 seconds shown in Fig. 3(c) and 3(d) slightly deviate from the results shown in Fig. 3(a), but, are all around the expected relative ratio (red dashed lines). Interestingly, the average polarization extinction ratio for H/V bases is as high as 59:1, which of course reflects the real performance of the device at single-photon level.

In order to qualify the integrated server suitable for MDI-QKD, we couple the pair of photons into one of on-chip Bell state analyzers, as is shown in Fig. 1(d), both prepared in D, and scan their relative delay by a motorized linear translation stage to find the zone of Hong-Ou-Mandel Interference [43]. This scanning may also be realized by tuning the time of the electronic trigger pulse for QKD emitter sources in Alice or Bob’s station. Photons from Alice and Bob are encoded independently in BB84 protocol bases by rotating half wave plates. Since our two PDCs can project incoming states H and V at the output ports 1, 4 and 2, 3 respectively, coincidence measurements could deterministically discriminate the states |ψ⁺〉 and |ψ⁻〉 by two-fold coincidences C12, C34 and C13, C24 via bunching or anti-bunching effect [44]. Meanwhile, two-fold coincidences C14 and C23 can not distinguish the states |ϕ⁺〉 and |ϕ⁻〉, and therefore are not used as successful events in MDI-QKD protocols [45]. The Visibilities for all combinations are 89.8%, 92.4%, 93.0%, 92.3%, 92.2% and 83.7% for C12, C13, C14, C23, C24 and C34 (Fig. 4(a)).

Fig. 4 Experimental results of Bell state analysis with integrated server. a. Hong-Ou-Mandel Interference for all the coincidence counts. An average visibility over 90% is reached. b.-e. Relative conditional probability distribution with different input states in rectilinear and diagonal bases. b. and d. show the theoretical distributions, and c. and e. show the experimental coincidence distributions.

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Two-photon data are collected for eight linearly independent input conditions Fig. 4(b) and 4(c) (HH, HV, VH, VV), and Fig. 4(d) and 4(e) (DD, DA, AD, AA), with half wave plates and polarization compensation. The gain values at each rectilinear ( $Q_{i, j}^{r}$ ) and diagonal ( $Q_{i, j}^{d}$ ) basis can be caculated from the coincidence measurements by [26]:

Q_{i, j}^{r} = \frac{1}{4} (C_{Sum}^{HH} + C_{Sum}^{VV} + C_{Sum}^{HV} + C_{Sum}^{VH})

Q_{i, j}^{d} = \frac{1}{4} (C_{Sum}^{+ +} + C_{Sum}^{- -} + C_{Sum}^{+ -} + C_{Sum}^{- +})

i and j represent the different average coincidence counts used by Alice and Bob while we adopt the successful events by:

C_{Sum}^{AB} = C_{12}^{AB} + C_{34}^{AB} + C_{13}^{AB} + C_{24}^{AB}

We get the final gain values:

Q_{i, j}^{r} = 1.37 \times 10^{- 6}

bits/pulse,

Q_{i, j}^{d} = 1.75 \times 10^{- 6}

bits/pulse. We estimate the quantum bit error rate (QBER) by:

E_{i, j}^{r} = \frac{C_{Sum}^{HH} + C_{Sum}^{VV}}{C_{Sum}^{HH} + C_{Sum}^{VV} + C_{Sum}^{HV} + C_{Sum}^{VH}}

E_{i, j}^{d} = \frac{C_{13}^{+ +} + C_{24}^{+ +} + C_{13}^{- -} + C_{24}^{- -}}{C_{Sum}^{+ +} + C_{Sum}^{- -} + C_{Sum}^{+ -} + C_{Sum}^{- +}} + \frac{C_{12}^{+ -} + C_{34}^{+ -} + C_{12}^{- +} + C_{34}^{- +}}{C_{Sum}^{+ +} + C_{Sum}^{- -} + C_{Sum}^{+ -} + C_{Sum}^{- +}}

From our experimental data, we estimate $E_{i, j}^{r} = 0.058$ , $E_{i, j}^{d} = 0.081$ . The nonideal QBER can be attributed to multi-photon events of the testing photon source, residual birefringence in PIC and polarization-dependent loss. The last two points are being improved to meet the stringent requirement for low QBER and therefore for high final bit rate.

In summary, we propose and experimentally demonstrate an integrated server for MDI-QKD network and its compatibility to a star-topology quantum access network. Every client sends their encoded photons to server through their sole channel. Server can link any two clients simply by switching their photons to one of Bell state analyzers on a photonic chip. All the combination between two clients is the same as a standard MDI-QKD and therefore is unconditionally secure. The number of required channels is much less than mesh-topology with point-to-point schemes for realizing fully connected MDI-QKD networks, which is particularly significant when the networks go to large scales.

Funding

National Key R&D Program of China (2017YFA0303700); National Natural Science Foundation of China (NSFC) (61734005, 11761141014, 11690033); Science and Technology Commission of Shanghai Municipality (STCSM) (15QA1402200, 16JC1400405, 17JC1400403); Shanghai Municipal Education Commission (SMEC)(16SG09, 2017-01-07-00-02-E00049); National Young 1000 Talents Plan.

Acknowledgments

The authors thank Jian-Wei Pan, Hang Li, Xiao-Ling Pang, and Jian-Peng Dou for helpful discussions.

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Year
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Publication

C. H. Bennett and G. Brassard, “Quantum cryptography: Public key distribution and coin tossing,” Theor. Comput. Sci. 560, 7–11 (2014).
[Crossref]
C. Elliott, “Building the quantum network,” New J. Phys. 4, 46 (2002).
[Crossref]
C.-W. Chou, J. Laurat, H. Deng, K. S. Choi, H. de Riedmatten, D. Felinto, and H. J. Kimble, “Functional quantum nodes for entanglement distribution over scalable quantum networks,” Science 316, 1316 (2007).
[Crossref] [PubMed]
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S. Pirandola and S. L. Braunstein, “Physics: Unite to build a quantum internet,” Nature 532, 169 (2016).
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N. Maring, P. Farrera, K. Kutluer, M. Mazzera, G. Heinze, and H. de Riedmatten, “Photonic quantum state transfer between a cold atomic gas and a crystal,” Nature 551, 485 (2017).
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P. C. Humphreys, N. Kalb, J. P. J. Morits, R. N. Schouten, R. F. L. Vermeulen, D. J. Twitchen, M. Markham, and R. Hanson, “Deterministic delivery of remote entanglement on a quantum network,” Nature 558, 268–273 (2018).
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L. Ji, J. Gao, A.-L. Yang, Z. Feng, X.-F. Lin, Z.-G. Li, and X.-M. Jin, “Towards quantum communications in free-space seawater,” Opt. Express 25, 19795–19806 (2017).
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J.-G. Ren, P. Xu, H.-L. Yong, L. Zhang, S.-K. Liao, J. Yin, W.-Y. Liu, W.-Q. Cai, M. Yang, L. Li, K.-X. Yang, X. Han, Y.-Q. Yao, J. Li, H.-Y. Wu, S. Wan, L. Liu, D.-Q. Liu, Y.-W. Kuang, Z.-P. He, P. Shang, C. Guo, R.-H. Zheng, K. Tian, Z.-C. Zhu, N.-L. Liu, C.-Y. Lu, R. Shu, Y.-A. Chen, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Ground-to-satellite quantum teleportation,” Nature 549, 70 (2017).
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C. Ma, W. D. Sacher, Z. Tang, J. C. Mikkelsen, Y. Yang, F. Xu, T. Thiessen, H.-K. Lo, and J. K. S. Poon, “Silicon photonic transmitter for polarization-encoded quantum key distribution,” Optica 3, 1274–1278 (2016).
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C. Autebert, J. Trapateau, A. Orieux, A. Lemaître, C. Gomez-Carbonell, E. Diamanti, I. Zaquine, and S. Ducci, “Multi-user quantum key distribution with entangled photons from an algaas chip,” Quantum Sci. Technol. 1, 01LT02 (2016).
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G. Mélen, T. Vogl, M. Rau, G. Corrielli, A. Crespi, R. Osellame, and H. Weinfurter, “Integrated quantum key distribution sender unit for daily-life implementations,” in Advances in Photonics of Quantum Computing, Memory, and Communication IX, vol. 9762 (International Society for Optics and Photonics, 2016), p. 97620A.
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D. Bacco, Y. Ding, K. Dalgaard, K. Rottwitt, and L. K. Oxenløwe, “Space division multiplexing chip-to-chip quantum key distribution,” Sci. Rep. 7, 12459 (2017).
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J. Choe, H. Ko, B. Choi, K. Kim, and C. J. Youn, “Silica planar lightwave circuit based integrated 1 × 4 polarization beam splitter module for free-space bb84 quantum key distribution,” IEEE Photonics J. 10, 1–8 (2018).
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D. Bunandar, A. Lentine, C. Lee, H. Cai, C. M. Long, N. Boynton, N. Martinez, C. DeRose, C. Chen, M. Grein, D. Trotter, A. Starbuck, A. Pomerene, S. Hamilton, F. N. C. Wong, R. Camacho, P. Davids, J. Urayama, and D. Englund, “Metropolitan quantum key distribution with silicon photonics,” Phys. Rev. X 8, 021009 (2018).
H.-K. Lo, M. Curty, and B. Qi, “Measurement-device-independent quantum key distribution,” Phys. Rev. Lett. 108, 130503 (2012).
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S. L. Braunstein and S. Pirandola, “Side-channel-free quantum key distribution,” Phys. Rev. Lett. 108, 130502 (2012).
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T. Ferreira da Silva, D. Vitoreti, G. B. Xavier, G. C. do Amaral, G. P. Temporão, and J. P. von der Weid, “Proof-of-principle demonstration of measurement-device-independent quantum key distribution using polarization qubits,” Phys. Rev. A 88, 052303 (2013).
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Z. Tang, Z. Liao, F. Xu, B. Qi, L. Qian, and H.-K. Lo, “Experimental demonstration of polarization encoding measurement-device-independent quantum key distribution,” Phys. Rev. Lett. 112, 190503 (2014).
[Crossref] [PubMed]
Y.-L. Tang, H.-L. Yin, S.-J. Chen, Y. Liu, W.-J. Zhang, X. Jiang, L. Zhang, J. Wang, L.-X. You, J.-Y. Guan, D.-X. Yang, Z. Wang, H. Liang, Z. Zhang, N. Zhou, X. Ma, T.-Y. Chen, Q. Zhang, and J.-W. Pan, “Measurement-device-independent quantum key distribution over 200 km,” Phys. Rev. Lett. 113, 190501 (2014).
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F. Xu, “Measurement-device-independent quantum communication with an untrusted source,” Phys. Rev. A 92, 012333 (2015).
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Y.-L. Tang, H.-L. Yin, Q. Zhao, H. Liu, X.-X. Sun, M.-Q. Huang, W.-J. Zhang, S.-J. Chen, L. Zhang, L.-X. You, Z. Wang, Y. Liu, C.-Y. Lu, X. Jiang, X. Ma, Q. Zhang, T.-Y. Chen, and J.-W. Pan, “Measurement-device-independent quantum key distribution over untrustful metropolitan network,” Phys. Rev. X 6, 011024 (2016).
R. Valivarthi, Q. Zhou, C. John, F. Marsili, V. B. Verma, M. D. Shaw, S. W. Nam, D. Oblak, and W. Tittel, “A cost-effective measurement-device-independent quantum key distribution system for quantum networks,” Quantum Sci. Technol. 2, 04LT01 (2017).
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W. Wang, F. Xu, and H.-K. Lo, “Enabling a scalable high-rate measurement-device-independent quantum key distribution network,” arXiv preprint arXiv:1807.03466 (2018).
K. M. Davis, K. Miura, N. Sugimoto, and K. Hirao, “Writing waveguides in glass with a femtosecond laser,” Opt. Lett. 21, 1729–1731 (1996).
[Crossref] [PubMed]
L. Sansoni, F. Sciarrino, G. Vallone, P. Mataloni, A. Crespi, R. Ramponi, and R. Osellame, “Polarization entangled state measurement on a chip,” Phys. Rev. Lett. 105, 200503 (2010).
[Crossref]
A. Crespi, R. Ramponi, R. Osellame, L. Sansoni, I. Bongioanni, F. Sciarrino, G. Vallone, and P. Mataloni, “Integrated photonic quantum gates for polarization qubits,” Nat. Commun. 2, 566 (2011).
[Crossref] [PubMed]
L. A. Fernandes, J. R. Grenier, P. R. Herman, J. S. Aitchison, and P. V. S. Marques, “Femtosecond laser fabrication of birefringent directional couplers as polarization beam splitters in fused silica,” Opt. Express 19, 11992–11999 (2011).
[Crossref] [PubMed]
G. Vest, M. Rau, L. Fuchs, G. Corrielli, H. Weier, S. Nauerth, A. Crespi, R. Osellame, and H. Weinfurter, “Design and evaluation of a handheld quantum key distribution sender module,” IEEE J. Sel. Top. Quant. Electron 21, 131–137 (2015).
[Crossref]
J. Gao, L.-F. Qiao, X.-F. Lin, Z.-Q. Jiao, Z. Feng, Z. Zhou, Z.-W. Gao, X.-Y. Xu, Y. Chen, H. Tang, and X.-M. Jin, “Non-classical photon correlation in a two-dimensional photonic lattice,” Opt. Express 24, 12607–12616 (2016).
[Crossref] [PubMed]
H. Tang, X.-F. Lin, Z. Feng, J.-Y. Chen, J. Gao, K. Sun, C.-Y. Wang, P.-C. Lai, X.-Y. Xu, Y. Wang, L.-F. Qiao, A.-L. Yang, and X.-M. Jin, “Experimental two-dimensional quantum walk on a photonic chip,” Sci. Adv. 4, 3174 (2018).
[Crossref]
C.-Y. Wang, J. Gao, and X.-M. Jin, “On-chip rotated polarization directional coupler fabricated by femtosecond laser direct writing,” Opt. Lett. 44, 102–105 (2019).
[Crossref]
I. Pitsios, F. Samara, G. Corrielli, A. Crespi, and R. Osellame, “Geometrically-controlled polarisation processing in femtosecond-laser-written photonic circuits,” Sci. Rep. 7, 11342 (2017).
[Crossref] [PubMed]
G. Corrielli, S. Atzeni, S. Piacentini, I. Pitsios, A. Crespi, and R. Osellame, “Symmetric polarization-insensitive directional couplers fabricated by femtosecond laser writing,” Opt. Express 26, 15101–15109 (2018).
[Crossref] [PubMed]
C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044–2046 (1987).
[Crossref] [PubMed]
T. F. da Silva, D. Vitoreti, G. B. Xavier, G. P. Temporão, and J. P. von der Weid, “Long-distance bell-state analysis of fully independent polarization weak coherent states,” J. Light. Technol. 31, 2881–2887 (2013).
[Crossref]
J. Calsamiglia and N. Lütkenhaus, “Maximum efficiency of a linear-optical bell-state analyzer,” Appl. Phys. B 72, 67–71 (2001).
[Crossref]

2019 (1)

C.-Y. Wang, J. Gao, and X.-M. Jin, “On-chip rotated polarization directional coupler fabricated by femtosecond laser direct writing,” Opt. Lett. 44, 102–105 (2019).
[Crossref]

2018 (5)

G. Corrielli, S. Atzeni, S. Piacentini, I. Pitsios, A. Crespi, and R. Osellame, “Symmetric polarization-insensitive directional couplers fabricated by femtosecond laser writing,” Opt. Express 26, 15101–15109 (2018).
[Crossref] [PubMed]

H. Tang, X.-F. Lin, Z. Feng, J.-Y. Chen, J. Gao, K. Sun, C.-Y. Wang, P.-C. Lai, X.-Y. Xu, Y. Wang, L.-F. Qiao, A.-L. Yang, and X.-M. Jin, “Experimental two-dimensional quantum walk on a photonic chip,” Sci. Adv. 4, 3174 (2018).
[Crossref]

P. C. Humphreys, N. Kalb, J. P. J. Morits, R. N. Schouten, R. F. L. Vermeulen, D. J. Twitchen, M. Markham, and R. Hanson, “Deterministic delivery of remote entanglement on a quantum network,” Nature 558, 268–273 (2018).
[Crossref] [PubMed]

J. Choe, H. Ko, B. Choi, K. Kim, and C. J. Youn, “Silica planar lightwave circuit based integrated 1 × 4 polarization beam splitter module for free-space bb84 quantum key distribution,” IEEE Photonics J. 10, 1–8 (2018).
[Crossref]

D. Bunandar, A. Lentine, C. Lee, H. Cai, C. M. Long, N. Boynton, N. Martinez, C. DeRose, C. Chen, M. Grein, D. Trotter, A. Starbuck, A. Pomerene, S. Hamilton, F. N. C. Wong, R. Camacho, P. Davids, J. Urayama, and D. Englund, “Metropolitan quantum key distribution with silicon photonics,” Phys. Rev. X 8, 021009 (2018).

2017 (8)

P. Sibson, C. Erven, M. Godfrey, S. Miki, T. Yamashita, M. Fujiwara, M. Sasaki, H. Terai, M. G. Tanner, C. M. Natarajan, R. H. Hadfield, J. L. O’Brien, and M. G. Thompson, “Chip-based quantum key distribution,” Nat. Commun. 8, 13984 (2017).
[Crossref] [PubMed]

D. Bacco, Y. Ding, K. Dalgaard, K. Rottwitt, and L. K. Oxenløwe, “Space division multiplexing chip-to-chip quantum key distribution,” Sci. Rep. 7, 12459 (2017).
[Crossref] [PubMed]

N. Maring, P. Farrera, K. Kutluer, M. Mazzera, G. Heinze, and H. de Riedmatten, “Photonic quantum state transfer between a cold atomic gas and a crystal,” Nature 551, 485 (2017).
[Crossref] [PubMed]

R. Valivarthi, Q. Zhou, C. John, F. Marsili, V. B. Verma, M. D. Shaw, S. W. Nam, D. Oblak, and W. Tittel, “A cost-effective measurement-device-independent quantum key distribution system for quantum networks,” Quantum Sci. Technol. 2, 04LT01 (2017).
[Crossref]

L. Ji, J. Gao, A.-L. Yang, Z. Feng, X.-F. Lin, Z.-G. Li, and X.-M. Jin, “Towards quantum communications in free-space seawater,” Opt. Express 25, 19795–19806 (2017).
[Crossref] [PubMed]

S.-K. Liao, W.-Q. Cai, W.-Y. Liu, L. Zhang, Y. Li, J.-G. Ren, J. Yin, Q. Shen, Y. Cao, Z.-P. Li, F.-Z. Li, X.-W. Chen, L.-H. Sun, J.-J. Jia, J.-C. Wu, X.-J. Jiang, J.-F. Wang, Y.-M. Huang, Q. Wang, Y.-L. Zhou, L. Deng, T. Xi, L. Ma, T. Hu, Q. Zhang, Y.-A. Chen, N.-L. Liu, X.-B. Wang, Z.-C. Zhu, C.-Y. Lu, R. Shu, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Satellite-to-ground quantum key distribution,” Nature 549, 43 (2017).
[Crossref] [PubMed]

J.-G. Ren, P. Xu, H.-L. Yong, L. Zhang, S.-K. Liao, J. Yin, W.-Y. Liu, W.-Q. Cai, M. Yang, L. Li, K.-X. Yang, X. Han, Y.-Q. Yao, J. Li, H.-Y. Wu, S. Wan, L. Liu, D.-Q. Liu, Y.-W. Kuang, Z.-P. He, P. Shang, C. Guo, R.-H. Zheng, K. Tian, Z.-C. Zhu, N.-L. Liu, C.-Y. Lu, R. Shu, Y.-A. Chen, C.-Z. Peng, J.-Y. Wang, and J.-W. Pan, “Ground-to-satellite quantum teleportation,” Nature 549, 70 (2017).
[Crossref] [PubMed]

I. Pitsios, F. Samara, G. Corrielli, A. Crespi, and R. Osellame, “Geometrically-controlled polarisation processing in femtosecond-laser-written photonic circuits,” Sci. Rep. 7, 11342 (2017).
[Crossref] [PubMed]

2016 (5)

J. Gao, L.-F. Qiao, X.-F. Lin, Z.-Q. Jiao, Z. Feng, Z. Zhou, Z.-W. Gao, X.-Y. Xu, Y. Chen, H. Tang, and X.-M. Jin, “Non-classical photon correlation in a two-dimensional photonic lattice,” Opt. Express 24, 12607–12616 (2016).
[Crossref] [PubMed]

C. Ma, W. D. Sacher, Z. Tang, J. C. Mikkelsen, Y. Yang, F. Xu, T. Thiessen, H.-K. Lo, and J. K. S. Poon, “Silicon photonic transmitter for polarization-encoded quantum key distribution,” Optica 3, 1274–1278 (2016).
[Crossref]

C. Autebert, J. Trapateau, A. Orieux, A. Lemaître, C. Gomez-Carbonell, E. Diamanti, I. Zaquine, and S. Ducci, “Multi-user quantum key distribution with entangled photons from an algaas chip,” Quantum Sci. Technol. 1, 01LT02 (2016).
[Crossref]

S. Pirandola and S. L. Braunstein, “Physics: Unite to build a quantum internet,” Nature 532, 169 (2016).
[Crossref] [PubMed]

Y.-L. Tang, H.-L. Yin, Q. Zhao, H. Liu, X.-X. Sun, M.-Q. Huang, W.-J. Zhang, S.-J. Chen, L. Zhang, L.-X. You, Z. Wang, Y. Liu, C.-Y. Lu, X. Jiang, X. Ma, Q. Zhang, T.-Y. Chen, and J.-W. Pan, “Measurement-device-independent quantum key distribution over untrustful metropolitan network,” Phys. Rev. X 6, 011024 (2016).

2015 (2)

F. Xu, “Measurement-device-independent quantum communication with an untrusted source,” Phys. Rev. A 92, 012333 (2015).
[Crossref]

G. Vest, M. Rau, L. Fuchs, G. Corrielli, H. Weier, S. Nauerth, A. Crespi, R. Osellame, and H. Weinfurter, “Design and evaluation of a handheld quantum key distribution sender module,” IEEE J. Sel. Top. Quant. Electron 21, 131–137 (2015).
[Crossref]

2014 (5)

Z. Tang, Z. Liao, F. Xu, B. Qi, L. Qian, and H.-K. Lo, “Experimental demonstration of polarization encoding measurement-device-independent quantum key distribution,” Phys. Rev. Lett. 112, 190503 (2014).
[Crossref] [PubMed]

Y.-L. Tang, H.-L. Yin, S.-J. Chen, Y. Liu, W.-J. Zhang, X. Jiang, L. Zhang, J. Wang, L.-X. You, J.-Y. Guan, D.-X. Yang, Z. Wang, H. Liang, Z. Zhang, N. Zhou, X. Ma, T.-Y. Chen, Q. Zhang, and J.-W. Pan, “Measurement-device-independent quantum key distribution over 200 km,” Phys. Rev. Lett. 113, 190501 (2014).
[Crossref] [PubMed]

C. H. Bennett and G. Brassard, “Quantum cryptography: Public key distribution and coin tossing,” Theor. Comput. Sci. 560, 7–11 (2014).
[Crossref]

B. J. Metcalf, J. B. Spring, P. C. Humphreys, N. Thomas-Peter, M. Barbieri, W. S. Kolthammer, X.-M. Jin, N. K. Langford, D. Kundys, J. C. Gates, B. J. Smith, P. G. R. Smith, and I. A. Walmsley, “Quantum teleportation on a photonic chip,” Nat. Photonics 8, 770 (2014).
[Crossref]

P. Zhang, K. Aungskunsiri, E. Martín-López, J. Wabnig, M. Lobino, R. W. Nock, J. Munns, D. Bonneau, P. Jiang, H. W. Li, A. Laing, J. G. Rarity, A. O. Niskanen, M. G. Thompson, and J. L. O’Brien, “Reference-frame-independent quantum-key-distribution server with a telecom tether for an on-chip client,” Phys. Rev. Lett. 112, 130501 (2014).
[Crossref] [PubMed]

2013 (3)

B. Fröhlich, J. F. Dynes, M. Lucamarini, A. W. Sharpe, Z. Yuan, and A. J. Shields, “A quantum access network,” Nature 501, 69 (2013).
[Crossref] [PubMed]

T. Ferreira da Silva, D. Vitoreti, G. B. Xavier, G. C. do Amaral, G. P. Temporão, and J. P. von der Weid, “Proof-of-principle demonstration of measurement-device-independent quantum key distribution using polarization qubits,” Phys. Rev. A 88, 052303 (2013).
[Crossref]

T. F. da Silva, D. Vitoreti, G. B. Xavier, G. P. Temporão, and J. P. von der Weid, “Long-distance bell-state analysis of fully independent polarization weak coherent states,” J. Light. Technol. 31, 2881–2887 (2013).
[Crossref]

2012 (3)

H.-K. Lo, M. Curty, and B. Qi, “Measurement-device-independent quantum key distribution,” Phys. Rev. Lett. 108, 130503 (2012).
[Crossref] [PubMed]

S. L. Braunstein and S. Pirandola, “Side-channel-free quantum key distribution,” Phys. Rev. Lett. 108, 130502 (2012).
[Crossref] [PubMed]

S. Tanzilli, A. Martin, F. Kaiser, M. P. De Micheli, O. Alibart, and D. B. Ostrowsky, “On the genesis and evolution of integrated quantum optics,” Laser Photonics Rev. 6, 115–143 (2012).
[Crossref]

2011 (2)

A. Crespi, R. Ramponi, R. Osellame, L. Sansoni, I. Bongioanni, F. Sciarrino, G. Vallone, and P. Mataloni, “Integrated photonic quantum gates for polarization qubits,” Nat. Commun. 2, 566 (2011).
[Crossref] [PubMed]

L. A. Fernandes, J. R. Grenier, P. R. Herman, J. S. Aitchison, and P. V. S. Marques, “Femtosecond laser fabrication of birefringent directional couplers as polarization beam splitters in fused silica,” Opt. Express 19, 11992–11999 (2011).
[Crossref] [PubMed]

2010 (2)

X.-M. Jin, J.-G. Ren, B. Yang, Z.-H. Yi, F. Zhou, X.-F. Xu, S.-K. Wang, D. Yang, Y.-F. Hu, S. Jiang, T. Yang, H. Yin, K. Chen, C.-Z. Peng, and J.-W. Pan, “Experimental free-space quantum teleportation,” Nat. Photonics 4, 376 (2010).
[Crossref]

L. Sansoni, F. Sciarrino, G. Vallone, P. Mataloni, A. Crespi, R. Ramponi, and R. Osellame, “Polarization entangled state measurement on a chip,” Phys. Rev. Lett. 105, 200503 (2010).
[Crossref]

2008 (2)

H. J. Kimble, “The quantum internet,” Nature 453, 1023 (2008).
[Crossref] [PubMed]

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320, 646–649 (2008).
[Crossref] [PubMed]

2007 (1)

C.-W. Chou, J. Laurat, H. Deng, K. S. Choi, H. de Riedmatten, D. Felinto, and H. J. Kimble, “Functional quantum nodes for entanglement distribution over scalable quantum networks,” Science 316, 1316 (2007).
[Crossref] [PubMed]

2002 (1)

C. Elliott, “Building the quantum network,” New J. Phys. 4, 46 (2002).
[Crossref]

2001 (1)

J. Calsamiglia and N. Lütkenhaus, “Maximum efficiency of a linear-optical bell-state analyzer,” Appl. Phys. B 72, 67–71 (2001).
[Crossref]

1996 (1)

K. M. Davis, K. Miura, N. Sugimoto, and K. Hirao, “Writing waveguides in glass with a femtosecond laser,” Opt. Lett. 21, 1729–1731 (1996).
[Crossref] [PubMed]

1987 (1)

C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between two photons by interference,” Phys. Rev. Lett. 59, 2044–2046 (1987).
[Crossref] [PubMed]

Aitchison, J. S.

Alibart, O.

Atzeni, S.

Aungskunsiri, K.

Autebert, C.

Bacco, D.

D. Bacco, Y. Ding, K. Dalgaard, K. Rottwitt, and L. K. Oxenløwe, “Space division multiplexing chip-to-chip quantum key distribution,” Sci. Rep. 7, 12459 (2017).
[Crossref] [PubMed]

Barbieri, M.

Bennett, C. H.

C. H. Bennett and G. Brassard, “Quantum cryptography: Public key distribution and coin tossing,” Theor. Comput. Sci. 560, 7–11 (2014).
[Crossref]

Bongioanni, I.

Bonneau, D.

Boynton, N.

Brassard, G.

C. H. Bennett and G. Brassard, “Quantum cryptography: Public key distribution and coin tossing,” Theor. Comput. Sci. 560, 7–11 (2014).
[Crossref]

Braunstein, S. L.

S. Pirandola and S. L. Braunstein, “Physics: Unite to build a quantum internet,” Nature 532, 169 (2016).
[Crossref] [PubMed]

S. L. Braunstein and S. Pirandola, “Side-channel-free quantum key distribution,” Phys. Rev. Lett. 108, 130502 (2012).
[Crossref] [PubMed]

Bunandar, D.

Cai, H.

Cai, W.-Q.

Calsamiglia, J.

J. Calsamiglia and N. Lütkenhaus, “Maximum efficiency of a linear-optical bell-state analyzer,” Appl. Phys. B 72, 67–71 (2001).
[Crossref]

Camacho, R.

Cao, Y.

Chen, C.

Chen, J.-Y.

Chen, K.

Chen, S.-J.

Chen, T.-Y.

Chen, X.-W.

Chen, Y.

Chen, Y.-A.

Choe, J.

Choi, B.

Choi, K. S.

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IEEE J. Sel. Top. Quant. Electron (1)

IEEE Photonics J. (1)

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Laser Photonics Rev. (1)

Nat. Commun. (2)

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B. Fröhlich, J. F. Dynes, M. Lucamarini, A. W. Sharpe, Z. Yuan, and A. J. Shields, “A quantum access network,” Nature 501, 69 (2013).
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Optica (1)

Phys. Rev. A (2)

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Phys. Rev. X (2)

Quantum Sci. Technol. (2)

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D. Bacco, Y. Ding, K. Dalgaard, K. Rottwitt, and L. K. Oxenløwe, “Space division multiplexing chip-to-chip quantum key distribution,” Sci. Rep. 7, 12459 (2017).
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C_{N}^{2} = N (N - 1) / 2

channels. d. Integrated server for proof-of-principle test. Two single photons from Alice and Bob are employed to qualify on-chip Bell state analyzer. Signals from off-chip avalanche photodiode detectors (APD) are processed by a field-programmable gate array (FPGA).