Abstract

Quantum cryptography is arguably the fastest growing area in quantum information science. Novel theoretical protocols are designed on a regular basis, security proofs are constantly improving, and experiments are gradually moving from proof-of-principle lab demonstrations to in-field implementations and technological prototypes. In this paper, we provide both a general introduction and a state-of-the-art description of the recent advances in the field, both theoretical and experimental. We start by reviewing protocols of quantum key distribution based on discrete variable systems. Next we consider aspects of device independence, satellite challenges, and protocols based on continuous-variable systems. We will then discuss the ultimate limits of point-to-point private communications and how quantum repeaters and networks may overcome these restrictions. Finally, we will discuss some aspects of quantum cryptography beyond standard quantum key distribution, including quantum random number generators and quantum digital signatures.

© 2020 Optical Society of America

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2020 (13)

S. Bäuml, K. Azuma, G. Kato, and D. Elkouss, “Linear programs for entanglement and key distribution in the quantum internet,” Commun. Phys. 355 (2020).
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S. Pirandola, “General upper bounds for distributing conferencing keys in arbitrary quantum networks,” IET Quantum Commun. 1, 22–25 (2020).
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P. J. Brown, S. Ragy, and R. Colbeck, “A framework for quantum-secure device-independent randomness expansion,” IEEE Trans. Inf. Theory 66, 2964–2987 (2020).
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Y. Zhang, H. Fu, and E. Knill, "Efficient randomness certification by quantum probability estimation," Phys. Rev. Res. 2, 013016 (2020).
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E. Kaur, M. M. Wilde, and A. Winter, “Fundamental limits on key rates in device-independent quantum key distribution,” New J. Phys. 22, 023039 (2020).
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H. Xu, Z.-W. Yu, C. Jiang, X.-L. Hu, and X.-B. Wang, “Improved results for sending-or-not-sending twin-field quantun key distribution: breaking the absolute limit of repeaterless key rate,” Phys. Rev. A 101, 042330 (2020).

M. Ghalaii, C. Ottaviani, R. Kumar, S. Pirandola, and M. Razavi, “Long-distance continuous-variable quantum key distribution with quantum scissors,” IEEE J. Sel. Top. Quantum Electron. 26, 6400212 (2020).
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C. Ottaviani, M. J. Woolley, M. Erementchouk, J. F. Federici, P. Mazumder, S. Pirandola, and C. Weedbrook, “Terahertz quantum cryptography,” IEEE J. Sel. Areas Commun. 38, 483–495 (2020).

M. Ghalaii, C. Ottaviani, R. Kumar, S. Pirandola, and M. Razavi, “Discrete-modulation continuous-variable quantum key distribution enhanced by quantum scissors,” IEEE J. Sel. Areas Commun. 38, 506–516 (2020).

Y. Zhang, Z. Chen, S. Pirandola, X. Wang, C. Zhou, B. Chu, Y. Zhao, B. Xu, S. Yu, and H. Guo, “Long-distance continuous-variable quantum key distribution over 202.81  km of fiber,” Phys. Rev. Lett. 125, 010502 (2020).

F. Xu, X. Ma, Q. Zhang, H.-K. Lo, and J.-W. Pan, “Quantum cryptography with realistic devices,” Rev. Mod. Phys. 92, 025002 (2020).

L. Banchi, J. Pereira, S. Lloyd, and S. Pirandola, “Convex optimization of programmable quantum computers,” npj Quantum Inf. 6, 42 (2020).
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K. Noh, S. Pirandola, and L. Jiang, “Enhanced energy-constrained quantum communication over bosonic Gaussian channels,” Nat. Commun. 11, 457 (2020).
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2019 (62)

K. Noh, V. V. Albert, and L. Jiang, “Improved quantum capacity bounds of Gaussian loss channels and achievable rates with Gottesman-Kitaev-Preskill codes,” IEEE Trans. Inf. Theory 65, 2563 (2019).
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R. Laurenza, S. Tserkis, L. Banchi, S. L. Braunstein, T. C. Ralph, and S. Pirandola, “Tight bounds for private communication over bosonic Gaussian channels based on teleportation simulation with optimal finite resources,” Phys. Rev. A 100, 042301 (2019).
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F. Rozpedek, R. Yehia, K. Goodenough, M. Ruf, P. C. Humphreys, R. Hanson, S. Wehner, and D. Elkouss, “Near-term quantum-repeater experiments with nitrogen-vacancy centers: overcoming the limitations of direct transmission,” Phys. Rev. A 99, 052330 (2019).
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F. Schmidt and P. van Loock, “Efficiencies of logical Bell measurements on Calderbank-Shor-Steane codes with static linear optics,” Phys. Rev. A 99, 062308 (2019).
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Y. Zhao, Y. Zhang, Y. Huang, B. Xu, S. Yu, and H. Guo, “Polarization attack on continuous-variable quantum key distribution,” J. Phys. B 52, 015501 (2019).
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S. Ren, R. Kumar, A. Wonfor, X. Tang, R. Penty, and I. White, “Reference pulse attack on continuous-variable quantum key distribution with local oscillator under trusted phase noise,” J. Opt. Soc. Am. B 36, B7–B15 (2019).
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E. Chitambar and G. Gour, “Quantum resource theories,” Rev. Mod. Phys. 91, 025001 (2019).
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S. Pirandola, R. Laurenza, C. Lupo, and J. L. Pereira, “Fundamental limits to quantum channel discrimination,” npj Quantum Inf. 5, 50 (2019).
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S. Pirandola, R. Laurenza, and L. Banchi, “Conditional channel simulation,” Ann. Phys. 400, 289–302 (2019).
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K. P. Seshadreesan, H. Krovi, and S. Guha, “Continuous-variable entanglement distillation over a pure loss channel with multiple quantum scissors,” Phys. Rev. A 100, 022315 (2019).
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M. Bergmann and P. van Loock, “A hybrid quantum repeater for qudits,” Phys. Rev. A 99, 032349 (2019).
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P. Wallden and E. Kashefi, “Cyber security in the quantum era,” Commun. ACM 62, 120 (2019).
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Y. Zhang, Z. Li, Z. Chen, C. Weedbrook, Y. Zhao, X. Wang, Y. Huang, C. Xu, X. Zhang, Z. Wang, M. Li, X. Zhang, Z. Zheng, B. Chu, X. Gao, N. Meng, W. Cai, Z. Wang, G. Wang, S. Yu, and H. Guo, “Continuous-variable QKD over 50  km commercial fiber,” Quantum Sci. Technol. 4, 035006 (2019).
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F. Laudenbach, B. Schrenk, C. Pacher, M. Hentschel, C. H. F. Fung, F. Karinou, A. Poppe, M. Peev, and H. Hübel, “Pilot-assisted intradyne reception for high-speed continuous-variable quantum key distribution with true local oscillator,” Quantum 3, 193 (2019).
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C. Zhou, X. Wang, Y. Zhang, Z. Zhang, S. Yu, and H. Guo, “Continuous-variable quantum key distribution with rateless reconciliation protocol,” Phys. Rev. Appl. 12, 054013 (2019).
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S. Ghorai, P. Grangier, E. Diamanti, and A. Leverrier, “Asymptotic security of continuous-variable quantum key distribution with a discrete modulation,” Phys. Rev. X 9, 021059 (2019).
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P. Wang, X. Wang, and Y. Li, “Continuous-variable measurement-device-independent quantum key distribution using modulated squeezed states and optical amplifiers,” Phys. Rev. A 99, 042309 (2019).
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H.-X. Ma, P. Huang, D.-Y. Bai, T. Wang, S.-Y. Wang, W.-S. Bao, and G.-H. Zeng, “Long-distance continuous-variable measurement-device-independent quantum key distribution with discrete modulation,” Phys. Rev. A 99, 022322 (2019).
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H.-L. Yin, W. Zhu, and Y. Fu, “Phase self-aligned continuous-variable measurement-device-independent quantum key distribution,” Sci. Rep. 9, 49 (2019).
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H.-X. Ma, P. Huang, T. Wang, D.-Y. Bai, S.-Y. Wang, W.-S. Bao, and G.-H. Zeng, “Security bound of continuous-variable measurement-device-independent quantum key distribution with imperfect phase reference calibration,” Phys. Rev. A 100, 052330 (2019).

D. Bai, P. Huang, Y. Zhu, H. Ma, T. Xiao, T. Wang, and G. Zeng, “Unidimensional continuous-variable measurement-device-independent quantum key distribution,” J. Phys. B: At. Mol. Opt. Phys. 52135502 (2019).

C. Ottaviani, C. Lupo, R. Laurenza, and S. Pirandola, “Modular network for high-rate quantum conferencing,” Commun. Phys. 2, 118 (2019).
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F. Grasselli, H. Kampermann, and D. Bruß, “Conference key agreement with single-photon interference,” New J. Phys. 21, 123002 (2019).

F. Laudenbach and C. Pacher, “Analysis of the trusted-device scenario in continuous-variable quantum key distribution,” Adv. Quantum Technol. 2, 1900055 (2019).
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N. Hosseinidehaj, N. Walk, and T. C. Ralph, “Optimal realistic attacks in continuous-variable quantum key distribution,” Phys. Rev. A 99, 052336 (2019).
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Y. Guo, W. Ye, H. Zhong, and Q. Liao, “Continuous-variable quantum key distribution with non-Gaussian quantum catalysis,” Phys. Rev. A 99, 032327 (2019).
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G. Wang, C. Ottaviani, H. Guo, and S. Pirandola, “Improving the lower bound to the secret-key capacity of the thermal amplifier channel,” Eur. Phys. J. D 73, 17 (2019).
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S. Ghorai, E. Diamanti, and A. Leverrier, “Composable security of two-way continuous-variable quantum key distribution without active symmetrization,” Phys. Rev. A 99, 012311 (2019).
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L. Calderaro, C. Agnesi, D. Dequal, F. Vedovato, M. Schiavon, A. Santamato, V. Luceri, G. Bianco, G. Vallone, and P. Villoresi, “Towards quantum communication from global navigation satellite system,” Quantum Sci. Technol. 4, 015012 (2019).
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N. Hosseinidehaj, Z. Babar, R. Malaney, S. X. Ng, and L. Hanzo, “Satellite-based continuous-variable quantum communications: state-of-the-art and a predictive outlook,” Commun. Surv. Tutorials 21, 881–919 (2019).
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J. Kohlrus, D. E. Bruschi, and I. Fuentes, “Quantum-metrology estimation of spacetime parameters of the Earth outperforming classical precision,” Phys. Rev. A 99, 032350 (2019).
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T. K. Paraïso, I. De Marco, T. Roger, D. G. Marangon, J. F. Dynes, M. Lucamarini, Z. Yuan, and A. J. Shields, “A modulator-free quantum key distribution transmitter chip,” npj Quantum Inf. 5, 42 (2019).
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C. Cui, Z.-Q. Yin, R. Wang, W. Chen, S. Wang, G.-C. Guo, and Z.-F. Han, “Twin-field quantum key distribution without phase postselection,” Phys. Rev. Appl. 11, 034053 (2019).
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F.-Y. Lu, Z.-Q. Yin, C.-H. Cui, G.-J. Fan-Yuan, R. Wang, S. Wang, W. Chen, D.-Y. He, G.-C. Guo, and Z.-F. Han, “Improving the performance of twin-field quantum key distribution,” Phys. Rev. A 100, 022306 (2019).

M. Curty, K. Azuma, and H.-K. Lo, “Simple security proof of twin-field type quantum key distribution protocol,” npj Quantum Inf. 5, 64 (2019).
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F. Grasselli and M. Curty, “Practical decoy-state method for twin-field quantum key distribution,” New J. Phys. 21, 073001 (2019).

X. Zhong, J. Hu, M. Curty, L. Qian, and H.-K. Lo, “Proof-of-principle experimental demonstration of twin-field type quantum key distribution,” Phys. Rev. Lett. 123, 100506 (2019).
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H.-L. Yin and Y. Fu, “Measurement-device-independent twin-field quantum key distribution,” Sci. Rep. 9, 3045 (2019).
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H.-L. Yin and Z.-B. Chen, “Twin-field quantum key distribution over 1000  km fibre,” Sci. Rep. 9, 14918 (2019).

H.-L. Yin and Z.-B. Chen, “Finite-key analysis for twin-field quantum key distribution with composable security,” Sci. Rep. 9, 17113 (2019).

C. H. Zhang, C.-M. Zhang, and Q. Wang, “Twin-field quantum key distribution with modified coherent states,” Opt. Lett. 44, 1468–1471 (2019).
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X. Y. Zhou, C. Zhang, C. Zhang, and Q. Wang, “Asymmetric sending or not sending twin-field quantum key distribution in practice,” Phys. Rev. A 99, 062316 (2019).
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M. Minder, M. Pittaluga, G. L. Roberts, M. Lucamarini, J. F. Dynes, Z. L. Yuan, and A. J. Shields, “Experimental quantum key distribution beyond the repeaterless secret key capacity,” Nat. Photonics 13, 334–338 (2019).
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S. Wang, D.-Y. He, Z.-Q. Yin, F.-Y. Lu, C.-H. Cui, W. Chen, Z. Zhou, G.-C. Guo, and Z.-F. Han, “Beating the fundamental rate-distance limit in a proof-of-principle quantum key distribution system,” Phys. Rev. X 9, 021046 (2019).
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Y. Liu, Z.-W. Yu, W. Zhang, J.-Y. Guan, J.-P. Chen, C. Zhang, X.-L. Hu, H. Li, C. Jiang, J. Lin, T.-Y. Chen, L. You, Z. Wang, X.-B. Wang, Q. Zhang, and J.-W. Pan, “Experimental twin-field quantum key distribution through sending or not sending,” Phys. Rev. Lett. 123, 100505 (2019).
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X.-B. Wang, X.-L. Hu, and Z.-W. Yu, “Practical long-distance side-channel-free quantum key distribution,” Phys. Rev. Appl. 12, 054034 (2019).
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C. H. Zhang, C.-M. Zhang, and Q. Wang, “Efficient passive measurement-device-independent quantum key distribution,” Phys. Rev. A 99, 052325 (2019).
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Z.-W. Yu, X.-L. Hu, C. Jiang, H. Xu, and X.-B. Wang, “Sending-or-not-sending twin-field quantum key distribution in practice,” Sci. Rep. 9, 3080 (2019).
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C. Jiang, Z.-W. Yu, X.-L. Hu, and X.-B. Wang, “Unconditional security of sending or not sending twin-field quantum key distribution with finite pulses,” Phys. Rev. Appl. 12, 024061 (2019).

R. Arnon-Friedman, R. Renner, and T. Vidick, “Simple and tight device-independent security proofs,” SIAM J. Comput. 48, 181–225 (2019).
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F. Dupuis and O. Fawzi, “Entropy accumulation with improved second-order term,” IEEE Trans. Inf. Theory 65, 7596–7612 (2019).

B. Da Lio, D. Bacco, D. Cozzolino, Y. Ding, K. Dalgaard, K. Rottwitt, and L. Oxenløwe, “Experimental demonstration of the DPTS QKD protocol over a 170  km fiber link,” Appl. Phys. Lett. 114, 011101 (2019).
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C. Lee, D. Bunandar, Z. Zhang, G. R. Steinbrecher, P. B. Dixon, F. N. C. Wong, J. H. Shapiro, S. A. Hamilton, and D. Englund, “Large-alphabet encoding for higher-rate quantum key distribution,” Opt. Express 27, 17539–17549 (2019).

D. Cozzolino, D. Bacco, B. Da Lio, K. Ingerslev, Y. Ding, K. Dalgaard, P. Kristensen, M. Galili, K. Rottwitt, S. Ramachandran, and L. K. Oxenløwe, “Orbital angular momentum states enabling fiber-based high-dimensional quantum communication,” Phys. Rev. Appl. 11, 064058 (2019).
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J. Wallnöfer, A. Pirker, M. Zwerger, and W. Dür, “Multipartite state generation in quantum networks with optimal scaling,” Sci. Rep. 9, 314 (2019).
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D. Miller, T. Holz, H. Kampermann, and D. Bruß, “Parameter regimes for surpassing the PLOB bound with error-corrected qudit repeaters,” Quantum 3, 216 (2019).
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G. Vardoyan, S. Guha, P. Nain, and D. Towsley, “On the stochastic analysis of a quantum entanglement switch,” SIGMETRICS Perform. Evaluation Review 47, 27–29 (2019).

S. Pirandola, “End-to-end capacities of a quantum communication network,” Commun. Phys. 2, 51 (2019).
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S. Pirandola, “Bounds for multi-end communication over quantum networks,” Quantum Sci. Technol. 4, 045006 (2019).
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M. Pant, H. Krovi, D. Towsley, L. Tassiulas, L. Jiang, P. Basu, D. Englund, and S. Guha, “Routing entanglement in the quantum internet,” npj Quantum Inf. 5, 25 (2019).
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A. Pirker, M. Zwerger, V. Dunjko, H. J. Briegel, and W. Dür, “Simple proof of confidentiality for private quantum channels in noisy environments,” Quantum Sci. Technol. 4, 025009 (2019).
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2018 (77)

T. P. W. Cope, K. Goodenough, and S. Pirandola, “Converse bounds for quantum and private communication over Holevo–Werner channels,” J. Phys. A 51, 494001 (2018).
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L. Rigovacca, G. Kato, S. Bäuml, M. S. Kim, W. J. Munro, and K. Azuma, “Versatile relative entropy bounds for quantum networks,” New J. Phys. 20, 013033 (2018).
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T. Holz, H. Kampermann, and D. Bruß, “Device-independent secret-key-rate analysis for quantum repeaters,” Phys. Rev. A 97, 012337 (2018).
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M. Zwerger, A. Pirker, V. Dunjko, H. J. Briegel, and W. Dür, “Long-range big quantum-data transmission,” Phys. Rev. Lett. 120, 030503 (2018).
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S.-K. Liao, W.-Q. Cai, J. Handsteiner, B. Liu, J. Yin, L. Zhang, D. Rauch, M. Fink, J.-G. Ren, W. Liu, Y. Li, Q. Shen, Y. Cao, F.-Z. Li, J.-F. Wang, Y.-M. Huang, L. Deng, T. Xi, L. Ma, T. Hu, L. Li, N.-L. Liu, F. Koidl, P. Wang, Y.-A. Chen, X.-B. Wang, M. A. Steindorfer, G. Kirchner, C.-Y. Lu, R. Shu, R. Ursin, T. Scheidl, C.-Z. Peng, J.-Y. Wang, A. Zeilinger, and J.-W. Pan, “Satellite-relayed intercontinental quantum network,” Phys. Rev. Lett. 120, 030501 (2018).
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C. Lupo, C. Ottaviani, P. Papanastasiou, and S. Pirandola, “Continuous-variable measurement-device-independent quantum key distribution: composable security against coherent attacks,” Phys. Rev. A 97, 052327 (2018).
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C. Lupo, C. Ottaviani, P. Papanastasiou, and S. Pirandola, “Parameter estimation with almost no public communication for continuous-variable quantum key distribution,” Phys. Rev. Lett. 120, 220505 (2018).
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M. Lucamarini, Z. L. Yuan, J. F. Dynes, and A. J. Shields, “Overcoming the rate-distance limit of quantum key distribution without quantum repeaters,” Nature 557, 400–403 (2018).
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M. Erhard, R. Fickler, M. Krenn, and A. Zeilinger, “Twisted photons: new quantum perspectives in high dimensions,” Light Sci. Appl. 7, 17146 (2018).
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C. H. Park, M. K. Woo, B. K. Park, M. S. Lee, Y. S. Kim, Y. W. Cho, S. Kim, S. W. Han, and S. Moon, “Practical plug-and-play measurement-device-independent quantum key distribution with polarization division multiplexing,” IEEE Access 6, 58587–58593 (2018).
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H. Liu, J. Wang, H. Ma, and S. Sun, “Polarization-multiplexing-based measurement-device-independent quantum key distribution without phase reference calibration,” Optica 5, 902–909 (2018).
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A. Boaron, G. Boso, D. Rusca, C. Autebert, M. Caloz, M. Perrenoud, and H. Zbinden, “Secure quantum key distribution over 421  km of optical fiber,” Phys. Rev. Lett. 121, 190502 (2018).
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D. Bunandar, N. Harris, Z. Zhang, C. Lee, R. Ding, T. Baehr-Jones, M. Hochberg, J. Shapiro, F. Wong, and D. Englund, “Wavelength-division multiplexed quantum key distribution on silicon photonic integrated devices,” Bull. Am. Phys. Soc. 63, A180009 (2018).

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H. A. Zaidi and P. van Loock, “Beating the one-half limit of ancilla-free linear optics Bell measurements,” Phys. Rev. Lett. 110, 260501 (2013).
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P. Jouguet, S. Kunz-Jacques, and E. Diamanti, “Preventing calibration attacks on the local oscillator in continuous-variable quantum key distribution,” Phys. Rev. A 87, 062313 (2013).
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D. Gonta and P. van Loock, “Dynamical quantum repeater using cavity QED and optical coherent states,” Phys. Rev. A 88, 052308 (2013).
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