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Quantum repeaters: From quantum networks to the quantum internet

Koji Azuma*, Sophia E. Economou†, David Elkouss‡, Paul Hilaire§, Liang Jiang∥, Hoi-Kwong Lo, and Ilan Tzitrin**

Koji Azuma*

  • NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato-Wakamiya, Atsugi, Kanagawa 243-0198, Japan and NTT Research Center for Theoretical Quantum Information, NTT Corporation, 3-1 Morinosato-Wakamiya, Atsugi, Kanagawa 243-0198, Japan

Sophia E. Economou†

  • Department of Physics, Virginia Tech, Blacksburg, Virginia 24061, USA

David Elkouss‡

  • QuTech, Delft University of Technology, Lorentzweg 1, 2628 CJ Delft, The Netherlands and Networked Quantum Devices Unit, Okinawa Institute of Science and Technology Graduate University, Okinawa, Japan

Paul Hilaire§

  • Department of Physics, Virginia Tech, Blacksburg, Virginia 24061, USA and Quandela SAS, 10 Boulevard Thomas Gobert, 91120 Palaiseau, France

Liang Jiang∥

  • Pritzker School of Molecular Engineering, The University of Chicago, Chicago, Illinois 60637, USA

Hoi-Kwong Lo

  • Quantum Bridge Technologies, Inc., 100 College Street, Toronto, Ontario M5G 1L5, Canada, Department of Physics, University of Hong Kong, Pokfulam, Hong Kong, and Center for Quantum Information and Quantum Control, Department of Physics and Department of Electrical and Computer Engineering, University of Toronto, Toronto, Ontario M5S 3G4, Canada

Ilan Tzitrin**

  • Department of Physics, University of Toronto, Toronto, Ontario, Canada

  • *koji.azuma@ntt.com
  • †economou@vt.edu
  • ‡david.elkouss@oist.jp
  • §paul.hilaire@quandela.com
  • ∥liang.jiang@uchicago.edu
  • hklo@ece.utoronto.ca
  • **itzitrin@physics.utoronto.ca
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Rev. Mod. Phys. 95, 045006 – Published 20 December, 2023

DOI: https://doi.org/10.1103/RevModPhys.95.045006

Abstract

A quantum internet is the holy grail of quantum information processing, enabling the deployment of a broad range of quantum technologies and protocols on a global scale. However, numerous challenges must be addressed before the quantum internet can become a reality. Perhaps the most crucial of these is the realization of a quantum repeater, an essential component in the long-distance transmission of quantum information. As the analog of a classical repeater, extender, or booster, the quantum repeater works to overcome loss and noise in the quantum channels constituting a quantum network. Here the conceptual frameworks and architectures for quantum repeaters, as well as the experimental progress toward their realization, are reviewed. Various near-term proposals to overcome the limits to the communication rates set by point-to-point quantum communication are also discussed. Finally, the manner in which quantum repeaters fit within the broader challenge of designing and implementing a quantum internet is overviewed.

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References (569)

  1. Abobeih, M. H., Y. Wang, J. Randall, S. J. H. Loenen, C. E. Bradley, M. Markham, D. J. Twitchen, B. M. Terhal, and T. H. Taminiau, 2022, “Fault-tolerant operation of a logical qubit in a diamond quantum processor,” Nature (London) 606, 884–889.
  2. Abobeih, Mohamed H., Julia Cramer, Michiel A. Bakker, Norbert Kalb, Matthew Markham, Daniel J. Twitchen, and Tim H. Taminiau, 2018, “One-second coherence for a single electron spin coupled to a multi-qubit nuclear-spin environment,” Nat. Commun. 9, 2552.
  3. Abruzzo, Silvestre, Hermann Kampermann, and Dagmar Bruß, 2014, “Measurement-device-independent quantum key distribution with quantum memories,” Phys. Rev. A 89, 012301.
  4. Afzelius, Mikael, Christoph Simon, Hugues de Riedmatten, and Nicolas Gisin, 2009, “Multimode quantum memory based on atomic frequency combs,” Phys. Rev. A 79, 052329.
  5. Aharonov, Dorit, Michael Ben-Or, Elad Eban, and Urmila Mahadev, 2017, “Interactive proofs for quantum computations,” arXiv:1704.04487.
  6. Aharonovich, I., S. Castelletto, D. A. Simpson, C.-H. Su, A. D. Greentree, and S. Prawer, 2011, “Diamond-based single-photon emitters,” Rep. Prog. Phys. 74, 076501.
  7. Aharonovich, Igor, Dirk Englund, and Milos Toth, 2016, “Solid-state single-photon emitters,” Nat. Photonics 10, 631–641.
  8. Albert, Victor V., et al., 2018, “Performance and structure of single-mode bosonic codes,” Phys. Rev. A 97, 032346.
  9. Ambainis, Andris, Harry Buhrman, Yevgeniy Dodis, and Hein Rohrig, 2004, “Multiparty quantum coin flipping,” in Proceedings of the 19th IEEE Annual Conference on Computational Complexity, Amherst, MA, 2004 (IEEE, New York), pp. 250–259, 10.1109/CCC.2004.1313848.
  10. Androvitsaneas, Petros, et al., 2019, “Efficient quantum photonic phase shift in a low Q-factor regime,” ACS Photonics 6, 429–435.
  11. Ang, James, et al., 2022, “Architectures for multinode superconducting quantum computers,” arXiv:2212.06167.
  12. Appel, Martin Hayhurst, et al., 2022, “Entangling a Hole Spin with a Time-Bin Photon: A Waveguide Approach for Quantum Dot Sources of Multiphoton Entanglement,” Phys. Rev. Lett. 128, 233602.
  13. Arcari, Marta, Immo Söllner, Alisa Javadi, S. Lindskov Hansen, Sahand Mahmoodian, Jin Liu, Henri Thyrrestrup, Eun Hye Lee, Jin Dong Song, and Søren Stobbe, et al. 2014, “Near-Unity Coupling Efficiency of a Quantum Emitter to a Photonic Crystal Waveguide,” Phys. Rev. Lett. 113, 093603.
  14. Arnold, C., V. Loo, A. Lemaître, I. Sagnes, O. Krebs, P. Voisin, P. Senellart, and L. Lanco, 2014, “Cavity-Enhanced Real-Time Monitoring of Single-Charge Jumps at the Microsecond Time Scale,” Phys. Rev. X 4, 021004.
  15. Arroyo-Camejo, Silvia, Andrii Lazariev, Stefan W. Hell, and Gopalakrishnan Balasubramanian, 2014, “Room temperature high-fidelity holonomic single-qubit gate on a solid-state spin,” Nat. Commun. 5, 4870.
  16. Asadi, F Kimiaee, S. C. Wein, and C. Simon, 2020, “Protocols for long-distance quantum communication with single Er167 ions,” Quantum Sci. Technol. 5, 045015.
  17. Asavanant, Warit, et al., 2019, “Generation of time-domain-multiplexed two-dimensional cluster state,” Science 366, 373–376.
  18. Atatüre, Mete, Dirk Englund, Nick Vamivakas, Sang-Yun Lee, and Joerg Wrachtrup, 2018, “Material platforms for spin-based photonic quantum technologies,” Nat. Rev. Mater. 3, 38–51.
  19. Augusiak, Remigiusz, and Paweł Horodecki, 2009, “Multipartite secret key distillation and bound entanglement,” Phys. Rev. A 80, 042307.
  20. Awschalom, David, 2020, “From long-distance entanglement to building a nationwide quantum internet: Report of the DOE Quantum Internet Blueprint workshop,” Brookhaven National Laboratory Technical Report No. BNL-216179-2020-FORE, 10.2172/1638794.
  21. Awschalom, David, et al., 2021, “Development of quantum interconnects (QuICs) for next-generation information technologies,” PRX Quantum 2, 017002.
  22. Awschalom, David D., Ronald Hanson, Jörg Wrachtrup, and Brian B. Zhou, 2018, “Quantum technologies with optically interfaced solid-state spins,” Nat. Photonics 12, 516–527.
  23. Azuma, Koji, 2023, “Networking quantum networks with minimum cost aggregation,” arXiv:2304.08921.
  24. Azuma, Koji, Stefan Bäuml, Tim Coopmans, David Elkouss, and Boxi Li, 2021, “Tools for quantum network design,” AVS Quantum Sci. 3, 014101.
  25. Azuma, Koji, Nobuyuki Imoto, and Masato Koashi, 2022, “Optimal supplier of single-error-type entanglement via coherent-state transmission,” Phys. Rev. A 105, 062432.
  26. Azuma, Koji, and Go Kato, 2012, “Optimal entanglement manipulation via coherent-state transmission,” Phys. Rev. A 85, 060303.
  27. Azuma, Koji, and Go Kato, 2017, “Aggregating quantum repeaters for the quantum internet,” Phys. Rev. A 96, 032332.
  28. Azuma, Koji, Akihiro Mizutani, and Hoi-kwong Lo, 2016, “Fundamental rate-loss trade-off for the quantum internet,” Nat. Commun. 7, 13523.
  29. Azuma, Koji, Naoya Sota, Masato Koashi, and Nobuyuki Imoto, 2010, “Tight bound on coherent-state-based entanglement generation over lossy channels,” Phys. Rev. A 81, 022325.
  30. Azuma, Koji, Naoya Sota, Ryo Namiki, Şahin Kaya Özdemir, Takashi Yamamoto, Masato Koashi, and Nobuyuki Imoto, 2009, “Optimal entanglement generation for efficient hybrid quantum repeaters,” Phys. Rev. A 80, 060303.
  31. Azuma, Koji, Hitoshi Takeda, Masato Koashi, and Nobuyuki Imoto, 2012, “Quantum repeaters and computation by a single module: Remote nondestructive parity measurement,” Phys. Rev. A 85, 062309.
  32. Azuma, Koji, Kiyoshi Tamaki, and Hoi-Kwong Lo, 2015, “All-photonic quantum repeaters,” Nat. Commun. 6, 6787.
  33. Azuma, Koji, Kiyoshi Tamaki, and William J. Munro, 2015, “All-photonic intercity quantum key distribution,” Nat. Commun. 6, 10171.
  34. Bacco, Davide, Jacob F. F. Bulmer, Manuel Erhard, Marcus Huber, and Stefano Paesani, 2021, “Proposal for practical multidimensional quantum networks,” Phys. Rev. A 104, 052618.
  35. Bacon, Dave, 2006, “Operator quantum error-correcting subsystems for self-correcting quantum memories,” Phys. Rev. A 73, 012340.
  36. Balasubramanian, Gopalakrishnan, et al., 2009, “Ultralong spin coherence time in isotopically engineered diamond,” Nat. Mater. 8, 383–387.
  37. Bar-Gill, Nir, Linh M. Pham, Andrejs Jarmola, Dmitry Budker, and Ronald L. Walsworth, 2013, “Solid-state electronic spin coherence time approaching one second,” Nat. Commun. 4, 1743.
  38. Barnum, Howard, Carlton M. Caves, Christopher A. Fuchs, Richard Jozsa, and Benjamin Schumacher, 1996, “Noncommuting Mixed States Cannot Be Broadcast,” Phys. Rev. Lett. 76, 2818.
  39. Barreiro, J. T., N. K. Langford, N. A. Peters, and P. G. Kwiat, 2005, “Generation of Hyperentangled Photon Pairs, Phys. Rev. Lett. 95, 260501.
  40. Barrett, Jonathan, Roger Colbeck, and Adrian Kent, 2013, “Memory Attacks on Device-Independent Quantum Cryptography,” Phys. Rev. Lett. 110, 010503.
  41. Barrett, S. D., Pieter Kok, Kae Nemoto, R. G. Beausoleil, W. J. Munro, and T. P. Spiller, 2005, “Symmetry analyzer for nondestructive Bell-state detection using weak nonlinearities,” Phys. Rev. A 71, 060302.
  42. Barrett, Sean D., and Pieter Kok, 2005, “Efficient high-fidelity quantum computation using matter qubits and linear optics,” Phys. Rev. A 71, 060310.
  43. Barros, H. G., A. Stute, T. E. Northup, C. Russo, P. O. Schmidt, and R. Blatt, 2009, “Deterministic single-photon source from a single ion,” New J. Phys. 11, 103004.
  44. Bartolucci, Sara, et al., 2023, “Fusion-based quantum computation,” Nat. Commun. 14, 912.
  45. Bauch, Erik, Connor A. Hart, Jennifer M. Schloss, Matthew J. Turner, John F. Barry, Pauli Kehayias, Swati Singh, and Ronald L. Walsworth, 2018, “Ultralong Dephasing Times in Solid-State Spin Ensembles via Quantum Control,” Phys. Rev. X 8, 031025.
  46. Bäuml, Stefan, and Koji Azuma, 2017, “Fundamental limitation on quantum broadcast networks, Quantum Sci. Technol. 2, 024004.
  47. Bäuml, Stefan, Koji Azuma, Go Kato, and David Elkouss, 2020, “Linear programs for entanglement and key distribution in the quantum internet,” Commun. Phys. 3, 55.
  48. Bäuml, Stefan, Matthias Christandl, Karol Horodecki, and Andreas Winter, 2015, “Limitations on quantum key repeaters,” Nat. Commun. 6, 6908.
  49. Bäuml, Stefan, Siddhartha Das, and Mark M. Wilde, 2018, “Fundamental Limits on the Capacities of Bipartite Quantum Interactions,” Phys. Rev. Lett. 121, 250504.
  50. Bayrakci, Veysel, and Fatih Ozaydin, 2022, “Quantum zeno repeaters,” Sci. Rep. 12, 15302.
  51. Bechtold, Alexander, Dominik Rauch, Fuxiang Li, Tobias Simmet, Per-Lennart Ardelt, Armin Regler, Kai Müller, Nikolai A. Sinitsyn, and Jonathan J. Finley, 2015, “Three-stage decoherence dynamics of an electron spin qubit in an optically active quantum dot,” Nat. Phys. 11, 1005–1008.
  52. Becker, Jonas N., Benjamin Pingault, David Groß, Mustafa Gündoǧan, Nadezhda Kukharchyk, Matthew Markham, Andrew Edmonds, Mete Atatüre, Pavel Bushev, and Christoph Becher, 2018, “All-Optical Control of the Silicon-Vacancy Spin in Diamond at Millikelvin Temperatures,” Phys. Rev. Lett. 120, 053603.
  53. Bell, B. A., D. A. Herrera-Martí, M. S. Tame, D. Markham, W. J. Wadsworth, and J. G. Rarity, 2014, “Experimental demonstration of a graph state quantum error-correction code,” Nat. Commun. 5, 3658.
  54. Bell, J. S., 1964, “On the Einstein Podolsky Rosen paradox,” Phys. Phys. Fiz. 1, 195–200.
  55. Bell, Tom J., Love A. Pettersson, and Stefano Paesani, 2023, “Optimizing graph codes for measurement-based loss tolerance,” PRX Quantum 4, 020328.
  56. Bennett, C. H., and G. Brassard, 1984, “Quantum cryptography: Public key distribution and coin tossing,” in Proceedings of IEEE International Conference on Computers, Systems, and Signal Processing, Bangalore, India, 1984 (IEEE, New York), pp. 175–179, 10.1016/j.tcs.2014.05.025.
  57. Bennett, C. H., G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. K. Wootters, 1993, “Teleporting an Unknown Quantum State via Dual Classical and Einstein-Podolsky-Rosen Channels,” Phys. Rev. Lett. 70, 1895.
  58. Bennett, C. H., G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, and W. K. Wootters, 1996, “Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels,” Phys. Rev. Lett. 76, 722–725.
  59. Bennett, Charles H., Herbert J. Bernstein, Sandu Popescu, and Benjamin Schumacher, 1996, “Concentrating partial entanglement by local operations,” Phys. Rev. A 53, 2046.
  60. Bennett, Charles H., Gilles Brassard, and N. David Mermin, 1992, “Quantum Cryptography without Bell’s Theorem,” Phys. Rev. Lett. 68, 557–559.
  61. Bennett, Charles H., David P. DiVincenzo, and John A. Smolin, 1997, “Capacities of Quantum Erasure Channels,” Phys. Rev. Lett. 78, 3217.
  62. Bennett, Charles H., David P. DiVincenzo, John A. Smolin, and William K. Wootters, 1996, “Mixed-state entanglement and quantum error correction,” Phys. Rev. A 54, 3824–3851.
  63. Ben-Or, Michael, and Avinatan Hassidim, 2005, “Fast quantum byzantine agreement,” in Proceedings of the Thirty-Seventh Annual ACM Symposium on Theory of Computing, Baltimore, 2005, edited by H. Gabow and Ronald Fagin (Association for Computing Machinery, New York), pp. 481–485, 10.1145/1060590.1060662.
  64. Benyoucef, M., M. Yacob, J. P. Reithmaier, J. Kettler, and P. Michler, 2013, “Telecom-wavelength (1.5  μm) single-photon emission from inp-based quantum dots,” Appl. Phys. Lett. 103, 162101.
  65. Bergeron, L., C. Chartrand, A. T. K. Kurkjian, K. J. Morse, H. Riemann, N. V. Abrosimov, P. Becker, H.-J. Pohl, M. L. W. Thewalt, and S. Simmons, 2020, “Silicon-integrated telecommunications photon-spin interface,” PRX Quantum 1, 020301.
  66. Bernien, Hannes, et al., 2013, “Heralded entanglement between solid-state qubits separated by three metres,” Nature (London) 497, 86–90.
  67. Berry, Michael, 1998, Introduction to Quantum Computation and Information, edited by Hoi-Kwong Lo, Sandu Popescu, and Tim Spiller (World Scientific, Singapore).
  68. Bersin, E., et al., 2023, “Development of a Boston-area 50-km fiber quantum network testbed,” arXiv:2307.15696.
  69. Bhaskar, Mihir K., et al., 2020, “Experimental demonstration of memory-enhanced quantum communication,” Nature (London) 580, 60–64.
  70. Biham, Eli, Bruno Huttner, and Tal Mor, 1996, “Quantum cryptographic network based on quantum memories,” Phys. Rev. A 54, 2651.
  71. Blinov, B. B., D. L. Moehring, L.-M. Duan, and Chris Monroe, 2004, “Observation of entanglement between a single trapped atom and a single photon,” Nature (London) 428, 153–157.
  72. Bloch, Matthieu, João Barros, Miguel R. D. Rodrigues, and Steven W. McLaughlin, 2008, “Wireless information-theoretic security,” IEEE Trans. Inf. Theory 54, 2515–2534.
  73. Boaron, Alberto, et al., 2018, “Secure Quantum Key Distribution over 421 km of Optical Fiber,” Phys. Rev. Lett. 121, 190502.
  74. Bock, Matthias, Pascal Eich, Stephan Kucera, Matthias Kreis, Andreas Lenhard, Christoph Becher, and Jürgen Eschner, 2018, “High-fidelity entanglement between a trapped ion and a telecom photon via quantum frequency conversion,” Nat. Commun. 9, 1998.
  75. Bonarota, M., J. L. Le Gouët, and T. Chanelière, 2011, “Highly multimode storage in a crystal,” New J. Phys. 13, 013013.
  76. Bonneau, Damien, Gabriel J. Mendoza, Jeremy L O’Brien, and Mark G. Thompson, 2015, “Effect of loss on multiplexed single-photon sources,” New J. Phys. 17, 043057.
  77. Boone, K., J.-P. Bourgoin, E. Meyer-Scott, K. Heshami, T. Jennewein, and C. Simon, 2015, “Entanglement over global distances via quantum repeaters with satellite links,” Phys. Rev. A 91, 052325.
  78. Borregaard, J., M. Zugenmaier, J. M. Petersen, H. Shen, G. Vasilakis, K. Jensen, E. S. Polzik, and A. S. Sørensen, 2016, “Scalable photonic network architecture based on motional averaging in room temperature gas,” Nat. Commun. 7, 11356.
  79. Borregaard, Johannes, Hannes Pichler, Tim Schröder, Mikhail D. Lukin, Peter Lodahl, and Anders S. Sørensen, 2020, “One-Way Quantum Repeater Based on Near-Deterministic Photon-Emitter Interfaces,” Phys. Rev. X 10, 021071.
  80. Bose, S., P. L. Knight, M. B. Plenio, and V. Vedral, 1999, “Proposal for Teleportation of an Atomic State via Cavity Decay,” Phys. Rev. Lett. 83, 5158.
  81. Bourassa, A., et al., 2020, “Entanglement and control of single nuclear spins in isotopically engineered silicon carbide,” Nat. Mater. 19, 1319.
  82. Bradley, C. E., J. Randall, M. H. Abobeih, R. C. Berrevoets, M. J. Degen, M. A. Bakker, M. Markham, D. J. Twitchen, and T. H. Taminiau, 2019, “A Ten-Qubit Solid-State Spin Register with Quantum Memory up to One Minute,” Phys. Rev. X 9, 031045.
  83. Brassard, Gilles, 2003, “Quantum communication complexity,” Found. Phys. 33, 1593–1616.
  84. Bratzik, S., H. Kampermann, and D. Bruss, 2014, “Secret key rates for an encoded quantum repeater,” Phys. Rev. A 89, 032335.
  85. Braunstein, Samuel L., and H. Jeff Kimble, 1998, “Teleportation of Continuous Quantum Variables,” Phys. Rev. Lett. 80, 869.
  86. Briegel, H.-J., W. Dür, J. I. Cirac, and P. Zoller, 1998, “Quantum Repeater: The Role of Imperfect Local Operations in Quantum Communication,” Phys. Rev. Lett. 81, 5932–5935.
  87. Briegel, Hans J., and Robert Raussendorf, 2001, “Persistent Entanglement in Arrays of Interacting Particles,” Phys. Rev. Lett. 86, 910–913.
  88. Broadbent, Anne, Joseph Fitzsimons, and Elham Kashefi, 2009, “Universal blind quantum computation,” in Proceedings of the 50th Annual IEEE Symposium on Foundations of Computer Science, Atlanta, 2009 (IEEE, New York), pp. 517–526, 10.1109/FOCS.2009.36.
  89. Broadbent, Anne, and Rabib Islam, 2020, “Quantum encryption with certified deletion,” in Theory of Cryptography Conference (Springer, New York), pp. 92–122, 10.1007/978-3-030-64381-2_4.
  90. Broadbent, Anne, and Christian Schaffner, 2016, “Quantum cryptography beyond quantum key distribution,” Des. Codes Cryptogr. 78, 351–382.
  91. Browne, Daniel E., and Terry Rudolph, 2005, “Resource-Efficient Linear Optical Quantum Computation,” Phys. Rev. Lett. 95, 010501.
  92. Brune, M., S. Haroche, V. Lefevre, J. M. Raimond, and N. Zagury, 1990, “Quantum Nondemolition Measurement of Small Photon Numbers by Rydberg-Atom Phase-Sensitive Detection,” Phys. Rev. Lett. 65, 976.
  93. Brunner, Nicolas, Daniel Cavalcanti, Stefano Pironio, Valerio Scarani, and Stephanie Wehner, 2014, “Bell nonlocality,” Rev. Mod. Phys. 86, 419–478.
  94. Buhrman, Harry, Nishanth Chandran, Serge Fehr, Ran Gelles, Vipul Goyal, Rafail Ostrovsky, and Christian Schaffner, 2011, “Position-based quantum cryptography: Impossibility and constructions,” in Advances in Cryptology—CRYPTO 2011, edited by Phillip Rogaway (Springer, Berlin), pp. 429–446, 10.1007/978-3-642-22792-9_24.
  95. Buhrman, Harry, Richard Cleve, John Watrous, and Ronald de Wolf, 2001, “Quantum Fingerprinting,” Phys. Rev. Lett. 87, 167902.
  96. Buterakos, Donovan, Edwin Barnes, and Sophia E. Economou, 2017, “Deterministic Generation of All-Photonic Quantum Repeaters from Solid-State Emitters,” Phys. Rev. X 7, 041023.
  97. Cabrillo, C., J. I. Cirac, P. Garcia-Fernandez, and P. Zoller, 1999, “Creation of entangled states of distant atoms by interference,” Phys. Rev. A 59, 1025.
  98. Cacciapuoti, Angela Sara, Marcello Caleffi, Francesco Tafuri, Francesco Saverio Cataliotti, Stefano Gherardini, and Giuseppe Bianchi, 2020, “Quantum internet: Networking challenges in distributed quantum computing,” IEEE Network 34, 137–143.
  99. Cacciapuoti, Angela Sara, Jessica Illiano, Seid Koudia, Kyrylo Simonov, and Marcello Caleffi, 2022, “The quantum internet: Enhancing classical Internet services one qubit at a time,” IEEE Network 36, 6–12.
  100. Calderbank, A. R., and Peter W. Shor, 1996, “Good quantum error-correcting codes exist,” Phys. Rev. A 54, 1098.
  101. Calsamiglia, John, and Norbert Lütkenhaus, 2001, “Maximum efficiency of a linear-optical Bell-state analyzer,” Appl. Phys. B 72, 67–71.
  102. Cartesian, 2021, “Addressing gaps in broadband infrastructure availability and service adoption,” https://www.cartesian.com/addressing-gaps-in-broadband-infrastructure-availability-and-service-adoption/.
  103. Castelvecchi, Davide, 2017, “IBM’s quantum cloud computer goes commercial,” Nature (London) 543, 159.
  104. Chailloux, André, and Iordanis Kerenidis, 2009, “Optimal quantum strong coin flipping,” in Proceedings of the 50th Annual IEEE Symposium on Foundations of Computer Science, Atlanta, 2009 (IEEE, New York), pp. 527–533, 10.1109/FOCS.2009.71.
  105. Chamberland, Christopher, and Michael E. Beverland, 2018, “Flag fault-tolerant error correction with arbitrary distance codes,” Quantum 2, 53.
  106. Chang, J., et al., 2021, “Detecting telecom single photons with (99.5−2.07+0.5) system detection efficiency and high time resolution,” APL Photonics 6, 036114.
  107. Chao, Rui, and Ben W. Reichardt, 2018, “Quantum Error Correction with Only Two Extra Qubits,” Phys. Rev. Lett. 121, 050502.
  108. Chen, Jiu-Peng, et al., 2020, “Sending-or-Not-Sending with Independent Lasers: Secure Twin-Field Quantum Key Distribution over 509 km,” Phys. Rev. Lett. 124, 070501.
  109. Chen, Jiu-Peng, et al., 2021, “Twin-field quantum key distribution over a 511 km optical fibre linking two distant metropolitan areas,” Nat. Photonics 15, 570–575.
  110. Chen, Kai, and Hoi-Kwong Lo, 2007, “Multi-partite quantum cryptographic protocols with noisy GHZ states,” Quantum Inf. Comput. 7, 689–715.
  111. Chen, Shuai, Yu-Ao Chen, Bo Zhao, Zhen-Sheng Yuan, Jörg Schmiedmayer, and Jian-Wei Pan, 2007, “Demonstration of a Stable Atom-Photon Entanglement Source for Quantum Repeaters,” Phys. Rev. Lett. 99, 180505.
  112. Chen, Yu-Ao, et al., 2021, “An integrated space-to-ground quantum communication network over 4,600 kilometres,” Nature (London) 589, 214–219.
  113. Childress, L., M. V. Gurudev Dutt, J. M. Taylor, A. S. Zibrov, F. Jelezko, J. Wrachtrup, P. R. Hemmer, and M. D. Lukin, 2006, “Coherent dynamics of coupled electron and nuclear spin qubits in diamond,” Science 314, 281–285.
  114. Childress, L., J. M. Taylor, A. S. Sørensen, and M. D. Lukin, 2006, “Fault-Tolerant Quantum Communication Based on Solid-State Photon Emitters,” Phys. Rev. Lett. 96, 070504.
  115. Childs, Andrew M., 2005, “Secure assisted quantum computation,” Quantum Inf. Comput. 5, 456–466.
  116. Chou, Chin-Wen, Julien Laurat, Hui Deng, Kyung Soo Choi, Hugues De Riedmatten, Daniel Felinto, and H. Jeff Kimble, 2007, “Functional quantum nodes for entanglement distribution over scalable quantum networks,” Science 316, 1316–1320.
  117. Christ, Andreas, and Christine Silberhorn, 2012, “Limits on the deterministic creation of pure single-photon states using parametric down-conversion,” Phys. Rev. A 85, 023829.
  118. Christandl, Matthias, and Alexander Müller-Hermes, 2017, “Relative entropy bounds on quantum, private and repeater capacities,” Commun. Math. Phys. 353, 821–852.
  119. Christandl, Matthias, and Stephanie Wehner, 2005, “Quantum anonymous transmissions,” in Proceedings of the International Conference on the Theory and Application of Cryptology and Information Security, Chennai, India, 2005, edited by Bimal Roy (Springer, New York), pp. 217–235, 10.1007/11593447_12.
  120. Christensen, Brad G., et al., 2013, “Detection-Loophole-Free Test of Quantum Nonlocality, and Applications,” Phys. Rev. Lett. 111, 130406.
  121. Chung, Joaquin, et al., 2021, “Illinois Express Quantum Network (IEQNET): Metropolitan-scale experimental quantum networking over deployed optical fiber,” in Quantum Information Science, Sensing, and Computation XIII, edited by Eric Donkor and Michael Hayduk, SPIE Proceedings Vol. 11726 (SPIE—International Society for Optical Engineering, Bellingham, WA), p. 1172602, 10.1117/12.2588007.
  122. Clerk, A. A., M. H. Devoret, S. M. Girvin, Florian Marquardt, and R. J. Schoelkopf, 2010, “Introduction to quantum noise, measurement, and amplification,” Rev. Mod. Phys. 82, 1155–1208.
  123. Cleve, Richard, and Harry Buhrman, 1997, “Substituting quantum entanglement for communication,” Phys. Rev. A 56, 1201.
  124. Cleve, Richard, Daniel Gottesman, and Hoi-Kwong Lo, 1999, “How to Share a Quantum Secret,” Phys. Rev. Lett. 83, 648.
  125. Clivati, Cecilia, et al., 2022, “Coherent phase transfer for real-world twin-field quantum key distribution,” Nat. Commun. 13, 157.
  126. Cogan, Dan, Zu-En Su, Oded Kenneth, and David Gershoni, 2023, “Deterministic generation of indistinguishable photons in a cluster state,” Nat. Photonics 17, 324–329.
  127. Collins, Daniel, Noah Linden, and Sandu Popescu, 2001, “Nonlocal content of quantum operations,” Phys. Rev. A 64, 032302.
  128. Collins, Matthew J., et al., 2013, “Integrated spatial multiplexing of heralded single-photon sources,” Nat. Commun. 4, 2582.
  129. Collins, O. A., S. D. Jenkins, A. Kuzmich, and T. A. B. Kennedy, 2007, “Multiplexed Memory-Insensitive Quantum Repeaters,” Phys. Rev. Lett. 98, 060502.
  130. Coopmans, Tim, et al., 2021, “NetSquid, a discrete-event simulation platform for quantum networks,” Commun. Phys. 4, 164.
  131. Corning, 2021, “Corning SMF-28 ULL optical fiber portfolio,” https://www.corning.com/optical-communications/worldwide/en/home/products/fiber/optical-fiber-products/smf-28-ull.html.
  132. Coste, N., et al., 2023, “High-rate entanglement between a semiconductor spin and indistinguishable photons,” Nat. Photonics 17, 582–587.
  133. Cramer, J., N. Kalb, M. A. Rol, B. Hensen, M. S. Blok, M. Markham, D. J. Twitchen, R. Hanson, and T. H. Taminiau, 2016, “Repeated quantum error correction on a continuously encoded qubit by real-time feedback,” Nat. Commun. 7, 11526.
  134. Cui, Chaohan, Zhen-Qiang Yin, Rong Wang, Wei Chen, Shuang Wang, Guang-Can Guo, and Zheng-Fu Han, 2019, “Twin-Field Quantum Key Distribution without Phase Postselection,” Phys. Rev. Appl. 11, 034053.
  135. Currás-Lorenzo, Guillermo, Álvaro Navarrete, Koji Azuma, Go Kato, Marcos Curty, and Mohsen Razavi, 2021, “Tight finite-key security for twin-field quantum key distribution,” npj Quantum Inf. 7, 22.
  136. Curty, Marcos, Koji Azuma, and Hoi-Kwong Lo, 2019, “Simple security proof of twin-field type quantum key distribution protocol,” npj Quantum Inf. 5, 64.
  137. Curty, Marcos, Koji Azuma, and Hoi-Kwong Lo, 2021, “A quantum leap in security,” Phys. Today 74, No. 3, 36.
  138. Curty, Marcos, and Hoi-Kwong Lo, 2019, “Foiling covert channels and malicious classical post-processing units in quantum key distribution,” npj Quantum Inf. 5, 14.
  139. Curty, Marcos, and Tobias Moroder, 2011, “Heralded-qubit amplifiers for practical device-independent quantum key distribution,” Phys. Rev. A 84, 010304.
  140. Curty, Marcos, Feihu Xu, Wei Cui, Charles Ci Wen Lim, Kiyoshi Tamaki, and Hoi-Kwong Lo, 2014, “Finite-key analysis for measurement-device-independent quantum key distribution,” Nat. Commun. 5, 3732.
  141. Dahlberg, Axel, et al., 2019, “A link layer protocol for quantum networks,” in Proceedings of the ACM Special Interest Group on Data Communication, Beijing, 2009 (Association for Computing Machinery, New York), pp. 159–173, 10.1145/3341302.3342070.
  142. Daiss, Severin, Stefan Langenfeld, Stephan Welte, Emanuele Distante, Philip Thomas, Lukas Hartung, Olivier Morin, and Gerhard Rempe, 2021, “A quantum-logic gate between distant quantum-network modules,” Science 371, 614–617.
  143. Damgård, Ivan B., Serge Fehr, Louis Salvail, and Christian Schaffner, 2007, “Secure identification and QKD in the bounded-quantum-storage model,” in Advances in Cryptology—CRYPTO 2007, Lecture Notes in Physics Vol. 4622, edited by Alfred Menezes (Springer, New York), pp. 342–359, 10.1007/978-3-540-74143-5_19.
  144. Damgård, Ivan B., Serge Fehr, Louis Salvail, and Christian Schaffner, 2008, “Cryptography in the bounded-quantum-storage model,” SIAM J. Comput. 37, 1865–1890.
  145. Das, Siddhartha, Stefan Bäuml, and Mark M. Wilde, 2020, “Entanglement and secret-key-agreement capacities of bipartite quantum interactions and read-only memory devices,” Phys. Rev. A 101, 012344.
  146. Das, Siddhartha, Stefan Bäuml, Marek Winczewski, and Karol Horodecki, 2021, “Universal Limitations on Quantum Key Distribution over a Network,” Phys. Rev. X 11, 041016.
  147. Degen, C. L., F. Reinhard, and P. Cappellaro, 2017, “Quantum sensing,” Rev. Mod. Phys. 89, 035002.
  148. De Greve, Kristiaan, et al., 2011, “Ultrafast coherent control and suppressed nuclear feedback of a single quantum dot hole qubit,” Nat. Phys. 7, 872–878.
  149. De Greve, Kristiaan, et al., 2012, “Quantum-dot spin-photon entanglement via frequency downconversion to telecom wavelength,” Nature (London) 491, 421–425.
  150. Delteil, Aymeric, Zhe Sun, Wei-bo Gao, Emre Togan, Stefan Faelt, and Atac Imamoğlu, 2016, “Generation of heralded entanglement between distant hole spins,” Nat. Phys. 12, 218–223.
  151. de Riedmatten, Hugues, Ivan Marcikic, Wolfgang Tittel, Hugo Zbinden, Daniel Collins, and Nicolas Gisin, 2004, “Long Distance Quantum Teleportation in a Quantum Relay Configuration,” Phys. Rev. Lett. 92, 047904.
  152. Deutsch, David, Artur Ekert, Richard Jozsa, Chiara Macchiavello, Sandu Popescu, and Anna Sanpera, 1996, “Quantum Privacy Amplification and the Security of Quantum Cryptography over Noisy Channels,” Phys. Rev. Lett. 77, 2818–2821.
  153. Devetak, Igor, 2005, “The private classical capacity and quantum capacity of a quantum channel,” IEEE Trans. Inf. Theory 51, 44–55.
  154. Devitt, Simon J., Andrew D. Greentree, Ashley M. Stephens, and Rodney Van Meter, 2016, “High-speed quantum networking by ship,” Sci. Rep. 6, 36163.
  155. Dias, Josephine, and T. C. Ralph, 2017, “Quantum repeaters using continuous-variable teleportation,” Phys. Rev. A 95, 022312.
  156. Dideriksen, Karsten B., Rebecca Schmieg, Michael Zugenmaier, and Eugene S. Polzik, 2021, “Room-temperature single-photon source with near-millisecond built-in memory,” Nat. Commun. 12, 3699.
  157. Dieks, D., 1982, “Communication by EPR devices,” Phys. Lett. 92A, 271–272.
  158. Dowling, Jonathan P., and Gerard J. Milburn, 2003, “Quantum technology: The second quantum revolution,” Phil. Trans. R. Soc. A 361, 1655–1674.
  159. Duan, L.-M., M. D. Lukin, J. I. Cirac, and P. Zoller, 2001, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature (London) 414, 413–418.
  160. Dudin, Y. O., L. Li, and A. Kuzmich, 2013, “Light storage on the time scale of a minute,” Phys. Rev. A 87, 031801.
  161. Dudin, Y. O., A. G. Radnaev, Ran Zhao, J. Z. Blumoff, T. A. B. Kennedy, and Alex Kuzmich, 2010, “Entanglement of Light-Shift Compensated Atomic Spin Waves with Telecom Light,” Phys. Rev. Lett. 105, 260502.
  162. Dupuis, Frederic, Omar Fawzi, and Stephanie Wehner, 2015, “Entanglement sampling and applications,” IEEE Trans. Inf. Theory 61, 1093–1112.
  163. Dür, W., and H. J. Briegel, 2007, “Entanglement purification and quantum error correction,” Rep. Prog. Phys. 70, 1381–1424.
  164. Dür, W., H.-J. Briegel, J. I. Cirac, and P. Zoller, 1999, “Quantum repeaters based on entanglement purification,” Phys. Rev. A 59, 169–181.
  165. Dür, W., G. Vidal, and J. I. Cirac, 2000, “Three qubits can be entangled in two inequivalent ways,” Phys. Rev. A 62, 062314.
  166. Durand, Alrik, et al., 2021, “Broad Diversity of Near-Infrared Single-Photon Emitters in Silicon,” Phys. Rev. Lett. 126, 083602.
  167. Eberhard, Phillippe H., and Ronald R. Ross, 1989, “Quantum field theory cannot provide faster-than-light communication,” Found. Phys. Lett. 2, 127–149.
  168. Ebert, M., M. Kwon, T. G. Walker, and M. Saffman, 2015, “Coherence and Rydberg Blockade of Atomic Ensemble Qubits,” Phys. Rev. Lett. 115, 093601.
  169. Economou, Sophia E., Netanel Lindner, and Terry Rudolph, 2010, “Optically Generated 2-Dimensional Photonic Cluster State from Coupled Quantum Dots,” Phys. Rev. Lett. 105, 093601.
  170. Egan, Laird, et al., 2021, “Fault-tolerant control of an error-corrected qubit,” Nature (London) 598, 281–286.
  171. Einstein, A., B. Podolsky, and N. Rosen, 1935, “Can quantum-mechanical description of physical reality be considered complete?,” Phys. Rev. 47, 777–780.
  172. Eisaman, M. D., J. Fan, A. Migdall, and S. V. Polyakov, 2011, “Invited review article: Single-photon sources and detectors,” Rev. Sci. Instrum. 82, 071101.
  173. Eisert, J., K. Jacobs, P. Papadopoulos, and M. B. Plenio, 2000, “Optimal local implementation of nonlocal quantum gates,” Phys. Rev. A 62, 052317.
  174. Eisert, J., S. Scheel, and M. B. Plenio, 2002, “Distilling Gaussian States with Gaussian Operations Is Impossible,” Phys. Rev. Lett. 89, 137903.
  175. Ekert, Artur K., 1991, “Quantum Cryptography Based on Bell’s Theorem,” Phys. Rev. Lett. 67, 661–663.
  176. Éthier-Majcher, G., D. Gangloff, R. Stockill, E. Clarke, M. Hugues, C. Le Gall, and M. Atatüre, 2017, “Improving a Solid-State Qubit through an Engineered Mesoscopic Environment,” Phys. Rev. Lett. 119, 130503.
  177. European Commission, 2022, “The European Quantum Communication Infrastructure (EuroQCI) initiative,” https://digital-strategy.ec.europa.eu/en/policies/european-quantum-communication-infrastructure-euroqci.
  178. Ewert, Fabian, Marcel Bergmann, and Peter van Loock, 2016, “Ultrafast Long-Distance Quantum Communication with Static Linear Optics,” Phys. Rev. Lett. 117, 210501.
  179. Ewert, Fabian, and Peter van Loock, 2014, “3/4-Efficient Bell Measurement with Passive Linear Optics and Unentangled Ancillae,” Phys. Rev. Lett. 113, 140403.
  180. Ewert, Fabian, and Peter van Loock, 2017, “Ultrafast fault-tolerant long-distance quantum communication with static linear optics,” Phys. Rev. A 95, 012327.
  181. Fern, Jesse, and K. Birgitta Whaley, 2008, “Lower bounds on the nonzero capacity of Pauli channels,” Phys. Rev. A 78, 062335.
  182. Fibre Optic Association, 2019, “FOA reference guide,” https://www.thefoa.org/tech/ref/testing/test/loss.html.
  183. Fitzsimons, Joseph F., 2017, “Private quantum computation: An introduction to blind quantum computing and related protocols,” npj Quantum Inf. 3, 23.
  184. Fiurášek, Jaromír, 2002, “Gaussian Transformations and Distillation of Entangled Gaussian States,” Phys. Rev. Lett. 89, 137904.
  185. Fiurášek, Jaromír, 2010, “Distillation and purification of symmetric entangled Gaussian states,” Phys. Rev. A 82, 042331.
  186. Fowler, A. G., D. S. Wang, C. D. Hill, T. D. Ladd, R. Van Meter, and L. C. L. Hollenberg, 2010, “Surface Code Quantum Communication,” Phys. Rev. Lett. 104, 180503.
  187. Fröhlich, Bernd, James F. Dynes, Marco Lucamarini, Andrew W. Sharpe, Zhiliang Yuan, and Andrew J. Shields, 2013, “A quantum access network,” Nature (London) 501, 69–72.
  188. Fuchs, G. D., Guido Burkard, P. V. Klimov, and D. D. Awschalom, 2011, “A quantum memory intrinsic to single nitrogen-vacancy centres in diamond,” Nat. Phys. 7, 789–793.
  189. Fujii, Keisuke, and Katsuji Yamamoto, 2009, “Entanglement purification with double selection,” Phys. Rev. A 80, 042308.
  190. Fukui, Kosuke, Rafael N. Alexander, and Peter van Loock, 2021, “All-optical long-distance quantum communication with Gottesman-Kitaev-Preskill qubits,” Phys. Rev. Res. 3, 033118.
  191. Fukui, Kosuke, Akihisa Tomita, and Atsushi Okamoto, 2017, “Analog Quantum Error Correction with Encoding a Qubit into an Oscillator,” Phys. Rev. Lett. 119, 180507.
  192. Furrer, Fabian, and William J. Munro, 2018, “Repeaters for continuous-variable quantum communication,” Phys. Rev. A 98, 032335.
  193. Gangloff, D. A., G. Ethier-Majcher, C. Lang, E. V. Denning, J. H. Bodey, D. M. Jackson, E. Clarke, M. Hugues, C. Le Gall, and M. Atatüre, 2019, “Quantum interface of an electron and a nuclear ensemble,” Science 364, 62.
  194. Gao, W. B., Parisa Fallahi, Emre Togan, Javier Miguel-Sánchez, and Atac Imamoglu, 2012, “Observation of entanglement between a quantum dot spin and a single photon,” Nature (London) 491, 426–430.
  195. Gavinsky, Dmitry, 2012, “Quantum money with classical verification,” in Proceedings of the IEEE 27th Conference on Computational Complexity, Porto, Portugal, 2012 (IEEE, New York), pp. 42–52, 10.1109/CCC.2012.10.
  196. Giedke, G., and J. I. Cirac, 2002, “Characterization of Gaussian operations and distillation of Gaussian states,” Phys. Rev. A 66, 032316.
  197. Gimeno-Segovia, Mercedes, 2016, “Towards practical linear optical quantum computing,” Ph.D. thesis (Imperial College London), 10.25560/43936.
  198. Gimeno-Segovia, Mercedes, Terry Rudolph, and Sophia E. Economou, 2019, “Deterministic Generation of Large-Scale Entangled Photonic Cluster State from Interacting Solid State Emitters,” Phys. Rev. Lett. 123, 070501.
  199. Giovannetti, Vittorio, Seth Lloyd, Lorenzo Maccone, and Peter W. Shor, 2003a, “Broadband channel capacities,” Phys. Rev. A 68, 062323.
  200. Giovannetti, Vittorio, Seth Lloyd, Lorenzo Maccone, and Peter W. Shor, 2003b, “Entanglement Assisted Capacity of the Broadband Lossy Channel,” Phys. Rev. Lett. 91, 047901.
  201. Gisin, Nicolas, Stefano Pironio, and Nicolas Sangouard, 2010, “Proposal for Implementing Device-Independent Quantum Key Distribution Based on a Heralded Qubit Amplifier,” Phys. Rev. Lett. 105, 070501.
  202. Giustina, Marissa, et al., 2013, “Bell violation using entangled photons without the fair-sampling assumption,” Nature (London) 497, 227–230.
  203. Google Quantum AI, 2023, “Suppressing quantum errors by scaling a surface code logical qubit,” Nature (London) 614, 676–681.
  204. Görlitz, Johannes, et al., 2020, “Spectroscopic investigations of negatively charged tin-vacancy centres in diamond,” New J. Phys. 22, 013048.
  205. Gottesman, Daniel, 1997, “Stabilizer codes and quantum error correction,” Ph.D. thesis (California Institute of Technology), 10.7907/rzr7-dt72.
  206. Gottesman, Daniel, 1999, “The Heisenberg representation of quantum computers,” in Group22: Proceedings of the XXII International Colloquium on Group Theoretical Methods in Physics, edited by S. P. Corney, R. Delbourgo, and P. D. Jarvis (International Press, Cambridge, MA), pp. 32–43.
  207. Gottesman, Daniel, and Isaac L. Chuang, 1999, “Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations,” Nature (London) 402, 390.
  208. Gottesman, Daniel, Thomas Jennewein, and Sarah Croke, 2012, “Longer-Baseline Telescopes Using Quantum Repeaters,” Phys. Rev. Lett. 109, 070503.
  209. Gottesman, Daniel, Alexei Kitaev, and John Preskill, 2001, “Encoding a qubit in an oscillator,” Phys. Rev. A 64, 012310.
  210. Greilich, A., A. Shabaev, D. R. Yakovlev, Al. L. Efros, I. A. Yugova, D. Reuter, A. D. Wieck, and M. Bayer, 2007, “Nuclei-induced frequency focusing of electron spin coherence,” Science 317, 1896–1899.
  211. Grice, W. P., 2011, “Arbitrarily complete Bell-state measurement using only linear optical elements,” Phys. Rev. A 84, 042331.
  212. Grosshans, Frederic, and Nicolas J. Cerf, 2004, “Continuous-Variable Quantum Cryptography Is Secure against Non-Gaussian Attacks,” Phys. Rev. Lett. 92, 047905.
  213. Guha, Saikat, 2011, “Structured Optical Receivers to Attain Superadditive Capacity and the Holevo Limit,” Phys. Rev. Lett. 106, 240502.
  214. Gündoğan, Mustafa, Jasminder S. Sidhu, Victoria Henderson, Luca Mazzarella, Janik Wolters, Daniel K. L. Oi, and Markus Krutzik, 2021, “Proposal for space-borne quantum memories for global quantum networking,” npj Quantum Inf. 7, 128.
  215. Gurudev Dutt, M. V., Jun Cheng, Yanwen Wu, Xiaodong Xu, D. G. Steel, A. S. Bracker, D. Gammon, Sophia E. Economou, Ren-Bao Liu, and L. J. Sham, 2006, “Ultrafast optical control of electron spin coherence in charged GaAs quantum dots,” Phys. Rev. B 74, 125306.
  216. Hadfield, R. H., 2009, “Single-photon detectors for optical quantum information applications,” Nat. Photonics 3, 696–705.
  217. Hasegawa, Yasushi, Rikizo Ikuta, Nobuyuki Matsuda, Kiyoshi Tamaki, Hoi-Kwong Lo, Takashi Yamamoto, Koji Azuma, and Nobuyuki Imoto, 2019, “Experimental time-reversed adaptive Bell measurement towards all-photonic quantum repeaters,” Nat. Commun. 10, 378.
  218. Hastings, Matthew B., 2009, “Superadditivity of communication capacity using entangled inputs,” Nat. Phys. 5, 255–257.
  219. Hein, M., J. Eisert, and H. J. Briegel, 2004, “Multiparty entanglement in graph states,” Phys. Rev. A 69, 062311.
  220. Hein, Marc, Wolfgang Dür, Jens Eisert, Robert Raussendorf, M. Nest, and H.-J. Briegel, 2006, “Entanglement in graph states and its applications,” in Quantum Computers, Algorithms and Chaos, edited by G. Casati, D. L. Shepelyansky, P. Zoller, and G. Benenti (IOS Press, Amsterdam), 10.3254/978-1-61499-018-5-115.
  221. Hensen, B., et al., 2015, “Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres,” Nature (London) 526, 682–686.
  222. Hermans, S. L. N., M. Pompili, H. K. C. Beukers, S. Baier, J. Borregaard, and R. Hanson, 2022, “Qubit teleportation between non-neighbouring nodes in a quantum network,” Nature (London) 605, 663–668.
  223. Herrera-Martí, David A., Austin G. Fowler, David Jennings, and Terry Rudolph, 2010, “Photonic implementation for the topological cluster-state quantum computer,” Phys. Rev. A 82, 032332.
  224. Heshami, Khabat, Duncan G. England, Peter C. Humphreys, Philip J. Bustard, Victor M. Acosta, Joshua Nunn, and Benjamin J. Sussman, 2016, “Quantum memories: Emerging applications and recent advances,” J. Mod. Opt. 63, 2005–2028.
  225. Higginbottom, Daniel B., et al., 2022, “Optical observation of single spins in silicon,” Nature (London) 607, 266–270.
  226. Hilaire, Paul, Edwin Barnes, and Sophia E. Economou, 2021, “Resource requirements for efficient quantum communication using all-photonic graph states generated from a few matter qubits,” Quantum 5, 397.
  227. Hilaire, Paul, Edwin Barnes, Sophia E. Economou, and Frédéric Grosshans, 2021, “Error-correcting entanglement swapping using a practical logical photon encoding,” Phys. Rev. A 104, 052623.
  228. Hilaire, Paul, Yaron Castor, Edwin Barnes, Sophia E. Economou, and Frédéric Grosshans, 2023, “Linear optical logical Bell state measurements with optimal loss-tolerance threshold,” PRX Quantum 4, 040322.
  229. Hilaire, Paul, Leonid Vidro, Hagai S. Eisenberg, and Sophia E. Economou, 2023, “Near-deterministic hybrid generation of arbitrary photonic graph states using a single quantum emitter and linear optics,” Quantum 7, 992.
  230. Hillery, Mark, Vladimír Bužek, and André Berthiaume, 1999, “Quantum secret sharing,” Phys. Rev. A 59, 1829.
  231. Horgan, John, 2016, “Is the gravitational-wave claim true? And was it worth the cost?,” https://blogs.scientificamerican.com/cross-check/is-the-gravitational-wave-claim-true-and-was-it-worth-the-cost.
  232. Horodecki, Karol, Michał Horodecki, Paweł Horodecki, and Jonathan Oppenheim, 2005, “Secure Key from Bound Entanglement,” Phys. Rev. Lett. 94, 160502.
  233. Horodecki, Michał, Paweł Horodecki, and Ryszard Horodecki, 1999, “General teleportation channel, singlet fraction, and quasidistillation,” Phys. Rev. A 60, 1888.
  234. Horodecki, Ryszard, Paweł Horodecki, Michał Horodecki, and Karol Horodecki, 2009, “Quantum entanglement,” Rev. Mod. Phys. 81, 865–942.
  235. Hosseini, Mahdi, Ben M. Sparkes, Geoff Campbell, Ping K. Lam, and Ben C. Buchler, 2011, “High efficiency coherent optical memory with warm rubidium vapour,” Nat. Commun. 2, 174.
  236. Howarth, Josh, 2021, “80+ amazing IoT statistics (2022–2030),” https://explodingtopics.com/blog/iot-stats.
  237. Hu, Peng, Hao Li, Lixing You, Heqing Wang, You Xiao, Jia Huang, Xiaoyan Yang, Weijun Zhang, Zhen Wang, and Xiaoming Xie, 2020, “Detecting single infrared photons toward optimal system detection efficiency,” Opt. Express 28, 36884–36891.
  238. Hu, Xiao-Min, et al., 2020, “Experimental High-Dimensional Quantum Teleportation,” Phys. Rev. Lett. 125, 230501.
  239. Hu, Xiao-Min, et al., 2021, “Long-Distance Entanglement Purification for Quantum Communication,” Phys. Rev. Lett. 126, 010503.
  240. Hucul, David, Ismail V. Inlek, Grahame Vittorini, Clayton Crocker, Shantanu Debnath, Susan M. Clark, and Christopher Monroe, 2015, “Modular entanglement of atomic qubits using photons and phonons,” Nat. Phys. 11, 37–42.
  241. Humphreys, Peter C., Norbert Kalb, Jaco P. J. Morits, Raymond N. Schouten, Raymond F. L. Vermeulen, Daniel J. Twitchen, Matthew Markham, and Ronald Hanson, 2018, “Deterministic delivery of remote entanglement on a quantum network,” Nature (London) 558, 268–273.
  242. Hwang, Won-Young, 2003, “Quantum Key Distribution with High Loss: Toward Global Secure Communication,” Phys. Rev. Lett. 91, 057901.
  243. Ikuta, Rikizo, Yoshiaki Kusaka, Tsuyoshi Kitano, Hiroshi Kato, Takashi Yamamoto, Masato Koashi, and Nobuyuki Imoto, 2011, “Wide-band quantum interface for visible-to-telecommunication wavelength conversion,” Nat. Commun. 2, 537.
  244. Ikuta, Rikizo, et al., 2018, “Polarization insensitive frequency conversion for an atom-photon entanglement distribution via a telecom network,” Nat. Commun. 9, 1997.
  245. Illiano, Jessica, Marcello Caleffi, Antonio Manzalini, and Angela Sara Cacciapuoti, 2022, “Quantum internet protocol stack: A comprehensive survey,” Comput. Networks 213, 109092.
  246. Imoto, N., H. A. Haus, and Y. Yamamoto, 1985, “Quantum nondemolition measurement of the photon number via the optical Kerr effect,” Phys. Rev. A 32, 2287.
  247. Inlek, Ismail Volkan, Clayton Crocker, Martin Lichtman, Ksenia Sosnova, and Christopher Monroe, 2017, “Multispecies Trapped-Ion Node for Quantum Networking,” Phys. Rev. Lett. 118, 250502.
  248. Inoue, Kyo, Edo Waks, and Yoshihisa Yamamoto, 2002, “Differential Phase Shift Quantum Key Distribution,” Phys. Rev. Lett. 89, 037902.
  249. Iwasaki, Takayuki, et al., 2015, “Germanium-vacancy single color centers in diamond,” Sci. Rep. 5, 12882.
  250. Jackson, Daniel M., Dorian A. Gangloff, Jonathan H. Bodey, Leon Zaporski, Clara Bachorz, Edmund Clarke, Maxime Hugues, Claire Le Gall, and Mete Atatüre, 2021, “Quantum sensing of a coherent single spin excitation in a nuclear ensemble,” Nat. Phys. 17, 585–590.
  251. Jacobs, B. C., T. B. Pittman, and J. D. Franson, 2002, “Quantum relays and noise suppression using linear optics,” Phys. Rev. A 66, 052307.
  252. Javadi, Alisa, et al., 2018, “Spin-photon interface and spin-controlled photon switching in a nanobeam waveguide,” Nat. Nanotechnol. 13, 398–403.
  253. Ji, Jia-Wei, Yu-Feng Wu, Stephen C. Wein, Faezeh Kimiaee Asadi, Roohollah Ghobadi, and Christoph Simon, 2022, “Proposal for room-temperature quantum repeaters with nitrogen-vacancy centers and optomechanics,” Quantum 6, 669.
  254. Jiang, Cong, Zong-Wen Yu, Xiao-Long Hu, and Xiang-Bin Wang, 2019, “Unconditional Security of Sending or Not Sending Twin-Field Quantum Key Distribution with Finite Pulses,” Phys. Rev. Appl. 12, 024061.
  255. Jiang, L., J. M. Taylor, N. Khaneja, and M. D. Lukin, 2007, “Optimal approach to quantum communication algorithms using dynamic programming,” Proc. Natl. Acad. Sci. U.S.A. 104, 17291–17296.
  256. Jiang, Liang, J. M. Taylor, Kae Nemoto, W. J. Munro, Rodney Van Meter, and M. D. Lukin, 2009, “Quantum repeater with encoding,” Phys. Rev. A 79, 032325.
  257. Jiang, Liang, Jacob M. Taylor, Anders S. Sørensen, and Mikhail D. Lukin, 2007, “Distributed quantum computation based on small quantum registers,” Phys. Rev. A 76, 062323.
  258. Joo, Jaewoo, Peter L. Knight, Jeremy L. O’Brien, and Terry Rudolph, 2007, “One-way quantum computation with four-dimensional photonic qudits,” Phys. Rev. A 76, 052326.
  259. Jozsa, Richard, 1994, “Fidelity for mixed quantum states,” J. Mod. Opt. 41, 2315–2323.
  260. Jozsa, Richard, Daniel S. Abrams, Jonathan P. Dowling, and Colin P. Williams, 2000, “Quantum Clock Synchronization Based on Shared Prior Entanglement,” Phys. Rev. Lett. 85, 2010–2013.
  261. Jungnickel, Dieter, 2005, Graphs, Networks and Algorithms (Springer, New York).
  262. Kalb, Norbert, Andreas A. Reiserer, Peter C. Humphreys, Jacob J. W. Bakermans, Sten J. Kamerling, Naomi H. Nickerson, Simon C. Benjamin, Daniel J. Twitchen, Matthew Markham, and Ronald Hanson, 2017, “Entanglement distillation between solid-state quantum network nodes,” Science 356, 928–932.
  263. Kaneda, Fumihiro, and Paul G. Kwiat, 2019, “High-efficiency single-photon generation via large-scale active time multiplexing,” Sci. Adv. 5, eaaw8586.
  264. Katz, Or, and Ofer Firstenberg, 2018, “Light storage for one second in room-temperature alkali vapor,” Nat. Commun. 9, 2074.
  265. Kent, Adrian, 2011, “Unconditionally secure bit commitment with flying qudits,” New J. Phys. 13, 113015.
  266. Kent, Adrian, William J. Munro, and Timothy P. Spiller, 2011, “Quantum tagging: Authenticating location via quantum information and relativistic signaling constraints,” Phys. Rev. A 84, 012326.
  267. Khabiboulline, Emil T., Johannes Borregaard, Kristiaan De Greve, and Mikhail D. Lukin, 2019, “Optical Interferometry with Quantum Networks,” Phys. Rev. Lett. 123, 070504.
  268. Khatri, Sumeet, Anthony J. Brady, Renée A Desporte, Manon P. Bart, and Jonathan P. Dowling, 2021, “Spooky action at a global distance: Analysis of space-based entanglement distribution for the quantum internet,” npj Quantum Inf. 7, 4.
  269. Khatri, Sumeet, and Mark M. Wilde, 2020, “Principles of quantum communication theory: A modern approach,” arXiv:2011.04672.
  270. Kilmer, Thomas, and Saikat Guha, 2019, “Boosting linear-optical Bell measurement success probability with predetection squeezing and imperfect photon-number-resolving detectors,” Phys. Rev. A 99, 032302.
  271. Kimble, H. J., 2008, “The quantum internet,” Nature (London) 453, 1023–1030.
  272. Kimiaee Asadi, F, N. Lauk, S. Wein, N. Sinclair, C. O’Brien, and C. Simon, 2018, “Quantum repeaters with individual rare-earth ions at telecommunication wavelengths,” Quantum 2, 93.
  273. Knill, E., R. Laflamme, and G. J. Milburn, 2001, “A scheme for efficient quantum computation with linear optics,” Nature (London) 409, 46–52.
  274. Knill, Emanuel, and Raymond Laflamme, 1996, “Concatenated quantum codes,” arXiv:quant-ph/9608012.
  275. Knill, Emanuel, and Raymond Laflamme, 1997, “Theory of quantum error-correcting codes,” Phys. Rev. A 55, 900.
  276. Koashi, M., 2009, “Simple security proof of quantum key distribution based on complementarity,” New J. Phys. 11, 045018.
  277. Koashi, Masato, and Nobuyuki Imoto, 1998, “No-Cloning Theorem of Entangled States,” Phys. Rev. Lett. 81, 4264–4267.
  278. Koashi, Masato, and Nobuyuki Imoto, 2002, “Operations that do not disturb partially known quantum states,” Phys. Rev. A 66, 022318.
  279. Kok, Pieter, W. J. Munro, Kae Nemoto, T. C. Ralph, Jonathan P. Dowling, and G. J. Milburn, 2007, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135–174.
  280. Kok, Pieter, Colin P. Williams, and Jonathan P. Dowling, 2003, “Construction of a quantum repeater with linear optics,” Phys. Rev. A 68, 022301.
  281. Komar, Peter, Eric M. Kessler, Michael Bishof, Liang Jiang, Anders S Sørensen, Jun Ye, and Mikhail D. Lukin, 2014, “A quantum network of clocks,” Nat. Phys. 10, 582–587.
  282. Konig, Robert, Stephanie Wehner, and Jürg Wullschleger, 2012, “Unconditional security from noisy quantum storage,” IEEE Trans. Inf. Theory 58, 1962–1984.
  283. Konno, Shunya, et al., 2023, “Propagating Gottesman-Kitaev-Preskill states encoded in an optical oscillator,” arXiv:2309.02306.
  284. Kozlowski, Wojciech, Axel Dahlberg, and Stephanie Wehner, 2020, “Designing a quantum network protocol,” in Proceedings of the 16th International Conference on Emerging Networking Experiments and Technologies, Barcelona, 2020 (Association for Computing Machinery, New York), pp. 1–16, 10.1145/3386367.3431293.
  285. Kozlowski, Wojciech, Stephanie Wehner, R. V. Meter, Bruno Rijsman, Angela Sara Cacciapuoti, Marcello Caleffi, and Shota Nagayama, 2020, “Architectural principles for a quantum internet,” 10.17487/RFC9340.
  286. Krastanov, Stefan, Victor V. Albert, and Liang Jiang, 2019, “Optimized entanglement purification,” Quantum 3, 123.
  287. Krutyanskiy, V., M. Meraner, J. Schupp, V. Krcmarsky, H. Hainzer, and B. P. Lanyon, 2019, “Light-matter entanglement over 50 km of optical fibre,” npj Quantum Inf. 5, 72.
  288. Krutyanskiy, Victor, Marco Canteri, Martin Meraner, James Bate, Vojtech Krcmarsky, Josef Schupp, Nicolas Sangouard, and Ben P. Lanyon, 2023, “Telecom-Wavelength Quantum Repeater Node Based on a Trapped-Ion Processor,” Phys. Rev. Lett. 130, 213601.
  289. Kwiat, P. G., 1997, “Hyper-entangled states,” J. Mod. Opt. 44, 2173.
  290. Lago-Rivera, Dario, Samuele Grandi, Jelena V. Rakonjac, Alessandro Seri, and Hugues de Riedmatten, 2021, “Telecom-heralded entanglement between multimode solid-state quantum memories,” Nature (London) 594, 37–40.
  291. Langenfeld, Stefan, Olivier Morin, Matthias Körber, and Gerhard Rempe, 2020, “A network-ready random-access qubits memory,” npj Quantum Inf. 6, 86.
  292. Langenfeld, Stefan, Philip Thomas, Olivier Morin, and Gerhard Rempe, 2021, “Quantum Repeater Node Demonstrating Unconditionally Secure Key Distribution,” Phys. Rev. Lett. 126, 230506.
  293. Lau, Hoi-Kwan, and Hoi-Kwong Lo, 2011, “Insecurity of position-based quantum-cryptography protocols against entanglement attacks,” Phys. Rev. A 83, 012322.
  294. Lauk, Nikolai, Neil Sinclair, Shabir Barzanjeh, Jacob P. Covey, Mark Saffman, Maria Spiropulu, and Christoph Simon, 2020, “Perspectives on quantum transduction,” Quantum Sci. Technol. 5, 020501.
  295. Laurenza, Riccardo, and Stefano Pirandola, 2017, “General bounds for sender-receiver capacities in multipoint quantum communications,” Phys. Rev. A 96, 032318.
  296. Lee, J. P., B. Villa, A. J. Bennett, R. M. Stevenson, D. J. P. Ellis, I. Farrer, D. A. Ritchie, and A. J. Shields, 2019, “A quantum dot as a source of time-bin entangled multi-photon states,” Quantum Sci. Technol. 4, 025011.
  297. Lee, J. P., L. M. Wells, B. Villa, S. Kalliakos, R. M. Stevenson, D. J. P. Ellis, I. Farrer, D. A. Ritchie, A. J. Bennett, and A. J. Shields, 2018, “Controllable Photonic Time-Bin Qubits from a Quantum dot,” Phys. Rev. X 8, 021078.
  298. Lee, Seung-Woo, Timothy C. Ralph, and Hyunseok Jeong, 2019, “Fundamental building block for all-optical scalable quantum networks,” Phys. Rev. A 100, 052303.
  299. Le Gall, François, Harumichi Nishimura, and Ansis Rosmanis, 2019, “Quantum advantage for the LOCAL model in distributed computing,” in Proceedings of the 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019), Berlin, 2019, edited by Rolf Niedermeier and Christophe Paul (Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, Wadern, Germany), 10.4230/LIPIcs.STACS.2019.49.
  300. Leghtas, Z., G. Kirchmair, B. Vlastakis, R. Schoelkopf, M. Devoret, and M. Mirrahimi, 2013, “Hardware-Efficient Autonomous Quantum Error Correction,” Phys. Rev. Lett. 111, 120501.
  301. Leon-Garcia, Alberto, and Martha Steenstrup, 2021, “The need for holistic network design,” IEEE Commun. Mag. 59, 4–5.
  302. Leung, Patrick M., and Timothy C. Ralph, 2006, “Quantum memory scheme based on optical fibers and cavities,” Phys. Rev. A 74, 022311.
  303. Levine, Harry, et al., 2019, “Parallel Implementation of High-Fidelity Multiqubit Gates with Neutral Atoms,” Phys. Rev. Lett. 123, 170503.
  304. Li, Bikun, Sophia E. Economou, and Edwin Barnes, 2022, “Photonic resource state generation from a minimal number of quantum emitters,” npj Quantum Inf. 8, 11.
  305. Li, Hang, Jian-Peng Dou, Xiao-Ling Pang, Tian-Huai Yang, Chao-Ni Zhang, Yuan Chen, Jia-Ming Li, Ian A. Walmsley, and Xian-Min Jin, 2021, “Heralding quantum entanglement between two room-temperature atomic ensembles,” Optica 8, 925–929.
  306. Li, Linshu, Chang-Ling Zou, Victor V. Albert, Sreraman Muralidharan, S. M. Girvin, and Liang Jiang, 2017, “Cat Codes with Optimal Decoherence Suppression for a Lossy Bosonic Channel,” Phys. Rev. Lett. 119, 030502.
  307. Li, Wei, et al., 2023, “Twin-Field Quantum Key Distribution without Phase Locking,” Phys. Rev. Lett. 130, 250802.
  308. Li, Ying, Sean D. Barrett, Thomas M. Stace, and Simon C. Benjamin, 2013, “Long range failure-tolerant entanglement distribution,” New J. Phys. 15, 023012.
  309. Li, Ying, Peter C. Humphreys, Gabriel J. Mendoza, and Simon C. Benjamin, 2015, “Resource Costs for Fault-Tolerant Linear Optical Quantum Computing,” Phys. Rev. X 5, 041007.
  310. Li, Zheng-Da, et al., 2019, “Experimental quantum repeater without quantum memory,” Nat. Photonics 13, 644–648.
  311. Li, Zhuo, Li-Juan Xing, and Xin-Mei Wang, 2008, “Quantum generalized Reed-Solomon codes: Unified framework for quantum maximum-distance-separable codes,” Phys. Rev. A 77, 012308.
  312. Liao, Sheng-Kai, et al., 2017, “Satellite-to-ground quantum key distribution,” Nature (London) 549, 43.
  313. Liao, Sheng-Kai, et al., 2018, “Satellite-Relayed Intercontinental Quantum Network,” Phys. Rev. Lett. 120, 030501.
  314. Lidar, Daniel A., and Todd A. Brun, 2013, Eds., Quantum Error Correction (Cambridge University Press, Cambridge, England).
  315. Lin, Jie, and Norbert Lütkenhaus, 2018, “Simple security analysis of phase-matching measurement-device-independent quantum key distribution,” Phys. Rev. A 98, 042332.
  316. Lindner, Netanel H., and Terry Rudolph, 2009, “Proposal for Pulsed On-Demand Sources of Photonic Cluster State Strings,” Phys. Rev. Lett. 103, 113602.
  317. Liorni, Carlo, Hermann Kampermann, and Dagmar Bruß, 2021, “Quantum repeaters in space,” New J. Phys. 23, 053021.
  318. Lita, Adriana E., Aaron J. Miller, and Sae Woo Nam, 2008, “Counting near-infrared single-photons with 95% efficiency,” Opt. Express 16, 3032–3040.
  319. Liu, Xiao, Jun Hu, Zong-Feng Li, Xue Li, Pei-Yun Li, Peng-Jun Liang, Zong-Quan Zhou, Chuan-Feng Li, and Guang-Can Guo, 2021, “Heralded entanglement distribution between two absorptive quantum memories,” Nature (London) 594, 41–45.
  320. Lo, Hoi-Kwong, 1997, “Insecurity of quantum secure computations,” Phys. Rev. A 56, 1154.
  321. Lo, Hoi-Kwong, 2000, “Classical-communication cost in distributed quantum-information processing: A generalization of quantum-communication complexity,” Phys. Rev. A 62, 012313.
  322. Lo, Hoi-Kwong, and H. F. Chau, 1999, “Unconditional security of quantum key distribution over arbitrarily long distances,” Science 283, 2050–2056.
  323. Lo, Hoi-Kwong, and Hoi Fung Chau, 1997, “Is Quantum Bit Commitment Really Possible?,” Phys. Rev. Lett. 78, 3410.
  324. Lo, Hoi-Kwong, and Hoi Fung Chau, 1998, “Why quantum bit commitment and ideal quantum coin tossing are impossible,” Physica (Amsterdam) 120D, 177–187.
  325. Lo, Hoi-Kwong, Marcos Curty, and Bing Qi, 2012, “Measurement-Device-Independent Quantum Key Distribution,” Phys. Rev. Lett. 108, 130503.
  326. Lo, Hoi-Kwong, Marcos Curty, and Kiyoshi Tamaki, 2014, “Secure quantum key distribution,” Nat. Photonics 8, 595–604.
  327. Lo, Hoi-Kwong, Xiongfeng Ma, and Kai Chen, 2005, “Decoy State Quantum Key Distribution,” Phys. Rev. Lett. 94, 230504.
  328. Lucamarini, M., Z. L. Yuan, J. F. Dynes, and A. J. Shields, 2018, “Overcoming the rate-distance limit of quantum key distribution without quantum repeaters,” Nature (London) 557, 400–403.
  329. Lukin, Daniil M., Melissa A. Guidry, and Jelena Vučković, 2020, “Integrated quantum photonics with silicon carbide: Challenges and prospects,” PRX Quantum 1, 020102.
  330. Luo, Yi-Han, et al., 2019, “Quantum Teleportation in High Dimensions,” Phys. Rev. Lett. 123, 070505.
  331. Luong, David, Liang Jiang, Jungsang Kim, and Norbert Lütkenhaus, 2016, “Overcoming lossy channel bounds using a single quantum repeater node,” Appl. Phys. B 122, 96.
  332. Lütkenhaus, N., J. Calsamiglia, and K.-A. Suominen, 1999, “Bell measurements for teleportation,” Phys. Rev. A 59, 3295.
  333. Lvovsky, Alexander I., Barry C. Sanders, and Wolfgang Tittel, 2009, “Optical quantum memory,” Nat. Photonics 3, 706–714.
  334. Ma, Xiao-song, Stefan Zotter, Johannes Kofler, Thomas Jennewein, and Anton Zeilinger, 2011, “Experimental generation of single photons via active multiplexing,” Phys. Rev. A 83, 043814.
  335. Ma, Xiongfeng, and Mohsen Razavi, 2012, “Alternative schemes for measurement-device-independent quantum key distribution,” Phys. Rev. A 86, 062319.
  336. Ma, Xiongfeng, Pei Zeng, and Hongyi Zhou, 2018, “Phase-Matching Quantum Key Distribution,” Phys. Rev. X 8, 031043.
  337. Ma, Yu, You-Zhi Ma, Zong-Quan Zhou, Chuan-Feng Li, and Guang-Can Guo, 2021, “One-hour coherent optical storage in an atomic frequency comb memory,” Nat. Commun. 12, 2381.
  338. Maeda, Kento, Toshihiko Sasaki, and Masato Koashi, 2019, “Repeaterless quantum key distribution with efficient finite-key analysis overcoming the rate-distance limit,” Nat. Commun. 10, 3140.
  339. Maiwald, Robert, Andrea Golla, Martin Fischer, Marianne Bader, Simon Heugel, Benoît Chalopin, Markus Sondermann, and Gerd Leuchs, 2012, “Collecting more than half the fluorescence photons from a single ion,” Phys. Rev. A 86, 043431.
  340. Maring, Nicolas, Pau Farrera, Kutlu Kutluer, Margherita Mazzera, Georg Heinze, and Hugues de Riedmatten, 2017, “Photonic quantum state transfer between a cold atomic gas and a crystal,” Nature (London) 551, 485–488.
  341. Marsili, F., et al., 2013, “Detecting single infrared photons with 93% system efficiency,” Nat. Photonics 7, 210–214.
  342. Martin, Leigh S., and K. Birgitta Whaley, 2019, “Single-shot deterministic entanglement between non-interacting systems with linear optics,” arXiv:1912.00067.
  343. Matsuo, Takaaki, Clément Durand, and Rodney Van Meter, 2019, “Quantum link bootstrapping using a RuleSet-based communication protocol,” Phys. Rev. A 100, 052320.
  344. Matthiesen, Clemens, Martin Geller, Carsten H. H. Schulte, Claire Le Gall, Jack Hansom, Zhengyong Li, Maxime Hugues, Edmund Clarke, and Mete Atatüre, 2013, “Phase-locked indistinguishable photons with synthesized waveforms from a solid-state source,” Nat. Commun. 4, 1600.
  345. Mayers, Dominic, 1997, “Unconditionally Secure Quantum Bit Commitment Is Impossible,” Phys. Rev. Lett. 78, 3414.
  346. Mayers, Dominic, 2001, “Unconditional security in quantum cryptography,” J. Assoc. Comput. Mach. 48, 351–406.
  347. Mayers, Dominic, and Andrew Yao, 1998, “Quantum cryptography with imperfect apparatus,” in Proceedings of the 39th Annual Symposium on Foundations of Computer Science (Cat. No. 98CB36280), Palo Alto, 1998 (IEEE, New York), pp. 503–509, 10.1109/SFCS.1998.743501.
  348. Mazurek, Paweł, Andrzej Grudka, Michał Horodecki, Paweł Horodecki, Justyna Łodyga, Łukasz Pankowski, and Anna Przysiężna, 2014, “Long-distance quantum communication over noisy networks without long-time quantum memory,” Phys. Rev. A 90, 062311.
  349. McGuinness, Hayden J., Michael G. Raymer, Colin J. McKinstrie, and Stojan Radic, 2010, “Quantum Frequency Translation of Single-Photon States in a Photonic Crystal Fiber,” Phys. Rev. Lett. 105, 093604.
  350. Menicucci, Nicolas C., Peter van Loock, Mile Gu, Christian Weedbrook, Timothy C. Ralph, and Michael A. Nielsen, 2006, “Universal Quantum Computation with Continuous-Variable Cluster States,” Phys. Rev. Lett. 97, 110501.
  351. Michael, Marios H., Matti Silveri, R. T. Brierley, Victor V. Albert, Juha Salmilehto, Liang Jiang, and S. M. Girvin, 2016, “New Class of Quantum Error-Correcting Codes for a Bosonic Mode,” Phys. Rev. X 6, 031006.
  352. Migdall, Alan L., D. Branning, and Stefania Castelletto, 2002, “Tailoring single-photon and multiphoton probabilities of a single-photon on-demand source,” Phys. Rev. A 66, 053805.
  353. Miller, Johanna L., 2016, “Three groups close the loopholes in tests of Bell’s theorem,” Phys. Today 69, No. 1, 14–16.
  354. Minder, M., M. Pittaluga, G. L. Roberts, M. Lucamarini, J. F. Dynes, Z. L. Yuan, and A. J. Shields, 2019, “Experimental quantum key distribution beyond the repeaterless secret key capacity,” Nat. Photonics 13, 334–338.
  355. Mirhosseini, Mohammad, Alp Sipahigil, Mahmoud Kalaee, and Oskar Painter, 2020, “Superconducting qubit to optical photon transduction,” Nature (London) 588, 599–603.
  356. Mirrahimi, M., Z. Leghtas, Victor V. Albert, S. Touzard, R. Schoelkopf, L. Jiang, and M. Devoret, 2014, “Dynamically protected cat-qubits: A new paradigm for universal quantum computation,” New J. Phys. 16, 045014.
  357. Mochon, Carlos, 2007, “Quantum weak coin flipping with arbitrarily small bias,” arXiv:0711.4114.
  358. Moehring, David L., Peter Maunz, Steve Olmschenk, Kelly C. Younge, Dzmitry N. Matsukevich, L.-M. Duan, and Christopher Monroe, 2007, “Entanglement of single-atom quantum bits at a distance,” Nature (London) 449, 68–71.
  359. Munro, W. J., K. A. Harrison, A. M. Stephens, S. J. Devitt, and Kae Nemoto, 2010, “From quantum multiplexing to high-performance quantum networking,” Nat. Photonics 4, 792–796.
  360. Munro, W. J., A. M. Stephens, S. J. Devitt, K. A. Harrison, and Kae Nemoto, 2012, “Quantum communication without the necessity of quantum memories,” Nat. Photonics 6, 777–781.
  361. Munro, W. J., R. Van Meter, Sebastien G. R. Louis, and Kae Nemoto, 2008, “High-Bandwidth Hybrid Quantum Repeater,” Phys. Rev. Lett. 101, 040502.
  362. Munro, William J., Koji Azuma, Kiyoshi Tamaki, and Kae Nemoto, 2015, “Inside quantum repeaters,” IEEE J. Sel. Top. Quantum Electron. 21, 78–90.
  363. Munro, William J., Nicolo’ Lo Piparo, Josephine Dias, Michael Hanks, and Kae Nemoto, 2022, “Designing tomorrow’s quantum internet,” AVS Quantum Sci. 4, 020503.
  364. Muralidharan, Sreraman, Jungsang Kim, Norbert Lütkenhaus, Mikhail D. Lukin, and Liang Jiang, 2014, “Ultrafast and Fault-Tolerant Quantum Communication across Long Distances,” Phys. Rev. Lett. 112, 250501.
  365. Muralidharan, Sreraman, Linshu Li, Jungsang Kim, Norbert Lütkenhaus, Mikhail D. Lukin, and Liang Jiang, 2016, “Optimal architectures for long distance quantum communication,” Sci. Rep. 6, 20463.
  366. Muralidharan, Sreraman, Chang-Ling Zou, Linshu Li, and Liang Jiang, 2018, “One-way quantum repeaters with quantum Reed-Solomon codes,” Phys. Rev. A 97, 052316.
  367. Muralidharan, Sreraman, Chang-Ling Zou, Linshu Li, Jianming Wen, and Liang Jiang, 2017, “Overcoming erasure errors with multilevel systems,” New J. Phys. 19, 013026.
  368. Murta, Gláucia, Federico Grasselli, Hermann Kampermann, and Dagmar Bruß, 2020, “Quantum conference key agreement: A review,” Adv. Quantum Technol. 3, 2000025.
  369. Nadlinger, D. P., et al., 2022, “Experimental quantum key distribution certified by Bell’s theorem,” Nature (London) 607, 682–686.
  370. Neu, Elke, Martin Fischer, Stefan Gsell, Matthias Schreck, and Christoph Becher, 2011, “Fluorescence and polarization spectroscopy of single silicon vacancy centers in heteroepitaxial nanodiamonds on iridium,” Phys. Rev. B 84, 205211.
  371. Neu, Elke, David Steinmetz, Janine Riedrich-Möller, Stefan Gsell, Martin Fischer, Matthias Schreck, and Christoph Becher, 2011, “Single photon emission from silicon-vacancy colour centres in chemical vapour deposition nano-diamonds on iridium,” New J. Phys. 13, 025012.
  372. Nguyen, C. T., et al., 2019a, “An integrated nanophotonic quantum register based on silicon-vacancy spins in diamond,” Phys. Rev. B 100, 165428.
  373. Nguyen, C. T., et al., 2019b, “Quantum Network Nodes Based on Diamond Qubits with an Efficient Nanophotonic Interface,” Phys. Rev. Lett. 123, 183602.
  374. Nickerson, Naomi H., Joseph F. Fitzsimons, and Simon C. Benjamin, 2014, “Freely Scalable Quantum Technologies Using Cells of 5-to-50 Qubits with Very Lossy and Noisy Photonic Links,” Phys. Rev. X 4, 041041.
  375. Nickerson, Naomi H., Ying Li, and Simon C. Benjamin, 2013, “Topological quantum computing with a very noisy network and local error rates approaching one percent,” Nat. Commun. 4, 1756.
  376. Nielsen, Michael A., 2004, “Optical Quantum Computation Using Cluster States,” Phys. Rev. Lett. 93, 040503.
  377. Nielsen, Michael A., and Isaac L. Chuang, 2010, Quantum Computation and Quantum Information: 10th Anniversary Edition (Cambridge University Press, Cambridge, England).
  378. Niset, Julien, Jaromír Fiurášek, and Nicolas J. Cerf, 2009, “No-Go Theorem for Gaussian Quantum Error Correction,” Phys. Rev. Lett. 102, 120501.
  379. NIST, 2021, “Post-quantum cryptography,” https://csrc.nist.gov/projects/post-quantum-cryptography.
  380. Niu, Daoheng, Yuxuan Zhang, Alireza Shabani, and Hassan Shapourian, 2023, “All-photonic one-way quantum repeaters with measurement-based error correction,” npj Quantum Inf. 9, 106.
  381. Noh, Kyungjoo, Victor V. Albert, and Liang Jiang, 2019, “Quantum capacity bounds of Gaussian thermal loss channels and achievable rates with Gottesman-Kitaev-Preskill codes,” IEEE Trans. Inf. Theory 65, 2563–2582.
  382. Noh, Kyungjoo, and Christopher Chamberland, 2020, “Fault-tolerant bosonic quantum error correction with the surface–Gottesman-Kitaev-Preskill code,” Phys. Rev. A 101, 012316.
  383. Noh, Kyungjoo, S. M. Girvin, and Liang Jiang, 2020, “Encoding an Oscillator into Many Oscillators,” Phys. Rev. Lett. 125, 080503.
  384. Olbrich, Fabian, Jonatan Höschele, Markus Müller, Jan Kettler, Simone Luca Portalupi, Matthias Paul, Michael Jetter, and Peter Michler, 2017, “Polarization-entangled photons from an InGaAs-based quantum dot emitting in the telecom C-band,” Appl. Phys. Lett. 111, 133106.
  385. Palyanov, Yuri N., Igor N. Kupriyanov, Yuri M. Borzdov, and Nikolay V. Surovtsev, 2015, “Germanium: A new catalyst for diamond synthesis and a new optically active impurity in diamond,” Sci. Rep. 5, 14789.
  386. Pan, Jian-Wei, Dik Bouwmeester, Harald Weinfurter, and Anton Zeilinger, 1998, “Experimental Entanglement Swapping: Entangling Photons That Never Interacted,” Phys. Rev. Lett. 80, 3891–3894.
  387. Pan, Jian-Wei, Sara Gasparoni, Rupert Ursin, Gregor Weihs, and Anton Zeilinger, 2003, “Experimental entanglement purification of arbitrary unknown states,” Nature (London) 423, 417–422.
  388. Pan, Jian-Wei, Christoph Simon, Časlav Brukner, and Anton Zeilinger, 2001, “Entanglement purification for quantum communication,” Nature (London) 410, 1067.
  389. Panayi, Christiana, Mohsen Razavi, Xiongfeng Ma, and Norbert Lütkenhaus, 2014, “Memory-assisted measurement-device-independent quantum key distribution,” New J. Phys. 16, 043005.
  390. Pang, Xiao-Ling, et al., 2020, “A hybrid quantum memory–enabled network at room temperature,” Sci. Adv. 6, eaax1425.
  391. Pant, Mihir, Hari Krovi, Dirk Englund, and Saikat Guha, 2017, “Rate-distance tradeoff and resource costs for all-optical quantum repeaters,” Phys. Rev. A 95, 012304.
  392. Park, Jiho, Heonoh Kim, and Han Seb Moon, 2019, “Polarization-Entangled Photons from a Warm Atomic Ensemble Using a Sagnac Interferometer,” Phys. Rev. Lett. 122, 143601.
  393. Peev, Momtchil, et al., 2009, “The SECOQC quantum key distribution network in Vienna,” New J. Phys. 11, 075001.
  394. Pegg, David T., Lee S. Phillips, and Stephen M. Barnett, 1998, “Optical State Truncation by Projection Synthesis,” Phys. Rev. Lett. 81, 1604–1606.
  395. Pichler, Hannes, Soonwon Choi, Peter Zoller, and Mikhail D. Lukin, 2017, “Universal photonic quantum computation via time-delayed feedback,” Proc. Natl. Acad. Sci. U.S.A. 114, 11362–11367.
  396. Pingault, Benjamin, David-Dominik Jarausch, Christian Hepp, Lina Klintberg, Jonas N. Becker, Matthew Markham, Christoph Becher, and Mete Atatüre, 2017, “Coherent control of the silicon-vacancy spin in diamond,” Nat. Commun. 8, 15579.
  397. Piparo, Nicoló Lo, Mohsen Razavi, and William J. Munro, 2017a, “Measurement-device-independent quantum key distribution with nitrogen vacancy centers in diamond,” Phys. Rev. A 95, 022338.
  398. Piparo, Nicoló Lo, Mohsen Razavi, and William J. Munro, 2017b, “Memory-assisted quantum key distribution with a single nitrogen-vacancy center,” Phys. Rev. A 96, 052313.
  399. Piparo, Nicoló Lo, Mohsen Razavi, and Christiana Panayi, 2015, “Measurement-device-independent quantum key distribution with ensemble-based memories,” IEEE J. Sel. Top. Quantum Electron. 21, 138–147.
  400. Pirandola, S., et al., 2020, “Advances in quantum cryptography,” Adv. Opt. Photonics 12, 1012–1236.
  401. Pirandola, Stefano, 2016, “Capacities of repeater-assisted quantum communications,” arXiv:1601.00966.
  402. Pirandola, Stefano, 2019, “End-to-end capacities of a quantum communication network,” Commun. Phys. 2, 51.
  403. Pirandola, Stefano, Riccardo Laurenza, Carlo Ottaviani, and Leonardo Banchi, 2017, “Fundamental limits of repeaterless quantum communications,” Nat. Commun. 8, 15043.
  404. Pirker, Alexander, and Wolfgang Dür, 2019, “A quantum network stack and protocols for reliable entanglement-based networks,” New J. Phys. 21, 033003.
  405. Pittaluga, Mirko, Mariella Minder, Marco Lucamarini, Mirko Sanzaro, Robert I. Woodward, Ming-Jun Li, Zhiliang Yuan, and Andrew J. Shields, 2021, “600-km repeater-like quantum communications with dual-band stabilization,” Nat. Photonics 15, 530–535.
  406. Pittman, T. B., B. C. Jacobs, and J. D. Franson, 2001, “Probabilistic quantum logic operations using polarizing beam splitters,” Phys. Rev. A 64, 062311.
  407. Plenio, Martin B., and Shashank Virmani, 2007, “An introduction to entanglement measures,” Quantum Inf. Comput. 7, 1–51.
  408. Pompili, M., et al., 2021, “Realization of a multinode quantum network of remote solid-state qubits,” Science 372, 259–264.
  409. Pompili, Matteo, et al., 2022, “Experimental demonstration of entanglement delivery using a quantum network stack,” npj Quantum Inf. 8, 121.
  410. Portmann, Christopher, and Renato Renner, 2022, “Security in quantum cryptography,” Rev. Mod. Phys. 94, 025008.
  411. Pu, Yun-Fei, Sheng Zhang, Yu-Kai Wu, Nan Jiang, Wei Chang, Chang Li, and Lu-Ming Duan, 2021, “Experimental demonstration of memory-enhanced scaling for entanglement connection of quantum repeater segments,” Nat. Photonics 15, 374–378.
  412. Quantum Protocol Zoo, 2019, https://wiki.veriqloud.fr.
  413. Quesada, N., L. G. Helt, J. Izaac, J. M. Arrazola, R. Shahrokhshahi, C. R. Myers, and K. K. Sabapathy, 2019, “Simulating realistic non-Gaussian state preparation,” Phys. Rev. A 100, 022341.
  414. Ralph, T. C., A. J. F. Hayes, and A. Gilchrist, 2005, “Loss-Tolerant Optical Qubits,” Phys. Rev. Lett. 95, 100501.
  415. Ralph, Timothy C., and A. P. Lund, 2009, “Nondeterministic noiseless linear amplification of quantum systems,” AIP Conf. Proc. 1110, 155–160.
  416. Rančić, Miloš, Morgan P. Hedges, Rose L. Ahlefeldt, and Matthew J. Sellars, 2018, “Coherence time of over a second in a telecom-compatible quantum memory storage material,” Nat. Phys. 14, 50–54.
  417. Raussendorf, R., J. Harrington, and K. Goyal, 2006, “A fault-tolerant one-way quantum computer,” Ann. Phys. (Amsterdam) 321, 2242–2270.
  418. Raussendorf, R., J. Harrington, and K. Goyal, 2007, “Topological fault-tolerance in cluster state quantum computation,” New J. Phys. 9, 199.
  419. Raussendorf, Robert, and Hans J. Briegel, 2001, “A One-Way Quantum Computer,” Phys. Rev. Lett. 86, 5188–5191.
  420. Raussendorf, Robert, and Jim Harrington, 2007, “Fault-Tolerant Quantum Computation with High Threshold in Two Dimensions,” Phys. Rev. Lett. 98, 190504.
  421. Razavi, M., M. Piani, and N. Lutkenhaus, 2009, “Quantum repeaters with imperfect memories: Cost and scalability,” Phys. Rev. A 80, 032301.
  422. Razavi, M., K. Thompson, H. Farmanbar, Ma. Piani, and Norbert Lütkenhaus, 2009, “Physical and architectural considerations in quantum repeaters,” Proc. SPIE Int. Soc. Opt. Eng. 7236, 723603–723613.
  423. Razavi, Mohsen, 2018, An Introduction to Quantum Communications Networks (Morgan & Claypool Publishers, San Rafael, CA).
  424. Redjem, W., et al., 2020, “Single artificial atoms in silicon emitting at telecom wavelengths,” Nat. Electron. 3, 738–743.
  425. Reichle, Rainer, Dietrich Leibfried, Emanuel Knill, Joseph Britton, R. B. Blakestad, John D. Jost, Christopher Langer, R. Ozeri, Signe Seidelin, and David J. Wineland, 2006, “Experimental purification of two-atom entanglement,” Nature (London) 443, 838–841.
  426. Reiserer, Andreas, Norbert Kalb, Gerhard Rempe, and Stephan Ritter, 2014, “A quantum gate between a flying optical photon and a single trapped atom,” Nature (London) 508, 237–240.
  427. Reiserer, Andreas, and Gerhard Rempe, 2015, “Cavity-based quantum networks with single atoms and optical photons,” Rev. Mod. Phys. 87, 1379–1418.
  428. Renner, Renato, 2008, “Security of quantum key distribution,” Int. J. Quantum Inf. 06, 1–127.
  429. Riedel, Daniel, Immo Söllner, Brendan J. Shields, Sebastian Starosielec, Patrick Appel, Elke Neu, Patrick Maletinsky, and Richard J. Warburton, 2017, “Deterministic Enhancement of Coherent Photon Generation from a Nitrogen-Vacancy Center in Ultrapure Diamond,” Phys. Rev. X 7, 031040.
  430. Riedl, Stefan, Matthias Lettner, Christoph Vo, Simon Baur, Gerhard Rempe, and Stephan Dürr, 2012, “Bose-Einstein condensate as a quantum memory for a photonic polarization qubit,” Phys. Rev. A 85, 022318.
  431. Riera-Sàbat, F., P. Sekatski, A. Pirker, and W. Dür, 2021, “Entanglement-Assisted Entanglement Purification,” Phys. Rev. Lett. 127, 040502.
  432. Rigovacca, Luca, Go Kato, Stefan Bäuml, Myungshik S. Kim, William J. Munro, and Koji Azuma, 2018, “Versatile relative entropy bounds for quantum networks,” New J. Phys. 20, 013033.
  433. Rivest, Ronald L., Adi Shamir, and Leonard Adleman, 1978, “A method for obtaining digital signatures and public-key cryptosystems,” Commun. ACM 21, 120–126.
  434. Roche, Calum, 2022, “How much money did CERN’s Large Hadron Collider cost to build and who paid for it?,” https://en.as.com/latest_news/how-much-money-did-cerns-large-hadron-collider-cost-to-build-and-who-paid-for-it-n.
  435. Rozpędek, Filip, Kenneth Goodenough, Jeremy Ribeiro, Norbert Kalb, V Caprara Vivoli, Andreas Reiserer, Ronald Hanson, Stephanie Wehner, and David Elkouss, 2018, “Parameter regimes for a single sequential quantum repeater,” Quantum Sci. Technol. 3, 034002.
  436. Rozpędek, Filip, Kyungjoo Noh, Qian Xu, Saikat Guha, and Liang Jiang, 2021, “Quantum repeaters based on concatenated bosonic and discrete-variable quantum codes,” npj Quantum Inf. 7, 102.
  437. Rozpędek, Filip, Raja Yehia, Kenneth Goodenough, Maximilian Ruf, Peter C. Humphreys, Ronald Hanson, Stephanie Wehner, and David Elkouss, 2019, “Near-term quantum-repeater experiments with nitrogen-vacancy centers: Overcoming the limitations of direct transmission,” Phys. Rev. A 99, 052330.
  438. Ruf, Maximilian, Noel H. Wan, Hyeongrak Choi, Dirk Englund, and Ronald Hanson, 2021, “Quantum networks based on color centers in diamond,” J. Appl. Phys. 130, 070901.
  439. Russo, Antonio, Edwin Barnes, and Sophia E. Economou, 2018, “Photonic graph state generation from quantum dots and color centers for quantum communications,” Phys. Rev. B 98, 085303.
  440. Russo, Antonio, Edwin Barnes, and Sophia E. Economou, 2019, “Generation of arbitrary all-photonic graph states from quantum emitters,” New J. Phys. 21, 055002.
  441. Sabapathy, Krishna Kumar, Haoyu Qi, Josh Izaac, and Christian Weedbrook, 2019, “Production of photonic universal quantum gates enhanced by machine learning,” Phys. Rev. A 100, 012326.
  442. Salvail, Louis, Momtchil Peev, Eleni Diamanti, Romain Alléaume, Norbert Lütkenhaus, and Thomas Länger, 2010, “Security of trusted repeater quantum key distribution networks,” J. Comput. Secur. 18, 61–87.
  443. Sangouard, Nicolas, Romain Dubessy, and Christoph Simon, 2009, “Quantum repeaters based on single trapped ions,” Phys. Rev. A 79, 042340.
  444. Sangouard, Nicolas, Christoph Simon, Hugues de Riedmatten, and Nicolas Gisin, 2011, “Quantum repeaters based on atomic ensembles and linear optics,” Rev. Mod. Phys. 83, 33–80.
  445. Sasaki, M., et al., 2011, “Field test of quantum key distribution in the Tokyo QKD network,” Opt. Express 19, 10387–10409.
  446. Sasaki, Masahide, Kentaro Kato, Masayuki Izutsu, and Osamu Hirota, 1998, “Quantum channels showing superadditivity in classical capacity,” Phys. Rev. A 58, 146.
  447. Sasaki, Toshihiko, Yoshihisa Yamamoto, and Masato Koashi, 2014, “Practical quantum key distribution protocol without monitoring signal disturbance,” Nature (London) 509, 475–478.
  448. Schaffner, Christian, 2010, “Simple protocols for oblivious transfer and secure identification in the noisy-quantum-storage model,” Phys. Rev. A 82, 032308.
  449. Schaibley, J. R., A. P. Burgers, G. A. McCracken, L.-M. Duan, P. R. Berman, D. G. Steel, A. S. Bracker, D. Gammon, and L. J. Sham, 2013, “Demonstration of Quantum Entanglement between a Single Electron Spin Confined to an InAs Quantum Dot and a Photon,” Phys. Rev. Lett. 110, 167401.
  450. Schön, C., E. Solano, F. Verstraete, J. I. Cirac, and M. M. Wolf, 2005, “Sequential Generation of Entangled Multiqubit States,” Phys. Rev. Lett. 95, 110503.
  451. Schrödinger, E., 1935, “Discussion of probability relations between separated systems,” Math. Proc. Cambridge Philos. Soc. 31, 555–563.
  452. Schwartz, Ido, Dan Cogan, Emma R. Schmidgall, Yaroslav Don, Liron Gantz, Oded Kenneth, Netanel H. Lindner, and David Gershoni, 2016, “Deterministic generation of a cluster state of entangled photons,” Science 354, 434–437.
  453. Scully, Marlan O., and M. Suhail Zubairy, 1997, Quantum Optics (Cambridge University Press, Cambridge, England).
  454. Senellart, Pascale, Glenn Solomon, and Andrew White, 2017, “High-performance semiconductor quantum-dot single-photon sources,” Nat. Nanotechnol. 12, 1026–1039.
  455. Seshadreesan, Kaushik P., Hari Krovi, and Saikat Guha, 2020, “Continuous-variable quantum repeater based on quantum scissors and mode multiplexing,” Phys. Rev. Res. 2, 013310.
  456. Seshadreesan, Kaushik P., Masahiro Takeoka, and Mark M. Wilde, 2016, “Bounds on entanglement distillation and secret key agreement for quantum broadcast channels,” IEEE Trans. Inf. Theory 62, 2849–2866.
  457. Shaham, Roy, Or Katz, and Ofer Firstenberg, 2022, “Strong coupling of alkali-metal spins to noble-gas spins with an hour-long coherence time,” Nat. Phys. 18, 506–510.
  458. Sheng, Yu-Bo, and Fu-Guo Deng, 2010, “Deterministic entanglement purification and complete nonlocal Bell-state analysis with hyperentanglement,” Phys. Rev. A 81, 032307.
  459. Sheng, Yu-Bo, Lan Zhou, and Gui-Lu Long, 2013, “Hybrid entanglement purification for quantum repeaters,” Phys. Rev. A 88, 022302.
  460. Shibata, H., H. Takesue, T. Honjo, T. Akazaki, and Y. Tokura, 2010, “Single-photon detection using magnesium diboride superconducting nanowires,” Appl. Phys. Lett. 97, 212504.
  461. Shibata, Hiroyuki, Toshimori Honjo, and Kaoru Shimizu, 2014, “Quantum key distribution over a 72 db channel loss using ultralow dark count superconducting single-photon detectors,” Opt. Lett. 39, 5078–5081.
  462. Shor, Peter W., 1997, “Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer,” SIAM J. Comput. 26, 1484–1509.
  463. Shor, Peter W., and John Preskill, 2000, “Simple Proof of Security of the BB84 Quantum Key Distribution Protocol,” Phys. Rev. Lett. 85, 441–444.
  464. Simon, C., et al., 2010, “Quantum memories: A review based on the European integrated project ‘Qubit applications (QAP),’ ” Eur. Phys. J. D 58, 1–22.
  465. Sinclair, Neil, et al., 2014, “Spectral Multiplexing for Scalable Quantum Photonics Using an Atomic Frequency Comb Quantum Memory and Feed-Forward Control,” Phys. Rev. Lett. 113, 053603.
  466. Sipahigil, Alp, Kay D. Jahnke, Lachlan J. Rogers, Tokuyuki Teraji, Junichi Isoya, Alexander S. Zibrov, Fedor Jelezko, and Mikhail D. Lukin, 2014, “Indistinguishable Photons from Separated Silicon-Vacancy Centers in Diamond,” Phys. Rev. Lett. 113, 113602.
  467. Slodička, L., G. Hétet, N. Röck, P. Schindler, M. Hennrich, and R. Blatt, 2013, “Atom-Atom Entanglement by Single-Photon Detection,” Phys. Rev. Lett. 110, 083603.
  468. Somaschi, N., et al., 2016, “Near-optimal single-photon sources in the solid state,” Nat. Photonics 10, 340–345.
  469. Stace, Thomas M., Sean D. Barrett, and Andrew C. Doherty, 2009, “Thresholds for Topological Codes in the Presence of Loss,” Phys. Rev. Lett. 102, 200501.
  470. Stephenson, L. J., D. P. Nadlinger, B. C. Nichol, S. An, P. Drmota, T. G. Ballance, K. Thirumalai, J. F. Goodwin, D. M. Lucas, and C. J. Ballance, 2020, “High-Rate, High-Fidelity Entanglement of Qubits across an Elementary Quantum Network,” Phys. Rev. Lett. 124, 110501.
  471. Stinaff, Eric A., Michael Scheibner, Allan S. Bracker, Ilya V. Ponomarev, Vladimir L. Korenev, Morgan E. Ware, Matt F. Doty, Thomas L. Reinecke, and Dan Gammon, 2006, “Optical signatures of coupled quantum dots,” Science 311, 636–639.
  472. Stockill, Robert, M. J. Stanley, Lukas Huthmacher, E. Clarke, M. Hugues, A. J. Miller, C. Matthiesen, C. Le Gall, and Mete Atatüre, 2017, “Phase-Tuned Entangled State Generation between Distant Spin Qubits,” Phys. Rev. Lett. 119, 010503.
  473. Stucki, Damien, et al., 2011, “Long-term performance of the SwissQuantum quantum key distribution network in a field environment,” New J. Phys. 13, 123001.
  474. Su, Daiqin, Casey R. Myers, and Krishna Kumar Sabapathy, 2019, “Conversion of Gaussian states to non-Gaussian states using photon-number-resolving detectors,” Phys. Rev. A 100, 052301.
  475. Sukachev, Denis D., Alp Sipahigil, Christian T. Nguyen, Mihir K. Bhaskar, Ruffin E. Evans, Fedor Jelezko, and Mikhail D. Lukin, 2017, “Silicon-Vacancy Spin Qubit in Diamond: A Quantum Memory Exceeding 10 ms with Single-Shot State Readout,” Phys. Rev. Lett. 119, 223602.
  476. Sun, Shuo, Hyochul Kim, Glenn S. Solomon, and Edo Waks, 2016, “A quantum phase switch between a single solid-state spin and a photon,” Nat. Nanotechnol. 11, 539–544.
  477. Takeoka, Masahiro, Saikat Guha, and Mark M. Wilde, 2014a, “Fundamental rate-loss tradeoff for optical quantum key distribution,” Nat. Commun. 5, 5235.
  478. Takeoka, Masahiro, Saikat Guha, and Mark M. Wilde, 2014b, “The squashed entanglement of a quantum channel,” IEEE Trans. Inf. Theory 60, 4987–4998.
  479. Takeoka, Masahiro, Kaushik P. Seshadreesan, and Mark M. Wilde, 2017, “Unconstrained Capacities of Quantum Key Distribution and Entanglement Distillation for Pure-Loss Bosonic Broadcast Channels,” Phys. Rev. Lett. 119, 150501.
  480. Tamaki, Kiyoshi, Marcos Curty, Go Kato, Hoi-Kwong Lo, and Koji Azuma, 2014, “Loss-tolerant quantum cryptography with imperfect sources,” Phys. Rev. A 90, 052314.
  481. Tamaki, Kiyoshi, Hoi-Kwong Lo, Chi-Hang Fred Fung, and Bing Qi, 2012, “Phase encoding schemes for measurement-device-independent quantum key distribution with basis-dependent flaw,” Phys. Rev. A 85, 042307.
  482. Tamaki, Kiyoshi, Hoi-Kwong Lo, Wenyuan Wang, and Marco Lucamarini, 2018, “Information theoretic security of quantum key distribution overcoming the repeaterless secret key capacity bound,” arXiv:1805.05511.
  483. Taminiau, T. H., J. J. T. Wagenaar, T. Van der Sar, Fedor Jelezko, Viatcheslav V. Dobrovitski, and R. Hanson, 2012, “Detection and Control of Individual Nuclear Spins Using a Weakly Coupled Electron Spin,” Phys. Rev. Lett. 109, 137602.
  484. Tan, Ting Rei, John P. Gaebler, Yiheng Lin, Yong Wan, R. Bowler, D. Leibfried, and David J. Wineland, 2015, “Multi-element logic gates for trapped-ion qubits,” Nature (London) 528, 380–383.
  485. Tani, Seiichiro, Hirotada Kobayashi, and Keiji Matsumoto, 2005, “Exact quantum algorithms for the leader election problem,” in Proceedings of the 22nd Annual Symposium on Theoretical Aspects of Computer Science, Stuttgart, 2005, edited by Volker Diekert and B. Durand (Springer, New York), pp. 581–592, 10.1007/978-3-540-31856-9_48.
  486. Tanzilli, S., W. Tittel, M. Halder, O. Alibart, P. Baldi, N. Gisin, and H. Zbinden, 2005, “A photonic quantum information interface,” Nature (London) 437, 116–120.
  487. Tchebotareva, Anna, et al., 2019, “Entanglement between a Diamond Spin Qubit and a Photonic Time-Bin Qubit at Telecom Wavelength,” Phys. Rev. Lett. 123, 063601.
  488. Terhal, Barbara M., 2015, “Quantum error correction for quantum memories,” Rev. Mod. Phys. 87, 307–346.
  489. Thomas, Philip, Leonardo Ruscio, Olivier Morin, and Gerhard Rempe, 2022, “Efficient generation of entangled multiphoton graph states from a single atom,” Nature (London) 608, 677–681.
  490. Togan, E., et al., 2010, “Quantum entanglement between an optical photon and a solid-state spin qubit,” Nature (London) 466, 730–734.
  491. Tomm, Natasha, et al., 2021, “A bright and fast source of coherent single photons,” Nat. Nanotechnol. 16, 399–403.
  492. Townsend, Kevin, 2022, “NIST post-quantum algorithm finalist cracked using a classical PC,” https://www.securityweek.com/nist-post-quantum-algorithm-finalist-cracked-using-classical-pc.
  493. Townsend, Paul D., 1997, “Quantum cryptography on multiuser optical fibre networks,” Nature (London) 385, 47–49.
  494. Trényi, Róbert, Koji Azuma, and Marcos Curty, 2019, “Beating the repeaterless bound with adaptive measurement-device-independent quantum key distribution,” New J. Phys. 21, 113052.
  495. Trusheim, Matthew E., et al., 2020, “Transform-Limited Photons from a Coherent Tin-Vacancy Spin in Diamond,” Phys. Rev. Lett. 124, 023602.
  496. Tzitrin, Ilan, 2018, “Local equivalence of complete bipartite and repeater graph states,” Phys. Rev. A 98, 032305.
  497. Tzitrin, Ilan, J. Eli Bourassa, Nicolas C. Menicucci, and Krishna Kumar Sabapathy, 2020, “Progress towards practical qubit computation using approximate Gottesman-Kitaev-Preskill codes,” Phys. Rev. A 101, 032315.
  498. Tzitrin, Ilan, Takaya Matsuura, Rafael N. Alexander, Guillaume Dauphinais, J. Eli Bourassa, Krishna K. Sabapathy, Nicolas C. Menicucci, and Ish Dhand, 2021, “Fault-tolerant quantum computation with static linear optics,” PRX Quantum 2, 040353.
  499. Uppu, Ravitej, et al., 2020, “Scalable integrated single-photon source,” Sci. Adv. 6, eabc8268.
  500. Ursin, Rupert, et al., 2007, “Entanglement-based quantum communication over 144 km,” Nat. Phys. 3, 481.
  501. Vaidman, Lev, 2003, “Instantaneous Measurement of Nonlocal Variables,” Phys. Rev. Lett. 90, 010402.
  502. van Leent, Tim, Matthias Bock, Robert Garthoff, Kai Redeker, Wei Zhang, Tobias Bauer, Wenjamin Rosenfeld, Christoph Becher, and Harald Weinfurter, 2020, “Long-Distance Distribution of Atom-Photon Entanglement at Telecom Wavelength,” Phys. Rev. Lett. 124, 010510.
  503. van Leent, Tim, et al., 2022, “Entangling single atoms over 33 km telecom fibre,” Nature (London) 607, 69–73.
  504. van Loock, P., T. D. Ladd, K. Sanaka, F. Yamaguchi, Kae Nemoto, W. J. Munro, and Y. Yamamoto, 2006, “Hybrid Quantum Repeater Using Bright Coherent Light,” Phys. Rev. Lett. 96, 240501.
  505. Van Meter, Rodney, 2014, Quantum Networking (John Wiley & Sons, New York).
  506. Van Meter, Rodney, Thaddeus D. Ladd, William J. Munro, and Kae Nemoto, 2009, “System design for a long-line quantum repeater,” IEEE/ACM Trans. Networking 17, 1002–1013.
  507. Van Meter, Rodney, and Joe Touch, 2013, “Designing quantum repeater networks,” IEEE Commun. Mag. 51, 64–71.
  508. Varnava, Michael, Daniel E. Browne, and Terry Rudolph, 2006, “Loss Tolerance in One-Way Quantum Computation via Counterfactual Error Correction,” Phys. Rev. Lett. 97, 120501.
  509. Varnava, Michael, Daniel E. Browne, and Terry Rudolph, 2007, “Loss tolerant linear optical quantum memory by measurement-based quantum computing,” New J. Phys. 9, 203.
  510. Varnava, Michael, Daniel E. Browne, and Terry Rudolph, 2008, “How Good Must Single Photon Sources and Detectors Be for Efficient Linear Optical Quantum Computation?,” Phys. Rev. Lett. 100, 060502.
  511. Vasconcelos, Rui, Sarah Reisenbauer, Cameron Salter, Georg Wachter, Daniel Wirtitsch, Jörg Schmiedmayer, Philip Walther, and Michael Trupke, 2020, “Scalable spin-photon entanglement by time-to-polarization conversion,” npj Quantum Inf. 6, 9.
  512. Vezvaee, Arian, Paul Hilaire, Matthew F. Doty, and Sophia E. Economou, 2022, “Deterministic Generation of Entangled Photonic Cluster States from Quantum Dot Molecules,” Phys. Rev. Appl. 18, L061003.
  513. Volz, Jürgen, Markus Weber, Daniel Schlenk, Wenjamin Rosenfeld, Johannes Vrana, Karen Saucke, Christian Kurtsiefer, and Harald Weinfurter, 2006, “Observation of Entanglement of a Single Photon with a Trapped Atom,” Phys. Rev. Lett. 96, 030404.
  514. Waks, Edo, Assaf Zeevi, and Yoshihisa Yamamoto, 2002, “Security of quantum key distribution with entangled photons against individual attacks,” Phys. Rev. A 65, 052310.
  515. Waldherr, Gerald, et al., 2014, “Quantum error correction in a solid-state hybrid spin register,” Nature (London) 506, 204–207.
  516. Wallnöfer, Julius, Frederik Hahn, Mustafa Gündoğan, Jasminder S. Sidhu, Fabian Wiesner, Nathan Walk, Jens Eisert, and Janik Wolters, 2022, “Simulating quantum repeater strategies for multiple satellites,” Commun. Phys. 5, 169.
  517. Walls, Daniel F., and Gerard J. Milburn, 2007, Quantum Optics (Springer Science+Business Media, New York).
  518. Wan, Noel H., et al., 2020, “Large-scale integration of artificial atoms in hybrid photonic circuits,” Nature (London) 583, 226–231.
  519. Wang, Hui, et al., 2019, “Towards optimal single-photon sources from polarized microcavities,” Nat. Photonics 13, 770–775.
  520. Wang, Pengfei, Chun-Yang Luan, Mu Qiao, Mark Um, Junhua Zhang, Ye Wang, Xiao Yuan, Mile Gu, Jingning Zhang, and Kihwan Kim, 2021, “Single ion qubit with estimated coherence time exceeding one hour,” Nat. Commun. 12, 233.
  521. Wang, Shuang, De-Yong He, Zhen-Qiang Yin, Feng-Yu Lu, Chao-Han Cui, Wei Chen, Zheng Zhou, Guang-Can Guo, and Zheng-Fu Han, 2019, “Beating the Fundamental Rate-Distance Limit in a Proof-of-Principle Quantum Key Distribution System,” Phys. Rev. X 9, 021046.
  522. Wang, Shuang, et al., 2022, “Twin-field quantum key distribution over 830-km fibre,” Nat. Photonics 16, 154–161.
  523. Wang, Xiang-Bin, 2005, “Beating the Photon-Number-Splitting Attack in Practical Quantum Cryptography,” Phys. Rev. Lett. 94, 230503.
  524. Wang, Xiang-Bin, Zong-Wen Yu, and Xiao-Long Hu, 2018, “Twin-field quantum key distribution with large misalignment error,” Phys. Rev. A 98, 062323.
  525. Wang, Ye, Mark Um, Junhua Zhang, Shuoming An, Ming Lyu, Jing-Ning Zhang, L.-M. Duan, Dahyun Yum, and Kihwan Kim, 2017, “Single-qubit quantum memory exceeding ten-minute coherence time,” Nat. Photonics 11, 646.
  526. Wehner, Stephanie, Marcos Curty, Christian Schaffner, and Hoi-Kwong Lo, 2010, “Implementation of two-party protocols in the noisy-storage model,” Phys. Rev. A 81, 052336.
  527. Wehner, Stephanie, David Elkouss, and Ronald Hanson, 2018, “Quantum internet: A vision for the road ahead,” Science 362, eaam9288.
  528. Wells, L. M., Sokratis Kalliakos, Bruno Villa, D. J. P. Ellis, R. M. Stevenson, A. J. Bennett, Ian Farrer, D. A. Ritchie, and A. J. Shields, 2019, “Photon Phase Shift at the Few-Photon Level and Optical Switching by a Quantum Dot in a Microcavity,” Phys. Rev. Appl. 11, 061001.
  529. Werner, Reinhard F., 2001, “All teleportation and dense coding schemes,” J. Phys. A 34, 7081.
  530. Wiesner, Stephen, 1983, “Conjugate coding,” ACM SIGACT News 15, 78–88.
  531. Wolf, Michael M., David Pérez-García, and Geza Giedke, 2007, “Quantum Capacities of Bosonic Channels,” Phys. Rev. Lett. 98, 130501.
  532. Wootters, W. K., and W. H. Zurek, 1982, “A single quantum cannot be cloned,” Nature (London) 299, 802–803.
  533. Wootters, William K., 1998, “Entanglement of Formation of an Arbitrary State of Two Qubits,” Phys. Rev. Lett. 80, 2245–2248.
  534. Xie, Yuan-Mei, Yu-Shuo Lu, Chen-Xun Weng, Xiao-Yu Cao, Zhao-Ying Jia, Yu Bao, Yang Wang, Yao Fu, Hua-Lei Yin, and Zeng-Bing Chen, 2022, “Breaking the rate-loss bound of quantum key distribution with asynchronous two-photon interference,” PRX Quantum 3, 020315.
  535. Xu, Feihu, Marcos Curty, Bing Qi, and Hoi-Kwong Lo, 2015, “Measurement-device-independent quantum cryptography,” IEEE J. Sel. Top. Quantum Electron. 21, 148–158.
  536. Xu, Feihu, Xiongfeng Ma, Qiang Zhang, Hoi-Kwong Lo, and Jian-Wei Pan, 2020, “Secure quantum key distribution with realistic devices,” Rev. Mod. Phys. 92, 025002.
  537. Xu, Zhongxiao, Yuelong Wu, Long Tian, Lirong Chen, Zhiying Zhang, Zhihui Yan, Shujing Li, Hai Wang, Changde Xie, and Kunchi Peng, 2013, “Long Lifetime and High-Fidelity Quantum Memory of Photonic Polarization Qubit by Lifting Zeeman Degeneracy,” Phys. Rev. Lett. 111, 240503.
  538. Yamamoto, Takashi, Masato Koashi, and Nobuyuki Imoto, 2001, “Concentration and purification scheme for two partially entangled photon pairs,” Phys. Rev. A 64, 012304.
  539. Yamamoto, Takashi, Masato Koashi, Şahin Kaya Özdemir, and Nobuyuki Imoto, 2003, “Experimental extraction of an entangled photon pair from two identically decohered pairs,” Nature (London) 421, 343–346.
  540. Yang, Sheng-Jun, Xu-Jie Wang, Xiao-Hui Bao, and Jian-Wei Pan, 2016, “An efficient quantum light-matter interface with sub-second lifetime,” Nat. Photonics 10, 381–384.
  541. Yehia, Raja, Simon Neves, Eleni Diamanti, and Iordanis Kerenidis, 2022, “Quantum city: Simulation of a practical near-term metropolitan quantum network,” arXiv:2211.01190.
  542. Yin, Juan, et al., 2017, “Satellite-based entanglement distribution over 1200 kilometers,” Science 356, 1140–1144.
  543. Yu, Leo, et al., 2015, “Two-photon interference at telecom wavelengths for time-bin-encoded single photons from quantum-dot spin qubits,” Nat. Commun. 6, 8955.
  544. Yu, Yong, et al., 2020, “Entanglement of two quantum memories via fibres over dozens of kilometres,” Nature (London) 578, 240–245.
  545. Yu, Zong-Wen, Xiao-Long Hu, Cong Jiang, Hai Xu, and Xiang-Bin Wang, 2019, “Sending-or-not-sending twin-field quantum key distribution in practice,” Sci. Rep. 9, 3080.
  546. Zaidi, Hussain A., Chris Dawson, Peter van Loock, and Terry Rudolph, 2015, “Near-deterministic creation of universal cluster states with probabilistic Bell measurements and three-qubit resource states,” Phys. Rev. A 91, 042301.
  547. Zanin, Guilherme Luiz, Maxime J. Jacquet, Michele Spagnolo, Peter Schiansky, Irati Alonso Calafell, Lee A. Rozema, and Philip Walther, 2021, “Fiber-compatible photonic feed-forward with 99% fidelity,” Opt. Express 29, 3425–3437.
  548. Zaske, Sebastian, et al., 2012, “Visible-to-Telecom Quantum Frequency Conversion of Light from a Single Quantum Emitter,” Phys. Rev. Lett. 109, 147404.
  549. Zeng, Pei, Hongyi Zhou, Weijie Wu, and Xiongfeng Ma, 2022, “Mode-pairing quantum key distribution,” Nat. Commun. 13, 3903.
  550. Zhan, Yuan, Paul Hilaire, Edwin Barnes, Sophia E. Economou, and Shuo Sun, 2023, “Performance analysis of quantum repeaters enabled by deterministically generated photonic graph states,” Quantum 7, 924.
  551. Zhan, Yuan, and Shuo Sun, 2020, “Deterministic Generation of Loss-Tolerant Photonic Cluster States with a Single Quantum Emitter,” Phys. Rev. Lett. 125, 223601.
  552. Zhang, Qiang, Xiao-Hui Bao, Chao-Yang Lu, Xiao-Qi Zhou, Tao Yang, Terry Rudolph, and Jian-Wei Pan, 2008, “Demonstration of a scheme for the generation of ‘event-ready’ entangled photon pairs from a single-photon source,” Phys. Rev. A 77, 062316.
  553. Zhang, Rui, Li-Zheng Liu, Zheng-Da Li, Yue-Yang Fei, Xu-Fei Yin, Li Li, Nai-Le Liu, Yingqiu Mao, Yu-Ao Chen, and Jian-Wei Pan, 2022, “Loss-tolerant all-photonic quantum repeater with generalized Shor code,” Optica 9, 152–158.
  554. Zhang, Wei, et al., 2022, “A device-independent quantum key distribution system for distant users,” Nature (London) 607, 687–691.
  555. Zhong, Han-Sen, et al., 2018, “12-Photon Entanglement and Scalable Scattershot Boson Sampling with Optimal Entangled-Photon Pairs from Parametric Down-Conversion,” Phys. Rev. Lett. 121, 250505.
  556. Zhong, Manjin, Morgan P. Hedges, Rose L. Ahlefeldt, John G. Bartholomew, Sarah E. Beavan, Sven M. Wittig, Jevon J. Longdell, and Matthew J. Sellars, 2015, “Optically addressable nuclear spins in a solid with a six-hour coherence time,” Nature (London) 517, 177–180.
  557. Zhong, Tian, and Philippe Goldner, 2019, “Emerging rare-earth doped material platforms for quantum nanophotonics,” Nanophotonics 8, 2003–2015.
  558. Zhong, Tian, Jonathan M. Kindem, Evan Miyazono, and Andrei Faraon, 2015, “Nanophotonic coherent light-matter interfaces based on rare-earth-doped crystals,” Nat. Commun. 6, 8206.
  559. Zhong, Xiaoqing, Jianyong Hu, Marcos Curty, Li Qian, and Hoi-Kwong Lo, 2019, “Proof-of-Principle Experimental Demonstration of Twin-Field Type Quantum Key Distribution,” Phys. Rev. Lett. 123, 100506.
  560. Zhong, Xiaoqing, Wenyuan Wang, Reem Mandil, Hoi-Kwong Lo, and Li Qian, 2022, “Simple Multiuser Twin-Field Quantum Key Distribution Network,” Phys. Rev. Appl. 17, 014025.
  561. Zhong, Xiaoqing, Wenyuan Wang, Li Qian, and Hoi-Kwong Lo, 2021, “Proof-of-principle experimental demonstration of twin-field quantum key distribution over optical channels with asymmetric losses,” npj Quantum Inf. 7, 6.
  562. Zhou, Lai, Jinping Lin, Yuan-Mei Xie, Yu-Shuo Lu, Yumang Jing, Hua-Lei Yin, and Zhiliang Yuan, 2023, “Experimental Quantum Communication Overcomes the Rate-Loss Limit Without Global Phase Tracking,” Phys. Rev. Lett. 130, 250801.
  563. Zhou, Lan, Wei Zhong, and Yu-Bo Sheng, 2020, “Purification of the residual entanglement,” Opt. Express 28, 2291–2301.
  564. Zhu, Hao-Tao, et al., 2023, “Experimental Mode-Pairing Measurement-Device-Independent Quantum Key Distribution without Global Phase Locking,” Phys. Rev. Lett. 130, 030801.
  565. Zukowski, M., A. Zeilinger, M. A. Horne, and A. K. Ekert, 1993, “Event-Ready-Detectors Bell Experiment via Entanglement Swapping,” Phys. Rev. Lett. 71, 4287.
  566. Zwerger, M., H. J. Briegel, and W. Dür, 2014, “Hybrid architecture for encoded measurement-based quantum computation,” Sci. Rep. 4, 5364.
  567. Zwerger, M., H. J. Briegel, and W. Dür, 2016, “Measurement-based quantum communication,” Appl. Phys. B 122, 50.
  568. Zwerger, M., W. Dür, and H. J. Briegel, 2012, “Measurement-based quantum repeaters,” Phys. Rev. A 85, 062326.
  569. Zwerger, M., A. Pirker, V. Dunjko, H. J. Briegel, and W. Dür, 2018, “Long-Range Big Quantum-Data Transmission,” Phys. Rev. Lett. 120, 030503.

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Rev. Mod. Phys. 95, 045006– Published 20 December, 2023
  • Received 20 October 2021
Article part of CHORUS
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