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Quantum NETwork: from theory to practice

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Abstract

The quantum internet is envisioned as the ultimate stage of the quantum revolution, which surpasses its classical counterpart in various aspects, such as the efficiency of data transmission, the security of network services, and the capability of information processing. Given its disruptive impact on the national security and the digital economy, a global race to build scalable quantum networks has already begun. With the joint effort of national governments, industrial participants, and research institutes, the development of quantum networks has advanced rapidly in recent years, bringing the first primitive quantum networks within reach. In this work, we aim to provide an up-to-date review of the field of quantum networks from both theoretical and experimental perspectives, contributing to a better understanding of the building blocks required for the establishment of a global quantum internet. We also introduce a newly developed quantum network toolkit to facilitate the exploration and evaluation of innovative ideas. Particularly, it provides dual quantum computing engines, supporting simulations in both the quantum circuit and measurement-based models. It also includes a compilation scheme for mapping quantum network protocols onto quantum circuits, enabling their emulations on real-world quantum hardware devices. We showcase the power of this toolkit with several featured demonstrations, including a simulation of the Micius quantum satellite experiment, a testing of a four-layer quantum network architecture with resource management, and a quantum emulation of the CHSH game. We hope this work can give a better understanding of the state-of-the-art development of quantum networks and provide the necessary tools to make further contributions along the way.

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References

  1. Kimble H J. The quantum internet. Nature, 2008, 453: 1023–1030

    Article  Google Scholar 

  2. Wehner S, Elkouss D, Hanson R. Quantum internet: a vision for the road ahead. Science, 2018, 362

  3. Caleffi M, Cacciapuoti A S, Bianchi G. Quantum internet: from communication to distributed computing! In: Proceedings of the 5th ACM International Conference on Nanoscale Computing and Communication, 2018. 1–4

  4. Castelvecchi D. The quantum internet has arrived (and it hasn’t). Nature, 2018, 554: 289–292

    Article  Google Scholar 

  5. Kozlowski W, Wehner S. Towards large-scale quantum networks. In: Proceedings of the 6th Annual ACM International Conference on Nanoscale Computing and Communication, 2019. 1–7

  6. Singh A, Dev K, Siljak H, et al. Quantum internet-applications, functionalities, enabling technologies, challenges, and research directions. IEEE Commun Surv Tut, 2021, 23: 2218–2247

    Article  Google Scholar 

  7. Wei S, Jing B, Zhang X, et al. Towards real-world quantum networks: a review. Laser Photon Rev, 2022, 16: 2100219

    Article  Google Scholar 

  8. Awschalom D, Berggren K K, Bernien H, et al. Development of quantum interconnects (QuICs) for next-generation information technologies. PRX Quantum, 2021, 2: 017002

    Article  Google Scholar 

  9. Gyongyosi L, Imre S. Advances in the quantum internet. Commun ACM, 2022, 65: 52–63

    Article  MATH  Google Scholar 

  10. Rohde P P. The Quantum Internet: The Second Quantum Revolution. Cambridge: Cambridge University Press, 2021

    Book  MATH  Google Scholar 

  11. Pirandola S, Braunstein S L. Physics: unite to build a quantum internet. Nature, 2016, 532: 169–171

    Article  Google Scholar 

  12. Ramakrishnan R K, Ravichandran A B, Kaushik I, et al. The quantum internet: a hardware review. J Ind Inst Sci, 2022, doi: https://doi.org/10.1007/s41745-022-00336-7

  13. Bennett C, Brassard G. Quantum cryptography: public key distribution and coin tossing. In: Proceedings of the IEEE International Conference on Computers, Systems, and Signal Processing, 1984. 175–179

  14. Ekert A K. Quantum cryptography based on Bell’s theorem. Phys Rev Lett, 1991, 67: 661–663

    Article  MathSciNet  MATH  Google Scholar 

  15. Broadbent A, Fitzsimons J, Kashefi E. Universal blind quantum computation. In: Proceedings of the 50th Annual IEEE Symposium on Foundations of Computer Science, 2009. 517–526

  16. Jozsa R, Abrams D S, Dowling J P, et al. Quantum clock synchronization based on shared prior entanglement. Phys Rev Lett, 2000, 85: 2010–2013

    Article  Google Scholar 

  17. Gottesman D, Jennewein T, Croke S. Longer-baseline telescopes using quantum repeaters. Phys Rev Lett, 2012, 109: 070503

    Article  Google Scholar 

  18. Cirac J I, Ekert A K, Huelga S F, et al. Distributed quantum computation over noisy channels. Phys Rev A, 1999, 59: 4249–4254

    Article  MathSciNet  Google Scholar 

  19. Crépeau C, Gottesman D, Smith A. Secure multi-party quantum computation. In: Proceedings of the 34th Annual ACM Symposium on Theory of Computing, 2002. 643–652

  20. Cuomo D, Caleffi M, Cacciapuoti A S. Towards a distributed quantum computing ecosystem. IET Quantum Commun, 2020, 1: 3–8

    Article  Google Scholar 

  21. Lu C Y, Cao Y, Peng C Z, et al. Micius quantum experiments in space. Rev Mod Phys, 2022, 94: 035001

    Article  Google Scholar 

  22. Liao S K, Cai W Q, Liu W Y, et al. Satellite-to-ground quantum key distribution. Nature, 2017, 549: 43–47

    Article  Google Scholar 

  23. Castelvecchi D. China’s quantum satellite clears major hurdle on way to ultrasecure communications. Nature, 2017, doi: https://doi.org/10.1038/nature.2017.22142

  24. Chen Y A, Zhang Q, Chen T Y, et al. An integrated space-to-ground quantum communication network over 4,600 kilometres. Nature, 2021, 589: 214–219

    Article  Google Scholar 

  25. Courtland R. China’s 2,000-km quantum link is almost complete [News]. IEEE Spectr, 2016, 53: 11–12

    Google Scholar 

  26. Pompili M, Hermans S L N, Baier S, et al. Realization of a multinode quantum network of remote solid-state qubits. Science, 2021, 372: 259–264

    Article  Google Scholar 

  27. Pirker A, Dür W. A quantum network stack and protocols for reliable entanglement-based networks. New J Phys, 2019, 21: 033003

    Article  MathSciNet  Google Scholar 

  28. Kozlowski W, Wehner S, Meter R V, et al. Architectural Principles for a Quantum Internet. RFC 9340. 2022

  29. Van Meter R, Satoh R, Benchasattabuse N, et al. A quantum internet architecture. 2021. ArXiv:2112.07092

  30. Coopmans T, Knegjens R, Dahlberg A, et al. NetSquid, a NETwork simulator for quantum information using discrete events. Commun Phys, 2021, 4: 164

    Article  Google Scholar 

  31. Wu X, Kolar A, Chung J, et al. SeQUeNCe: a customizable discrete-event simulator of quantum networks. Quantum Sci Technol, 2021, 6: 045027

    Article  Google Scholar 

  32. Satoh R, Hajdušek M, Benchasattabuse N, et al. QuISP: a quantum internet simulation package. 2021. ArXiv:2112.07093

  33. Bartlett B. A distributed simulation framework for quantum networks and channels. 2018. ArXiv:1808.07047

  34. Mailloux L O, Morris J D, Grimaila M R, et al. A modeling framework for studying quantum key distribution system implementation nonidealities. IEEE Access, 2015, 3: 110–130

    Article  Google Scholar 

  35. Leone H, Miller N R, Singh D, et al. QuNet: cost vector analysis & multi-path entanglement routing in quantum networks. 2021. ArXiv:2105.00418

  36. Slussarenko S, Pryde G J. Photonic quantum information processing: a concise review. Appl Phys Rev, 2019, 6: 041303

    Article  Google Scholar 

  37. Krantz P, Kjaergaard M, Yan F, et al. A quantum engineer’s guide to superconducting qubits. Appl Phys Rev, 2019, 6: 021318

    Article  Google Scholar 

  38. Bruzewicz C D, Chiaverini J, McConnell R, et al. Trapped-ion quantum computing: progress and challenges. Appl Phys Rev, 2019, 6: 021314

    Article  Google Scholar 

  39. Hillery M. Coherence as a resource in decision problems: the Deutsch-Jozsa algorithm and a variation. Phys Rev A, 2016, 93: 012111

    Article  Google Scholar 

  40. Hayashi M, Fang K, Wang K. Finite block length analysis on quantum coherence distillation and incoherent randomness extraction. IEEE Trans Inform Theory, 2021, 67: 3926–3944

    Article  MathSciNet  MATH  Google Scholar 

  41. Díaz M G, Fang K, Wang X, et al. Using and reusing coherence to realize quantum processes. Quantum, 2018, 2: 100

    Article  Google Scholar 

  42. Fang K, Wang X, Lami L, et al. Probabilistic distillation of quantum coherence. Phys Rev Lett, 2018, 121: 070404

    Article  MathSciNet  Google Scholar 

  43. Regula B, Fang K, Wang X, et al. One-shot coherence distillation. Phys Rev Lett, 2018, 121: 010401

    Article  Google Scholar 

  44. Ahnefeld F, Theurer T, Egloff D, et al. Coherence as a resource for Shor’s algorithm. Phys Rev Lett, 2022, 129: 120501

    Article  MathSciNet  Google Scholar 

  45. Bennett C H, Brassard G, Crépeau C, et al. Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. Phys Rev Lett, 1993, 70: 1895–1899

    Article  MathSciNet  MATH  Google Scholar 

  46. Acín A, Brunner N, Gisin N, et al. Device-independent security of quantum cryptography against collective attacks. Phys Rev Lett, 2007, 98: 230501

    Article  Google Scholar 

  47. Bell J S. On the Einstein Podolsky Rosen paradox. Phys Phys Fizika, 1964, 1: 195–200

    Article  MathSciNet  Google Scholar 

  48. Freedman S J, Clauser J F. Experimental test of local hidden-variable theories. Phys Rev Lett, 1972, 28: 938–941

    Article  Google Scholar 

  49. Aspect A, Dalibard J, Roger G. Experimental test of Bell’s inequalities using time-varying analyzers. Phys Rev Lett, 1982, 49: 1804–1807

    Article  MathSciNet  Google Scholar 

  50. Ou Z Y, Mandel L. Violation of Bell’s inequality and classical probability in a two-photon correlation experiment. Phys Rev Lett, 1988, 61: 50–53

    Article  MathSciNet  Google Scholar 

  51. Hensen B, Bernien H, Dréau A E, et al. Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres. Nature, 2015, 526: 682–686

    Article  Google Scholar 

  52. Giustina M, Versteegh M A M, Wengerowsky S, et al. Significant-loophole-free test of Bell’s theorem with entangled photons. Phys Rev Lett, 2015, 115: 250401

    Article  Google Scholar 

  53. Shalm L K, Meyer-Scott E, Christensen B G, et al. Strong loophole-free test of local realism. Phys Rev Lett, 2015, 115: 250402

    Article  Google Scholar 

  54. Handsteiner J, Friedman A S, Rauch D, et al. Cosmic Bell test: measurement settings from milky way stars. Phys Rev Lett, 2017, 118: 060401

    Article  Google Scholar 

  55. Yin J, Cao Y, Li Y H, et al. Satellite-based entanglement distribution over 1200 kilometers. Science, 2017, 356: 1140–1144

    Article  Google Scholar 

  56. Nielsen M A, Chuang I L. Quantum Computation and Quantum Information. Cambridge: Cambridge University Press, 2012

    Book  MATH  Google Scholar 

  57. Xiao Y, Fang K, Gour G. The complementary information principle of quantum mechanics. 2019. ArXiv:1908.07694

  58. Briegel H J, Browne D E, Dür W, et al. Measurement-based quantum computation. Nat Phys, 2009, 5: 19–26

    Article  Google Scholar 

  59. Wootters W K, Zurek W H. A single quantum cannot be cloned. Nature, 1982, 299: 802–803

    Article  MATH  Google Scholar 

  60. Briegel H J, Duür W, Cirac J I, et al. Quantum repeaters: the role of imperfect local operations in quantum communication. Phys Rev Lett, 1998, 81: 5932–5935

    Article  Google Scholar 

  61. Duan L M, Lukin M D, Cirac J I, et al. Long-distance quantum communication with atomic ensembles and linear optics. Nature, 2001, 414: 413–418

    Article  Google Scholar 

  62. Muralidharan S, Li L, Kim J, et al. Optimal architectures for long distance quantum communication. Sci Rep, 2016, 6: 20463

    Article  Google Scholar 

  63. Zwerger M, Pirker A, Dunjko V, et al. Long-range big quantum-data transmission. Phys Rev Lett, 2018, 120: 030503

    Article  Google Scholar 

  64. Brand S, Coopmans T, Elkouss D. Efficient computation of the waiting time and fidelity in quantum repeater chains. IEEE J Sel Areas Commun, 2020, 38: 619–639

    Article  Google Scholar 

  65. Li B, Coopmans T, Elkouss D. Efficient optimization of cutoffs in quantum repeater chains. IEEE Trans Quantum Eng, 2021, 2: 1–15

    Article  Google Scholar 

  66. Rozpedek F, Noh K, Xu Q, et al. Quantum repeaters based on concatenated bosonic and discrete-variable quantum codes. npj Quantum Inf, 2021, 7: 102

    Article  Google Scholar 

  67. Rozpędek F, Goodenough K, Ribeiro J, et al. Parameter regimes for a single sequential quantum repeater. Quantum Sci Technol, 2018, 3: 034002

    Article  Google Scholar 

  68. Coutinho B C, Munro W J, Nemoto K, et al. Robustness of noisy quantum networks. Commun Phys, 2022, 5: 105

    Article  Google Scholar 

  69. Zhou Z. A multiplexed quantum repeater based on absorptive quantum memories. Sci China Inf Sci, 2021, 64: 217501

    Article  Google Scholar 

  70. Sangouard N, Simon C, de Riedmatten H, et al. Quantum repeaters based on atomic ensembles and linear optics. Rev Mod Phys, 2011, 83: 33–80

    Article  Google Scholar 

  71. Gottesman D. An introduction to quantum error correction and fault-tolerant quantum computation. 2009. ArXiv:0904.2557

  72. Munro W J, Azuma K, Tamaki K, et al. Inside quantum repeaters. IEEE J Sel Top Quantum Electron, 2015, 21: 78–90

    Article  Google Scholar 

  73. Lago-Rivera D, Grandi S, Rakonjac J V, et al. Telecom-heralded entanglement between multimode solid-state quantum memories. Nature, 2021, 594: 37–40

    Article  Google Scholar 

  74. Liu X, Hu J, Li Z F, et al. Heralded entanglement distribution between two absorptive quantum memories. Nature, 2021, 594: 41–45

    Article  Google Scholar 

  75. Pu Y F, Zhang S, Wu Y K, et al. Experimental demonstration of memory-enhanced scaling for entanglement connection of quantum repeater segments. Nat Photon, 2021, 15: 374–378

    Article  Google Scholar 

  76. Cao Y, Zhao Y, Wang Q, et al. The evolution of quantum key distribution networks: on the road to the qinternet. IEEE Commun Surv Tut, 2022, 24: 839–894

    Article  Google Scholar 

  77. Sidhu J S, Joshi S K, Gündoğan M, et al. Advances in space quantum communications. IET Quantum Commun, 2021, 2: 182–217

    Article  Google Scholar 

  78. Belenchia A, Carlesso M, Bayraktar Ö, et al. Quantum physics in space. Phys Rep, 2022, 951: 1–70

    Article  Google Scholar 

  79. Neumann S P, Joshi S K, Fink M, et al. Q3Sat: quantum communications uplink to a 3U CubeSat-feasibility & design. EPJ Quantum Technol, 2018, 5: 4

    Article  Google Scholar 

  80. Knips L, Auer M, Baliuka A, et al. QUBE–towards quantum key distribution with small satellites. In: Proceedings of Quantum 2.0. Optica Publishing Group, 2022

  81. Kerstel E, Gardelein A, Barthelemy M, et al. Nanobob: a CubeSat mission concept for quantum communication experiments in an uplink configuration. EPJ Quantum Technol, 2018, 5: 6

    Article  Google Scholar 

  82. Dalibot C, Tustain S. The preliminary thermal design for the SPEQTRE CubeSat. In: Proceedings of International Conference on Environmental Systems, 2020

  83. Greenberger D M, Horne M A, Zeilinger A. Going beyond Bell’s theorem. In: Proceedings of Bell’s Theorem, Quantum Theory and Conceptions of the Universe, 1989. 69–72

  84. Dai W, Rinaldi A, Towsley D. Entanglement swapping in quantum switches: protocol design and stability analysis. 2021. ArXiv:2110.04116

  85. Nain P, Vardoyan G, Guha S, et al. On the analysis of a multipartite entanglement distribution switch. Proc ACM Meas Anal Comput Syst, 2020, 4: 1–39

    Article  Google Scholar 

  86. Vardoyan G, Nain P, Guha S, et al. On the capacity region of bipartite and tripartite entanglement switching. 2019. ArXiv:1901.06786

  87. Vardoyan G, Guha S, Nain P, et al. On the stochastic analysis of a quantum entanglement switch. SIGMETRICS Perform Eval Rev, 2019, 47: 27–29

    Article  Google Scholar 

  88. Lütkenhaus N, Jahma M. Quantum key distribution with realistic states: photon-number statistics in the photon-number splitting attack. New J Phys, 2002, 4: 44

    Article  Google Scholar 

  89. Eisaman M D, Fan J, Migdall A, et al. Invited review article: single-photon sources and detectors. Rev Sci Instrum, 2011, 82: 071101

    Article  Google Scholar 

  90. Migdall A, Polyakov S V, Fan J, et al. Single-photon Generation and Detection: Physics and Applications. New York: Academic Press, 2013

    Google Scholar 

  91. Senellart P, Solomon G, White A. High-performance semiconductor quantum-dot single-photon sources. Nat Nanotech, 2017, 12: 1026–1039

    Article  Google Scholar 

  92. Arakawa Y, Holmes M J. Progress in quantum-dot single photon sources for quantum information technologies: a broad spectrum overview. Appl Phys Rev, 2020, 7: 021309

    Article  Google Scholar 

  93. Strauf S, Stoltz N G, Rakher M T, et al. High-frequency single-photon source with polarization control. Nat Photon, 2007, 1: 704–708

    Article  Google Scholar 

  94. Shields A J. Semiconductor quantum light sources. Nat Photon, 2007, 1: 215–223

    Article  Google Scholar 

  95. Kim J, Benson O, Kan H, et al. A single-photon turnstile device. Nature, 1999, 397: 500–503

    Article  Google Scholar 

  96. Chu X L, Götzinger S, Sandoghdar V. A single molecule as a high-fidelity photon gun for producing intensity-squeezed light. Nat Photon, 2017, 11: 58–62

    Article  Google Scholar 

  97. De Martini F, Di Giuseppe G, Marrocco M. Single-mode generation of quantum photon states by excited single molecules in a microcavity trap. Phys Rev Lett, 1996, 76: 900–903

    Article  Google Scholar 

  98. Kako S, Santori C, Hoshino K, et al. A gallium nitride single-photon source operating at 200 K. Nat Mater, 2006, 5: 887–892

    Article  Google Scholar 

  99. Kuhn A, Hennrich M, Rempe G. Deterministic single-photon source for distributed quantum networking. Phys Rev Lett, 2002, 89: 067901

    Article  Google Scholar 

  100. Blinov B B, Moehring D L, Duan L M, et al. Observation of entanglement between a single trapped atom and a single photon. Nature, 2004, 428: 153–157

    Article  Google Scholar 

  101. Maurer C, Becher C, Russo C, et al. A single-photon source based on a single Ca+ ion. New J Phys, 2004, 6: 94

    Article  Google Scholar 

  102. Kurtsiefer C, Mayer S, Zarda P, et al. Stable solid-state source of single photons. Phys Rev Lett, 2000, 85: 290–293

    Article  Google Scholar 

  103. Babinec T M, Hausmann B J M, Khan M, et al. A diamond nanowire single-photon source. Nat Nanotech, 2010, 5: 195–199

    Article  Google Scholar 

  104. Alléaume R, Treussart F, Messin G, et al. Experimental open-air quantum key distribution with a single-photon source. New J Phys, 2004, 6: 92

    Article  Google Scholar 

  105. Pittman T B, Franson J D, Jacobs B C. Investigation of a single-photon source based on quantum interference. New J Phys, 2007, 9: 195

    Article  Google Scholar 

  106. Grangier P, Roger G, Aspect A. Experimental evidence for a photon anticorrelation effect on a beam splitter: a new light on single-photon interferences. Europhys Lett, 1986, 1: 173–179

    Article  Google Scholar 

  107. Hong C K, Mandel L. Experimental realization of a localized one-photon state. Phys Rev Lett, 1986, 56: 58–60

    Article  Google Scholar 

  108. Fasel S, Alibart O, Tanzilli S, et al. High-quality asynchronous heralded single-photon source at telecom wavelength. New J Phys, 2004, 6: 163

    Article  Google Scholar 

  109. Meyer-Scott E, Silberhorn C, Migdall A. Single-photon sources: approaching the ideal through multiplexing. Rev Sci Instrum, 2020, 91: 041101

    Article  Google Scholar 

  110. Wang H, Qin J, Ding X, et al. Boson sampling with 20 input photons and a 60-mode interferometer in a 60-mode interferometer in a 1014-dimensional Hilbert space. Phys Rev Lett, 2019, 123: 250503

    Article  Google Scholar 

  111. Thomas S, Senellart P. The race for the ideal single-photon source is on. Nat Nanotechnol, 2021, 16: 367–368

    Article  Google Scholar 

  112. Tomm N, Javadi A, Antoniadis N O, et al. A bright and fast source of coherent single photons. Nat Nanotechnol, 2021, 16: 399–403

    Article  Google Scholar 

  113. Wei Y, Liu S, Li X, et al. Tailoring solid-state single-photon sources with stimulated emissions. Nat Nanotechnol, 2022, 17: 470–476

    Article  Google Scholar 

  114. Hadfield R H. Single-photon detectors for optical quantum information applications. Nat Photon, 2009, 3: 696–705

    Article  Google Scholar 

  115. Komiyama S, Astafiev O, Antonov V, et al. A single-photon detector in the far-infrared range. Nature, 2000, 403: 405–407

    Article  Google Scholar 

  116. Cova S, Ghioni M, Lotito A, et al. Evolution and prospects for single-photon avalanche diodes and quenching circuits. J Modern Opt, 2004, 51: 1267–1288

    Article  Google Scholar 

  117. Rosfjord K M, Yang J K W, Dauler E A, et al. Nanowire single-photon detector with an integrated optical cavity and anti-reflection coating. Opt Express, 2006, 14: 527–534

    Article  Google Scholar 

  118. Takesue H, Diamanti E, Langrock C, et al. 1.5-µm single photon counting using polarization-independent up-conversion detector. Opt Express, 2006, 14: 13067–13072

    Article  Google Scholar 

  119. Peacock A, Verhoeve P, Rando N, et al. Single optical photon detection with a superconducting tunnel junction. Nature, 1996, 381: 135–137

    Article  Google Scholar 

  120. Rosenberg D, Lita A, Miller A, et al. Noise-free high-efficiency photon-number-resolving detectors. Phys Rev A, 2005, 71: 061803

    Article  Google Scholar 

  121. Fujiwara M, Sasaki M. Direct measurement of photon number statistics at telecom wavelengths using a charge integration photon detector. Appl Opt, 2007, 46: 3069–3074

    Article  Google Scholar 

  122. Gansen E J, Rowe M A, Greene M B, et al. Photon-number-discriminating detection using a quantum-dot, optically gated, field-effect transistor. Nat Photon, 2007, 1: 585–588

    Article  Google Scholar 

  123. Reddy D V, Nerem R R, Nam S W, et al. Superconducting nanowire single-photon detectors with 98% system detection efficiency at 1550 nm. Optica, 2020, 7: 1649–1653

    Article  Google Scholar 

  124. Korzh B, Zhao Q Y, Allmaras J P, et al. Demonstration of sub-3 ps temporal resolution with a superconducting nanowire single-photon detector. Nat Photon, 2020, 14: 250–255

    Article  Google Scholar 

  125. Lu C Y, Pan J W. Push-button photon entanglement. Nat Photon, 2014, 8: 174–176

    Article  Google Scholar 

  126. Burnham D C, Weinberg D L. Observation of simultaneity in parametric production of optical photon pairs. Phys Rev Lett, 1970, 25: 84–87

    Article  Google Scholar 

  127. Pan J W, Chen Z B, Lu C Y, et al. Multiphoton entanglement and interferometry. Rev Mod Phys, 2012, 84: 777–838

    Article  Google Scholar 

  128. Anwar A, Perumangatt C, Steinlechner F, et al. Entangled photon-pair sources based on three-wave mixing in bulk crystals. Rev Sci Instrum, 2021, 92: 041101

    Article  Google Scholar 

  129. Bock M, Lenhard A, Chunnilall C, et al. Highly efficient heralded single-photon source for telecom wavelengths based on a PPLN waveguide. Opt Express, 2016, 24: 23992–24001

    Article  Google Scholar 

  130. Aspect A, Grangier P, Roger G. Experimental tests of realistic local theories via Bell’s theorem. Phys Rev Lett, 1981, 47: 460–463

    Article  Google Scholar 

  131. Young R J, Stevenson R M, Atkinson P, et al. Improved fidelity of triggered entangled photons from single quantum dots. New J Phys, 2006, 8: 29

    Article  Google Scholar 

  132. Akopian N, Lindner N H, Poem E, et al. Entangled photon pairs from semiconductor quantum dots. Phys Rev Lett, 2006, 96: 130501

    Article  Google Scholar 

  133. Wang H, Hu H, Chung T H, et al. On-demand semiconductor source of entangled photons which simultaneously has high fidelity, efficiency, and indistinguishability. Phys Rev Lett, 2019, 122: 113602

    Article  Google Scholar 

  134. Hammerer K, Sørensen A S, Polzik E S. Quantum interface between light and atomic ensembles. Rev Mod Phys, 2010, 82: 1041–1093

    Article  Google Scholar 

  135. Stannigel K, Rabl P, Sørensen A S, et al. Optomechanical transducers for long-distance quantum communication. Phys Rev Lett, 2010, 105: 220501

    Article  Google Scholar 

  136. Lauk N, Sinclair N, Barzanjeh S, et al. Perspectives on quantum transduction. Quantum Sci Technol, 2020, 5: 020501

    Article  Google Scholar 

  137. Bochmann J, Vainsencher A, Awschalom D D, et al. Nanomechanical coupling between microwave and optical photons. Nat Phys, 2013, 9: 712–716

    Article  Google Scholar 

  138. Andrews R W, Peterson R W, Purdy T P, et al. Bidirectional and efficient conversion between microwave and optical light. Nat Phys, 2014, 10: 321–326

    Article  Google Scholar 

  139. Jiang W, Sarabalis C J, Dahmani Y D, et al. Efficient bidirectional piezo-optomechanical transduction between microwave and optical frequency. Nature Commun, 2020, 11: 1166

    Article  Google Scholar 

  140. Wang C H, Li F, Jiang L. Quantum capacities of transducers. Nat Commun, 2022, 13: 6698

    Article  Google Scholar 

  141. Higginbotham A P, Burns P S, Urmey M D, et al. Harnessing electro-optic correlations in an efficient mechanical converter. Nat Phys, 2018, 14: 1038–1042

    Article  Google Scholar 

  142. Han X, Fu W, Zou C L, et al. Microwave-optical quantum frequency conversion. Optica, 2021, 8: 1050–1064

    Article  Google Scholar 

  143. Julsgaard B, Kozhekin A, Polzik E S. Experimental long-lived entanglement of two macroscopic objects. Nature, 2001, 413: 400–403

    Article  Google Scholar 

  144. Chou C W, de Riedmatten H, Felinto D, et al. Measurement-induced entanglement for excitation stored in remote atomic ensembles. Nature, 2005, 438: 828–832

    Article  Google Scholar 

  145. Vernaz-Gris P, Huang K, Cao M, et al. Highly-efficient quantum memory for polarization qubits in a spatially-multiplexed cold atomic ensemble. Nat Commun, 2018, 9: 1–6

    Article  Google Scholar 

  146. Heller L, Farrera P, Heinze G, et al. Cold-atom temporally multiplexed quantum memory with cavity-enhanced noise suppression. Phys Rev Lett, 2020, 124: 210504

    Article  Google Scholar 

  147. Choi K S, Deng H, Laurat J, et al. Mapping photonic entanglement into and out of a quantum memory. Nature, 2008, 452: 67–71

    Article  Google Scholar 

  148. Usmani I, Clausen C, Bussieres F, et al. Heralded quantum entanglement between two crystals. Nat Photon, 2012, 6: 234–237

    Article  Google Scholar 

  149. Ortu A, Holzuapfel A, Etesse J, et al. Storage of photonic time-bin qubits for up to 20 ms in a rare-earth doped crystal. npj Quantum Inf, 2022, 8: 29

    Article  Google Scholar 

  150. Lvovsky A I, Sanders B C, Tittel W. Optical quantum memory. Nat Photon, 2009, 3: 706–714

    Article  Google Scholar 

  151. Simon C, Afzelius M, Appel J, et al. Quantum memories. Eur Phys J D, 2010, 58: 1–22

    Article  Google Scholar 

  152. Heshami K, England D G, Humphreys P C, et al. Quantum memories: emerging applications and recent advances. J Modern Opt, 2016, 63: 2005–2028

    Article  Google Scholar 

  153. Bussieres F, Sangouard N, Afzelius M, et al. Prospective applications of optical quantum memories. J Modern Opt, 2013, 60: 1519–1537

    Article  MathSciNet  MATH  Google Scholar 

  154. Novikova I, Walsworth R L, Xiao Y. Electromagnetically induced transparency-based slow and stored light in warm atoms. Laser Photon Rev, 2012, 6: 333–353

    Article  Google Scholar 

  155. Ma L, Slattery O, Tang X. Optical quantum memory based on electromagnetically induced transparency. J Opt, 2017, 19: 043001

    Article  Google Scholar 

  156. Wang Y, Li J, Zhang S, et al. Efficient quantum memory for single-photon polarization qubits. Nat Photon, 2019, 13: 346–351

    Article  Google Scholar 

  157. Ma L, Slattery O, Tang X. Optical quantum memory and its applications in quantum communication systems. J Res Natl Inst Stan, 2020, 125: 125002

    Article  Google Scholar 

  158. Zhu T X, Liu C, Jin M, et al. On-demand integrated quantum memory for polarization qubits. Phys Rev Lett, 2022, 128: 180501

    Article  Google Scholar 

  159. Stas P J, Huan Y Q, Machielse B, et al. Robust multi-qubit quantum network node with integrated error detection. Science, 2022, 378: 557–560

    Article  Google Scholar 

  160. Inagaki T, Matsuda N, Tadanaga O, et al. Entanglement distribution over 300 km of fiber. Opt Express, 2013, 21: 23241

    Article  Google Scholar 

  161. Yin H L, Chen T Y, Yu Z W, et al. Measurement-device-independent quantum key distribution over a 404 km optical fiber. Phys Rev Lett, 2016, 117: 190501

    Article  Google Scholar 

  162. Villoresi P, Jennewein T, Tamburini F, et al. Experimental verification of the feasibility of a quantum channel between space and Earth. New J Phys, 2008, 10: 033038

    Article  Google Scholar 

  163. Hughes R J, Nordholt J E. Quantum space race heats up. Nat Photon, 2017, 11: 456–458

    Article  Google Scholar 

  164. Buttler W T, Hughes R J, Kwiat P G, et al. Practical free-space quantum key distribution over 1 km. Phys Rev Lett, 1998, 81: 3283–3286

    Article  Google Scholar 

  165. Ma X S, Herbst T, Scheidl T, et al. Quantum teleportation over 143 kilometres using active feed-forward. Nature, 2012, 489: 269–273

    Article  Google Scholar 

  166. Steinlechner F, Ecker S, Fink M, et al. Distribution of high-dimensional entanglement via an intra-city free-space link. Nat Commun, 2017, 8: 1–7

    Article  Google Scholar 

  167. Valivarthi R, Puigibert M G, Zhou Q, et al. Quantum teleportation across a metropolitan fibre network. Nat Photon, 2016, 10: 676–680

    Article  Google Scholar 

  168. Sun Q C, Mao Y L, Chen S J, et al. Quantum teleportation with independent sources and prior entanglement distribution over a network. Nat Photon, 2016, 10: 671–675

    Article  Google Scholar 

  169. Pugh C J, Kaiser S, Bourgoin J P, et al. Airborne demonstration of a quantum key distribution receiver payload. Quantum Sci Technol, 2017, 2: 024009

    Article  Google Scholar 

  170. Wang J Y, Yang B, Liao S K, et al. Direct and full-scale experimental verifications towards ground-satellite quantum key distribution. Nat Photon, 2013, 7: 387–393

    Article  Google Scholar 

  171. Liu H Y, Tian X H, Gu C, et al. Drone-based entanglement distribution towards mobile quantum networks. Natl Sci Rev, 2020, 7: 921–928

    Article  Google Scholar 

  172. Ren J G, Xu P, Yong H L, et al. Ground-to-satellite quantum teleportation. Nature, 2017, 549: 70–73

    Article  Google Scholar 

  173. Liao S K, Cai W Q, Handsteiner J, et al. Satellite-relayed intercontinental quantum network. Phys Rev Lett, 2018, 120: 030501

    Article  Google Scholar 

  174. Pirandola S, Laurenza R, Ottaviani C, et al. Fundamental limits of repeaterless quantum communications. Nat Commun, 2017, 8: 1–5

    Article  Google Scholar 

  175. Pirandola S. Capacities of repeater-assisted quantum communications. 2016. ArXiv:1601.00966

  176. Wang X, Fang K, Tomamichel M. On Converse bounds for classical communication over quantum channels. IEEE Trans Inform Theory, 2019, 65: 4609–4619

    Article  MathSciNet  MATH  Google Scholar 

  177. Wang X, Fang K, Duan R. Semidefinite programming converse bounds for quantum communication. IEEE Trans Inform Theory, 2018, 65: 2583–2592

    Article  MathSciNet  MATH  Google Scholar 

  178. Fang K, Fawzi H. Geometric Renyi divergence and its applications in quantum channel capacities. Commun Math Phys, 2021, 384: 1615–1677

    Article  MATH  Google Scholar 

  179. Fang K, Gour G, Wang X. Towards the ultimate limits of quantum channel discrimination. 2021. ArXiv:2110.14842

  180. Fawzi H, Fawzi O. Defining quantum divergences via convex optimization. Quantum, 2021, 5: 387

    Article  Google Scholar 

  181. Fawzi O, Shayeghi A, Ta H. A hierarchy of efficient bounds on quantum capacities exploiting symmetry. IEEE Trans Inform Theory, 2022, 68: 7346–7360

    Article  MathSciNet  Google Scholar 

  182. Wang X, Xie W, Duan R. Semidefinite programming converse bounds for classical communication over quantum channels. In: Proceedings of IEEE International Symposium on Information Theory (ISIT), 2017. 1728–1732

  183. Fang K, Wang X, Tomamichel M, et al. Quantum channel simulation and the channel’s smooth max-information. IEEE Trans Inform Theory, 2019, 66: 2129–2140

    Article  MathSciNet  MATH  Google Scholar 

  184. Fang K, Fawzi O, Renner R, et al. Chain rule for the quantum relative entropy. Phys Rev Lett, 2020, 124: 100501

    Article  MathSciNet  Google Scholar 

  185. Dahlberg A, Skrzypczyk M, Coopmans T, et al. A link layer protocol for quantum networks. In: Proceedings of the ACM Special Interest Group on Data Communication, 2019. 159–173

  186. Kozlowski W, Dahlberg A, Wehner S. Designing a quantum network protocol. In: Proceedings of the 16th International Conference on Emerging Networking Experiments and Technologies, 2020. 1–16

  187. Illiano J, Caleffi M, Manzalini A, et al. Quantum internet protocol stack: a comprehensive survey. Comput Netw, 2022, 213: 109092

    Article  Google Scholar 

  188. DiAdamo S, Qi B, Miller G, et al. Packet switching in quantum networks: a path to quantum internet. 2022. ArXiv:2205.07507

  189. Pirker A, Wallnoüfer J, Duür W. Modular architectures for quantum networks. New J Phys, 2018, 20: 053054

    Article  MathSciNet  Google Scholar 

  190. Zhang H, Li Y, Zhang C, et al. Connection-oriented and connectionless quantum internet considering quantum repeaters. 2022, ArXiv:2208.03930

  191. Zwerger M, Duür W, Briegel H J. Measurement-based quantum repeaters. Phys Rev A, 2012, 85: 062326

    Article  Google Scholar 

  192. Zwerger M, Briegel H J, Duür W. Measurement-based quantum communication. Appl Phys B, 2016, 122: 1–5

    Article  Google Scholar 

  193. Cerf V, Kahn R. A protocol for packet network intercommunication. IEEE Trans Commun, 1974, 22: 637–648

    Article  MATH  Google Scholar 

  194. Boschi D, Branca S, De Martini F, et al. Experimental realization of teleporting an unknown pure quantum state via dual classical and Einstein-Podolsky-Rosen channels. Phys Rev Lett, 1998, 80: 1121–1125

    Article  MathSciNet  MATH  Google Scholar 

  195. Bouwmeester D, Pan J W, Mattle K, et al. Experimental quantum teleportation. Nature, 1997, 390: 575–579

    Article  MATH  Google Scholar 

  196. Pirandola S, Eisert J, Weedbrook C, et al. Advances in quantum teleportation. Nat Photon, 2015, 9: 641–652

    Article  Google Scholar 

  197. Liu S, Lou Y, Jing J. Orbital angular momentum multiplexed deterministic all-optical quantum teleportation. Nat Commun, 2020, 11: 3875

    Article  Google Scholar 

  198. Ursin R, Jennewein T, Aspelmeyer M, et al. Quantum teleportation across the Danube. Nature, 2004, 430: 849

    Article  Google Scholar 

  199. Riebe M, Hüffner H, Roos C F, et al. Deterministic quantum teleportation with atoms. Nature, 2004, 429: 734–737

    Article  Google Scholar 

  200. Leuenberger M N, Flatte M E, Awschalom D D. Teleportation of electronic many-qubit states encoded in the electron spin of quantum dots via single photons. Phys Rev Lett, 2005, 94: 107401

    Article  Google Scholar 

  201. Zukowski M, Zeilinger A, Horne M A, et al. ‘Event-ready-detectors’ Bell experiment via entanglement swapping. Phys Rev Lett, 1993, 71: 4287–4290

    Article  Google Scholar 

  202. Pan J W, Bouwmeester D, Weinfurter H, et al. Experimental entanglement swapping: entangling photons that never interacted. Phys Rev Lett, 1998, 80: 3891–3894

    Article  MathSciNet  MATH  Google Scholar 

  203. Kaltenbaek R, Prevedel R, Aspelmeyer M, et al. High-fidelity entanglement swapping with fully independent sources. Phys Rev A, 2009, 79: 040302

    Article  Google Scholar 

  204. Jennewein T, Weihs G, Pan J W, et al. Experimental nonlocality proof of quantum teleportation and entanglement swapping. Phys Rev Lett, 2001, 88: 017903

    Article  Google Scholar 

  205. de Riedmatten H, Marcikic I, van Houwelingen J A W, et al. Long-distance entanglement swapping with photons from separated sources. Phys Rev A, 2005, 71: 050302

    Article  Google Scholar 

  206. Wu Q L, Namekata N, Inoue S. High-fidelity entanglement swapping at telecommunication wavelengths. J Phys B-At Mol Opt Phys, 2013, 46: 235503

    Article  Google Scholar 

  207. Halder M, Beveratos A, Gisin N, et al. Entangling independent photons by time measurement. Nat Phys, 2007, 3: 692–695

    Article  Google Scholar 

  208. Xue Y, Yoshizawa A, Tsuchida H. Polarization-based entanglement swapping at the telecommunication wavelength using spontaneous parametric down-conversion photon-pair sources. Phys Rev A, 2012, 85: 032337

    Article  Google Scholar 

  209. Takesue H, Miquel B. Entanglement swapping using telecom-band photons generated in fibers. Opt Express, 2009, 17: 10748–10756

    Article  Google Scholar 

  210. Sun Q C, Jiang Y F, Mao Y L, et al. Field test of entanglement swapping over 100-km optical fiber with independent 1-GHz-clock sequential time-bin entangled photon-pair sources. 2017. ArXiv:1704.03960

  211. Huang C X, Hu X M, Guo Y, et al. Entanglement swapping and quantum correlations via symmetric joint measurements. Phys Rev Lett, 2022, 129: 030502

    Article  Google Scholar 

  212. Liu S, Lou Y, Chen Y, et al. All-optical entanglement swapping. Phys Rev Lett, 2022, 128: 060503

    Article  Google Scholar 

  213. van Meter R, Satoh T, Ladd T D, et al. Path selection for quantum repeater networks. NetwSci, 2013, 3: 82–95

    Google Scholar 

  214. Caleffi M. Optimal routing for quantum networks. IEEE Access, 2017, 5: 22299–22312

    Article  Google Scholar 

  215. Schoute E, Mancinska L, Islam T, et al. Shortcuts to quantum network routing. 2016. ArXiv:1610.05238

  216. Bugalho L, Coutinho B C, Monteiro F A, et al. Distributing multipartite entanglement over noisy quantum networks. 2021. ArXiv:2103.14759

  217. Gyongyosi L, Imre S. Decentralized base-graph routing for the quantum internet. Phys Rev A, 2018, 98: 022310

    Article  Google Scholar 

  218. Gyongyosi L, Imre S. Entanglement-gradient routing for quantum networks. Sci Rep, 2017, 7: 14255

    Article  Google Scholar 

  219. Chakraborty K, Rozpedek F, Dahlberg A, et al. Distributed routing in a quantum internet. 2019. ArXiv:1907.11630

  220. Perseguers S, LapeyreJr G J, Cavalcanti D, et al. Distribution of entanglement in large-scale quantum networks. Rep Prog Phys, 2013, 76: 096001

    Article  MathSciNet  Google Scholar 

  221. Hahn F, Pappa A, Eisert J. Quantum network routing and local complementation. npj Quantum Inf, 2019, 5: 76

    Article  Google Scholar 

  222. Pant M, Krovi H, Towsley D, et al. Routing entanglement in the quantum internet. npj Quantum Inf, 2019, 5: 1–9

    Article  Google Scholar 

  223. Shi S, Qian C. Concurrent entanglement routing for quantum networks: model and designs. In: Proceedings of the Annual Conference of the ACM Special Interest Group on Data Communication on the Applications, Technologies, Architectures, and Protocols for Computer Communication, 2020. 62–65

  224. Bennett C H, Wiesner S J. Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states. Phys Rev Lett, 1992, 69: 2881–2884

    Article  MathSciNet  MATH  Google Scholar 

  225. Bennett C H, DiVincenzo D P, Smolin J A, et al. Mixed-state entanglement and quantum error correction. Phys Rev A, 1996, 54: 3824–3851

    Article  MathSciNet  MATH  Google Scholar 

  226. Bennett C H, Brassard G, Popescu S, et al. Purification of noisy entanglement and faithful teleportation via noisy channels. Phys Rev Lett, 1996, 76: 722–725

    Article  Google Scholar 

  227. Deutsch D, Ekert A, Jozsa R, et al. Quantum privacy amplification and the security of quantum cryptography over noisy channels. Phys Rev Lett, 1996, 77: 2818–2821

    Article  Google Scholar 

  228. Buscemi F, Datta N. Distilling entanglement from arbitrary resources. J Math Phys, 2010, 51: 102201

    Article  MathSciNet  MATH  Google Scholar 

  229. Brandao F G S L, Datta N. One-shot rates for entanglement manipulation under non-entangling maps. IEEE Trans Inform Theory, 2011, 57: 1754–1760

    Article  MathSciNet  MATH  Google Scholar 

  230. Datta N, Leditzky F. Second-order asymptotics for source coding, dense coding, and pure-state entanglement conversions. IEEE Trans Inform Theory, 2015, 61: 582–608

    Article  MathSciNet  MATH  Google Scholar 

  231. Rozpedek F, Schiet T, Thinh L P, et al. Optimizing practical entanglement distillation. Phys Rev A, 2018, 97: 062333

    Article  Google Scholar 

  232. Fang K, Liu Z W. No-go theorems for quantum resource purification: new approach and channel theory. PRX Quantum, 2022, 3: 010337

    Article  Google Scholar 

  233. Regula B, Fang K, Wang X, et al. One-shot entanglement distillation beyond local operations and classical communication. New J Phys, 2019, 21: 103017

    Article  MathSciNet  Google Scholar 

  234. Fang K, Wang X, Tomamichel M, et al. Non-asymptotic entanglement distillation. IEEE Trans Inform Theory, 2019, 65: 6454–6465

    Article  MathSciNet  MATH  Google Scholar 

  235. Zhao X, Zhao B, Wang Z, et al. Practical distributed quantum information processing with LOCCNet. npj Quantum Inf, 2021, 7: 159

    Article  Google Scholar 

  236. Fang K, Fawzi H. The sum-of-squares hierarchy on the sphere and applications in quantum information theory. Math Program, 2021, 190: 331–360

    Article  MathSciNet  MATH  Google Scholar 

  237. Regula B, Takagi R. Fundamental limitations on distillation of quantum channel resources. Nat Commun, 2021, 12: 4411

    Article  Google Scholar 

  238. Zhang H, Xu X, Zhang C, et al. Variational quantum circuit learning of entanglement purification in multi-degree-of-freedom. 2022. ArXiv:2209.08306

  239. Fang K, Liu Z W. No-go theorems for quantum resource purification. Phys Rev Lett, 2020, 125: 060405

    Article  MathSciNet  Google Scholar 

  240. Kalb N, Reiserer A A, Humphreys P C, et al. Entanglement distillation between solid-state quantum network nodes. Science, 2017, 356: 928–932

    Article  MathSciNet  MATH  Google Scholar 

  241. Abdelkhalek D, Syllwasschy M, Cerf N J, et al. Efficient entanglement distillation without quantum memory. Nat Commun, 2016, 7: 1–7

    Article  Google Scholar 

  242. Ecker S, Sohr P, Bulla L, et al. Experimental single-copy entanglement distillation. Phys Rev Lett, 2021, 127: 040506

    Article  Google Scholar 

  243. Gottesman D. Stabilizer codes and quantum error correction. 1997. ArXiv:quant-ph/9705052

  244. Gaitan F. Quantum Error Correction and Fault Tolerant Quantum Computing. Boca Raton: CRC Press, 2008

    MATH  Google Scholar 

  245. Lidar D A, Brun T A. Quantum Error Correction. Cambridge: Cambridge University Press, 2013

    Book  Google Scholar 

  246. Terhal B M. Quantum error correction for quantum memories. Rev Mod Phys, 2015, 87: 307–346

    Article  MathSciNet  Google Scholar 

  247. Suter D, Álvarez G A. Colloquium: protecting quantum information against environmental noise. Rev Mod Phys, 2016, 88: 041001

    Article  MathSciNet  Google Scholar 

  248. Ofek N, Petrenko A, Heeres R, et al. Extending the lifetime of a quantum bit with error correction in superconducting circuits. Nature, 2016, 536: 441–445

    Article  Google Scholar 

  249. Linke N M, Gutierrez M, Landsman K A, et al. Fault-tolerant quantum error detection. Sci Adv, 2017, 3: e1701074

    Article  Google Scholar 

  250. Wootton J R, Loss D. Repetition code of 15 qubits. Phys Rev A, 2018, 97: 052313

    Article  Google Scholar 

  251. Harper R, Flammia S T. Fault-tolerant logical gates in the IBM quantum experience. Phys Rev Lett, 2019, 122: 080504

    Article  Google Scholar 

  252. Livingston W P, Blok M S, Flurin E, et al. Experimental demonstration of continuous quantum error correction. Nat Commun, 2022, 13: 2307

    Article  Google Scholar 

  253. Rivest R L, Shamir A, Adleman L. A method for obtaining digital signatures and public-key cryptosystems. Commun ACM, 1978, 21: 120–126

    Article  MathSciNet  MATH  Google Scholar 

  254. Shor P. Algorithms for quantum computation: discrete logarithms and factoring. In: Proceedings of the 35th Annual Symposium on Foundations of Computer Science, 1994. 124–134

  255. Travagnin M, Lewis A. Quantum Key Distribution In-field Implementations. EUR 29865 EN, Publications Office of the European Union. 2019

  256. Zhang Q, Xu F, Chen Y A, et al. Large scale quantum key distribution: challenges and solutions [Invited]. Opt Express, 2018, 26: 24260

    Article  Google Scholar 

  257. Hwang W Y. Quantum key distribution with high loss: toward global secure communication. Phys Rev Lett, 2003, 91: 057901

    Article  Google Scholar 

  258. Wang X B. Beating the photon-number-splitting attack in practical quantum cryptography. Phys Rev Lett, 2005, 94: 230503

    Article  Google Scholar 

  259. Lo H K, Ma X, Chen K. Decoy state quantum key distribution. Phys Rev Lett, 2005, 94: 230504

    Article  Google Scholar 

  260. Lo H K, Curty M, Qi B. Measurement-device-independent quantum key distribution. Phys Rev Lett, 2012, 108: 130503

    Article  Google Scholar 

  261. Zhang G W, Chen W, Fan-Yuan G J, et al. Polarization-insensitive quantum key distribution using planar lightwave circuit chips. Sci China Inf Sci, 2022, 65: 200506

    Article  Google Scholar 

  262. Xu F, Ma X, Zhang Q, et al. Secure quantum key distribution with realistic devices. Rev Mod Phys, 2020, 92: 025002

    Article  MathSciNet  Google Scholar 

  263. Pirandola S, Andersen U L, Banchi L, et al. Advances in quantum cryptography. Adv Opt Photon, 2020, 12: 1012

    Article  Google Scholar 

  264. George I, Lin J, van Himbeeck T, et al. Finite-key analysis of quantum key distribution with characterized devices using entropy accumulation. 2022. ArXiv:2203.06554

  265. Lucamarini M, Yuan Z L, Dynes J F, et al. Overcoming the rate-distance limit of quantum key distribution without quantum repeaters. Nature, 2018, 557: 400–403

    Article  Google Scholar 

  266. Wang S, Yin Z Q, He D Y, et al. Twin-field quantum key distribution over 830-km fibre. Nat Photon, 2022, 16: 154–161

    Article  Google Scholar 

  267. Ren S, Wang Y, Su X. Hybrid quantum key distribution network. Sci China Inf Sci, 2022, 65: 200502

    Article  MathSciNet  Google Scholar 

  268. Fitzsimons J F. Private quantum computation: an introduction to blind quantum computing and related protocols. npj Quantum Inf, 2017, 3: 23

    Article  Google Scholar 

  269. Morimae T, Koshiba T. Impossibility of perfectly-secure one-round delegated quantum computing for classical client. Quantum Inform Comput, 2019, 19: 214–221

    Article  MathSciNet  Google Scholar 

  270. Aaronson S, Cojocaru A, Gheorghiu A, et al. Complexity-theoretic limitations on blind delegated quantum computation. 2017. ArXiv:1704.08482

  271. Mantri A, Demarie T F, Fitzsimons J F. Universality of quantum computation with cluster states and (X, Y)-plane measurements. Sci Rep, 2017, 7: 42861

    Article  Google Scholar 

  272. Morimae T, Fujii K. Blind quantum computation protocol in which Alice only makes measurements. Phys Rev A, 2013, 87: 050301

    Article  Google Scholar 

  273. Shan R T, Chen X, Yuan K G. Multi-party blind quantum computation protocol with mutual authentication in network. Sci China Inf Sci, 2021, 64: 162302

    Article  MathSciNet  Google Scholar 

  274. Reichardt B W, Unger F, Vazirani U. Classical command of quantum systems. Nature, 2013, 496: 456–460

    Article  Google Scholar 

  275. McKague M. Interactive proofs for BQP via self-tested graph states. Theor Comput, 2016, 12: 1–42

    Article  MathSciNet  MATH  Google Scholar 

  276. Barz S, Kashefi E, Broadbent A, et al. Demonstration of blind quantum computing. Science, 2012, 335: 303–308

    Article  MathSciNet  MATH  Google Scholar 

  277. Huang H L, Zhao Q, Ma X, et al. Experimental blind quantum computing for a classical client. Phys Rev Lett, 2017, 119: 050503

    Article  Google Scholar 

  278. Greganti C, Roehsner M C, Barz S, et al. Demonstration of measurement-only blind quantum computing. New J Phys, 2016, 18: 013020

    Article  Google Scholar 

  279. Lynch N A. Distributed Algorithms. San Francisco: Morgan Kaufmann Publishers Inc., 1996

    MATH  Google Scholar 

  280. Tani S, Kobayashi H, Matsumoto K. Exact quantum algorithms for the leader election problem. ACM Trans Comput Theory, 2012, 4: 1–24

    Article  MATH  Google Scholar 

  281. Angluin D. Local and global properties in networks of processors (extended abstract). In: Proceedings of the 12th Annual ACM Symposium on Theory of Computing, 1980. 82–83

  282. Itai A, Rodeh M. Symmetry breaking in distributed networks. Inf Comput, 1990, 88: 60–87

    Article  MathSciNet  MATH  Google Scholar 

  283. Yamashita M, Kameda T. Computing on anonymous networks. I. Characterizing the solvable cases. IEEE Trans Parallel Distrib Syst, 1996, 7: 69–89

    Article  Google Scholar 

  284. Kobayashi H, Matsumoto K, Tani S. Simpler exact leader election via quantum reduction. Chicago J Theor Comp Sci, 2014, 20: 1–31

    Article  MathSciNet  MATH  Google Scholar 

  285. Okubo Y, Wang X B, Jiang Y K, et al. Experimental demonstration of quantum leader election in linear optics. Phys Rev A, 2008, 77: 032343

    Article  Google Scholar 

  286. van Meter R, Nemoto K, Munro W. Communication links for distributed quantum computation. IEEE Trans Comput, 2007, 56: 1643–1653

    Article  MathSciNet  MATH  Google Scholar 

  287. Buhrman H, Ruohrig H. Distributed quantum computing. In: Mathematical Foundations of Computer Science. Berlin: Springer, 2003

    Book  Google Scholar 

  288. van Meter R, Devitt S J. The path to scalable distributed quantum computing. Computer, 2016, 49: 31–42

    Article  Google Scholar 

  289. Beals R, Brierley S, Gray O, et al. Efficient distributed quantum computing. Proc R Soc A, 2013, 469: 20120686

    Article  MathSciNet  MATH  Google Scholar 

  290. Bravyi S, Dial O, Gambetta J M, et al. The future of quantum computing with superconducting qubits. J Appl Phys, 2022, 132: 160902

    Article  Google Scholar 

  291. Piveteau C, Sutter D. Circuit knitting with classical communication. 2022. ArXiv:2205.00016

  292. DiAdamo S, Ghibaudi M, Cruise J. Distributed quantum computing and network control for accelerated VQE. IEEE Trans Quantum Eng, 2021, 2: 1–21

    Google Scholar 

  293. Parekh R, Ricciardi A, Darwish A, et al. Quantum algorithms and simulation for parallel and distributed quantum computing. 2022. ArXiv:2106.06841

  294. Haner T, Steiger D S, Hoefler T, et al. Distributed quantum computing with QMPI. In: Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis, 2021. 1–13

  295. Ferrari D, Cacciapuoti A S, Amoretti M, et al. Compiler design for distributed quantum computing. IEEE Trans Quantum Eng, 2021, 2: 1–20

    Article  Google Scholar 

  296. Eisert J, Jacobs K, Papadopoulos P, et al. Optimal local implementation of nonlocal quantum gates. Phys Rev A, 2000, 62: 052317

    Article  Google Scholar 

  297. Gottesman D, Chuang I L. Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations. Nature, 1999, 402: 390–393

    Article  Google Scholar 

  298. Chou K S, Blumoff J Z, Wang C S, et al. Deterministic teleportation of a quantum gate between two logical qubits. Nature, 2018, 561: 368–373

    Article  Google Scholar 

  299. Wan Y, Kienzler D, Erickson S D, et al. Quantum gate teleportation between separated qubits in a trapped-ion processor. Science, 2019, 364: 875–878

    Article  Google Scholar 

  300. Daiss S, Langenfeld S, Welte S, et al. A quantum-logic gate between distant quantum-network modules. Science, 2021, 371: 614–617

    Article  Google Scholar 

  301. Cleve R, Dam W V, Nielsen M, et al. Quantum entanglement and the communication complexity of the inner product function. In: Proceedings of NASA International Conference on Quantum Computing and Quantum Communications, 1998. 61–74

  302. Buhrman H, Cleve R, Wigderson A. Quantum vs. classical communication and computation. In: Proceedings of the 30th Annual ACM Symposium on Theory of Computing, 1998. 63–68

  303. Anshu A, Touchette D, Yao P, et al. Exponential separation of quantum communication and classical information. In: Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing, 2017. 277–288

  304. Brukner C, Zukowski M, Pan J W, et al. Bell’s inequalities and quantum communication complexity. Phys Rev Lett, 2004, 92: 127901

    Article  MathSciNet  MATH  Google Scholar 

  305. Wei K, Tischler N, Zhao S R, et al. Experimental quantum switching for exponentially superior quantum communication complexity. Phys Rev Lett, 2019, 122: 120504

    Article  Google Scholar 

  306. Buhrman H, Cleve R, Watrous J, et al. Quantum fingerprinting. Phys Rev Lett, 2001, 87: 167902

    Article  Google Scholar 

  307. Zhong X, Xu F, Lo H K, et al. Efficient experimental quantum fingerprinting with channel multiplexing and simultaneous detection. Nat Commun, 2021, 12: 4464

    Article  Google Scholar 

  308. Einstein A. Zur elektrodynamik bewegter Kuorper. Ann Phys, 1905, 322: 891–921

    Article  MATH  Google Scholar 

  309. Eddington A S. The Mathematical Theory of Relativity. Cambridge: Cambridge University Press, 1923

    MATH  Google Scholar 

  310. Yurtsever U, Dowling J P. Lorentz-invariant look at quantum clock-synchronization protocols based on distributed entanglement. Phys Rev A, 2002, 65: 052317

    Article  Google Scholar 

  311. Krčo M, Paul P. Quantum clock synchronization: multiparty protocol. Phys Rev A, 2002, 66: 024305

    Article  MathSciNet  Google Scholar 

  312. Ben-Av R, Exman I. Optimized multiparty quantum clock synchronization. Phys Rev A, 2011, 84: 014301

    Article  Google Scholar 

  313. Kómár P, Kessler E M, Bishof M, et al. A quantum network of clocks. Nat Phys, 2014, 10: 582–587

    Article  Google Scholar 

  314. Quan R, Zhai Y, Wang M, et al. Demonstration of quantum synchronization based on second-order quantum coherence of entangled photons. Sci Rep, 2016, 6: 30453

    Article  Google Scholar 

  315. Giovannetti V, Lloyd S, Maccone L. Quantum-enhanced positioning and clock synchronization. Nature, 2001, 412: 417–419

    Article  Google Scholar 

  316. Valencia A, Scarcelli G, Shih Y. Distant clock synchronization using entangled photon pairs. Appl Phys Lett, 2004, 85: 2655–2657

    Article  Google Scholar 

  317. Kong X, Xin T, Wei S, et al. Implementation of multiparty quantum clock synchronization. 2017. ArXiv:1708.06050

  318. Lee J, Shen L, Cere A, et al. Symmetrical clock synchronization with time-correlated photon pairs. Appl Phys Lett, 2019, 114: 101102

    Article  Google Scholar 

  319. Troupe J, Haldar S, Agullo I, et al. Quantum clock synchronization for future NASA deep space quantum links and fundamental science. 2022. ArXiv:2209.15122

  320. Lawson P. Principles of long baseline stellar interferometry. JPL, 2000. https://hdl.handle.net/1813/41240

  321. Zernike F. The concept of degree of coherence and its application to optical problems. Physica, 1938, 5: 785–795

    Article  Google Scholar 

  322. Khabiboulline E T, Borregaard J, De Greve K, et al. Optical interferometry with quantum networks. Phys Rev Lett, 2019, 123: 070504

    Article  Google Scholar 

  323. Khabiboulline E T, Borregaard J, De Greve K, et al. Quantum-assisted telescope arrays. Phys Rev A, 2019, 100: 022316

    Article  Google Scholar 

  324. Cacciapuoti A S, Caleffi M, Tafuri F, et al. Quantum internet: networking challenges in distributed quantum computing. IEEE Netw, 2020, 34: 137–143

    Article  Google Scholar 

  325. Satoh T, Nagayama S, Suzuki S, et al. Attacking the quantum internet. IEEE Trans Quantum Eng, 2021, 2: 1–17

    Article  Google Scholar 

  326. Bernstein D J, Lange T. Post-quantum cryptography. Nature, 2017, 549: 188–194

    Article  Google Scholar 

  327. Wang J, Liu L, Lyu S, et al. Quantum-safe cryptography: crossroads of coding theory and cryptography. Sci China Inf Sci, 2022, 65: 111301

    Article  MathSciNet  Google Scholar 

  328. Huang Y, Zhang F, Liu Z, et al. Pseudorandom number generator based on supersingular elliptic curve isogenies. Sci China Inf Sci, 2022, 65: 159101

    Article  Google Scholar 

  329. Tao Y, Ji Y, Zhang R. Generalizing Lyubashevsky-Wichs trapdoor sampler for NTRU lattices. Sci China Inf Sci, 2022, 65: 159103

    Article  MathSciNet  Google Scholar 

  330. Liu J, Yu Y, Bi H, et al. Post quantum secure fair data trading with deterability based on machine learning. Sci China Inf Sci, 2022, 65: 170308

    Article  Google Scholar 

  331. Bavdekar R, Chopde E J, Agrawal A, et al. Post quantum cryptography: a review of techniques, challenges and standardizations. In: Proceedings of International Conference on Information Networking (ICOIN), 2023. 146–151

  332. Wehrle K, Günes M, Gross J. Modeling and Tools for Network Simulation. Berlin: Springer, 2010

    Book  MATH  Google Scholar 

  333. Baidu Quantum. QNET. 2022. Official website at https://quantum-hub.baidu.com/qnet/, Source code available at https://github.com/baidu/QCompute/tree/master/Extensions/QuantumNetwork

  334. Deutsch D E. Quantum computational networks. Proc Royal Soc London A, 1989, 425: 73–90

    MathSciNet  MATH  Google Scholar 

  335. Barenco A, Bennett C H, Cleve R, et al. Elementary gates for quantum computation. Phys Rev A, 1995, 52: 3457–3467

    Article  Google Scholar 

  336. Morimae T. Verification for measurement-only blind quantum computing. Phys Rev A, 2014, 89: 060302

    Article  Google Scholar 

  337. Li X, Fang K. Methods, devices and electronic apparatus for quantum computing. Patent No. CN202210324719.5, 2022

  338. Fang K, Li X. Method and device for operating quantum system of one-way quantum computer calculation model. Patent No. CN202210858691.3, 2022

  339. Fang K, Zhao J. Methods, devices and electronic apparatus for simulating quantum network protocols. Patent No. CN202210885409.0, 2022

  340. Dahlberg A, van der Vecht B, Donne C D, et al. NetQASM-a low-level instruction set architecture for hybrid quantum-classical programs in a quantum internet. Quantum Sci Technol, 2022, 7: 035023

    Article  Google Scholar 

  341. Fang K, Li Y. Request processing methods, apparatus and electronic device. Patent No. CN2022114860192, 2022

  342. Fang K, Li Y. Quantum key distribution method, apparatus and electronic device. Patent No. CN2022114862164, 2022

  343. Clauser J F, Horne M A, Shimony A, et al. Proposed experiment to test local hidden-variable theories. Phys Rev Lett, 1969, 23: 880–884

    Article  MATH  Google Scholar 

  344. Montanaro A, de Wolf R. A survey of quantum property testing. 2013. ArXiv:1310.2035

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Acknowledgements

We would like to thank Yu-Ao CHEN, Shusen LIU, Jingbo WANG, Kun WANG, Xin WANG, and Zihe WANG for discussions on the development of QNET. We also thank Jie LIN for suggesting relevant references on single-photon sources and detectors.

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  1. Institute for Quantum Computing, Baidu Research, Beijing, 100193, China

    Kun Fang, Jingtian Zhao, Xiufan Li, Yifei Li & Runyao Duan

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  1. Kun Fang
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  2. Jingtian Zhao
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  3. Xiufan Li
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Correspondence to Kun Fang or Runyao Duan.

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Fang, K., Zhao, J., Li, X. et al. Quantum NETwork: from theory to practice. Sci. China Inf. Sci. 66, 180509 (2023). https://doi.org/10.1007/s11432-023-3773-4

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