Advertisement

Time-Multiplexed Methods for Optical Quantum Information Processing

  • Michelle VictoraEmail author
  • Fumihiro Kaneda
  • Fedor Bergmann
  • Jia Jun Wong
  • Austin Graf
  • Paul KwiatEmail author
Chapter
Part of the Springer Series in Optical Sciences book series (SSOS, volume 217)

Abstract

Quantum information processing with photons can be greatly enhanced by incorporating time-multiplexing methods. Not only can time-bin encoding be very useful in its own right, multiplexing techniques can lead to more efficient single- and multi-photon sources, improved detectors, and high-bandwidth quantum memories, as well as enhanced applications such as quantum random walks and entanglement swapping. Here we present an overview of some of the methods used and the results achievable when explicitly using the time degree of freedom of photons.

References

  1. 1.
    T. Pittman, It’s a good time for time-bin qubits. Physics 6, 110 (2013)CrossRefGoogle Scholar
  2. 2.
    T.M. Graham, J.T. Barreiro, M. Mohseni, P.G. Kwiat, Hyperentanglement-enabled direct characterization of quantum dynamics. Phys. Rev. Lett. 110, 060404 (2013)ADSCrossRefGoogle Scholar
  3. 3.
    M.D. Eisaman, J. Fan, A. Migdall, S.V. Polyakov, Invited review article: single-photon sources and detectors. Rev. Sci. Instrum. 82, 071101 (2011)ADSCrossRefGoogle Scholar
  4. 4.
    J. McKeever, A. Boca, A.D. Boozer, R. Miller, J.R. Buck, Deterministic generation of single photons from one atom trapped in a cavity. Science 303, 1992–1994 (2004)ADSCrossRefGoogle Scholar
  5. 5.
    M. Hijlkema, B. Weber, H.P. Specht et al., A single-photon server with just one atom. Nat. Phys. 3, 253–255 (2007)CrossRefGoogle Scholar
  6. 6.
    M. Keller, B. Lange, K. Hayasaka, W. Lange, H. Walther, Continuous generation of single photons with controlled waveform in an ion-trap cavity system. Nature 431, 1075–1078 (2004)ADSCrossRefGoogle Scholar
  7. 7.
    P. Michler, A. Kiraz, C. Becher et al., A quantum dot single-photon turnstile device. Science 290, 2282–2285 (2000)ADSCrossRefGoogle Scholar
  8. 8.
    A.J. Bennett, D.C. Unitt, P. Atkinson et al., High performance single photon sources from photolithographically defined pillar microcavities. Opt. Express 13, 50–55 (2005)ADSCrossRefGoogle Scholar
  9. 9.
    A. Beveratos, R. Brouri, T. Gacoin et al., Single photon quantum cryptography. Phys. Rev. Lett. 89, 187901 (2002)ADSCrossRefGoogle Scholar
  10. 10.
    N. Mizuochi, T. Makino, H. Kato et al., Electrically driven single-photon source at room temperature in diamond. Nat. Photon. 6, 299–303 (2012)ADSCrossRefGoogle Scholar
  11. 11.
    C. Santori, D. Fattal, J. Vu\(\breve{\rm c}\)ković et al., Indistinguishable photons from a single-photon device. Nature 419, 594–597 (2002)ADSCrossRefGoogle Scholar
  12. 12.
    Y.-J. Wei, Y.-M. He, M.-C. Chen et al., Deterministic and robust generation of single photons from a single quantum dot with 99.5% indistinguishability using adiabatic rapid passage. Nano Lett. 14, 6515–6519 (2014)ADSCrossRefGoogle Scholar
  13. 13.
    A.K. Nowak, S.L. Portalupi, V. Giesz et al., Deterministic and electrically tunable bright single-photon source. Nat. Commun. 5, 3240 (2014)CrossRefGoogle Scholar
  14. 14.
    X. Ding, Y. He, Z.-C. Duan et al., On-demand single photons with high extraction efficiency and near-unity indistinguishability from a resonantly driven quantum dot in a micropillar. Phys. Rev. Lett. 116, 020401 (2016)ADSCrossRefGoogle Scholar
  15. 15.
    C.K. Hong, Z.Y. Ou, L. Mandel, Measurement of subpicosecond time intervals between two photons by interference. Phys. Rev. Lett. 59, 2044–2046 (1987)ADSCrossRefGoogle Scholar
  16. 16.
    J.-W. Pan, Z.-B. Chen, C.-Y. Lu et al., Multiphoton entanglement and interferometry. Rev. Mod. Phys. 84, 777–838 (2012)ADSCrossRefGoogle Scholar
  17. 17.
    C.K. Hong, L. Mandel, Experimental realization of a localized one-photon state. Phys. Rev. Lett. 56, 58–60 (1986)ADSCrossRefGoogle Scholar
  18. 18.
    B.G. Christensen, K.T. McCusker, J.B. Altepeter et al., Detection-loophole-free test of quantum nonlocality, and applications. Phys. Rev. Lett. 111, 130406 (2013)ADSCrossRefGoogle Scholar
  19. 19.
    M.D.C. Pereira, F.E.B. Becerra, B.L. Glebov et al., Demonstrating highly symmetric single-mode, single-photon heralding efficiency in spontaneous parametric downconversion. Opt. Lett. 38, 1609 (2013)ADSCrossRefGoogle Scholar
  20. 20.
    M. Giustina, A. Mech, S. Ramelow et al., Bell violation using entangled photons without the fair-sampling assumption. Nature 497, 227–230 (2013)ADSCrossRefGoogle Scholar
  21. 21.
    P.J. Mosley, J.S. Lundeen, B.J. Smith, I.A. Walmsley, Conditional preparation of single photons using parametric downconversion: a recipe for purity. New J. Phys. 10, 093011 (2008)ADSCrossRefGoogle Scholar
  22. 22.
    P.G. Evans, R.S. Bennink, W.P. Grice et al., Bright source of spectrally uncorrelated polarization-entangled photons with nearly single-mode emission. Phys. Rev. Lett. 105, 253601 (2010)ADSCrossRefGoogle Scholar
  23. 23.
    J.B. Spring, P.S. Salter, B.J. Metcalf et al., On-chip low loss heralded source of pure single photons. Opt. Express 21, 13522–13532 (2013)ADSCrossRefGoogle Scholar
  24. 24.
    R. Krischek, W. Wieczorek, A. Ozawa et al., Ultraviolet enhancement cavity for ultrafast nonlinear optics and high-rate multiphoton entanglement experiments. Nat. Photonics 4, 170–173 (2010)ADSCrossRefGoogle Scholar
  25. 25.
    Y.-F. Huang, B.-H. Liu, L. Peng et al., Experimental generation of an eight-photon Greenberger-Horne-Zeilinger state. Nat. Commun. 2, 546 (2011)CrossRefGoogle Scholar
  26. 26.
    X.-C. Yao, T.-X. Wang, P. Xu et al., Observation of eight-photon entanglement. Nat. Photonics 6, 225–228 (2012)ADSCrossRefGoogle Scholar
  27. 27.
    F. Kaneda, P.G. Kwiat, High-efficiency single-photon generation via large-scale active time multiplexing. arxiv:1803.04801v1 (2018)
  28. 28.
    A.L. Migdall, D. Branning, S. Castelletto, Tailoring single-photon and multiphoton probabilities of a single-photon on-demand source. Phys. Rev. A 66, 053805 (2002)ADSCrossRefGoogle Scholar
  29. 29.
    X. Ma, S. Zotter, J. Kofler et al., Experimental generation of single photons via active multiplexing. Phys. Rev. A 83, 043814 (2011)ADSCrossRefGoogle Scholar
  30. 30.
    M.J. Collins, C. Xiong, I.H. Rey et al., Integrated spatial multiplexing of heralded single-photon sources. Nat. Commun. 4, 2582 (2013)CrossRefGoogle Scholar
  31. 31.
    R.J.A. Francis-Jones, P.J. Mosley, Exploring the limits of multiplexed photon-pair sources for the preparation of pure single-photon states. arXiv:1409.1394 (2014)
  32. 32.
    D. Bonneau, G.J. Mendoza, J.L. O’Brien, M.G. Thompson, Effect of loss on multiplexed single-photon sources. New J. Phys. 17, 043057 (2015)ADSCrossRefGoogle Scholar
  33. 33.
    T. Pittman, B. Jacobs, J. Franson, Single photons on psudodemand from stored parametric down-conversion. Phys. Rev. A 66, 042303 (2002)ADSCrossRefGoogle Scholar
  34. 34.
    E. Jeffrey, N.A. Peters, P.G. Kwiat, Towards a periodic deterministic source of arbitrary single-photon states. New J. Phys. 6, 100 (2004)ADSCrossRefGoogle Scholar
  35. 35.
    K. McCusker, P.G. Kwiat, Efficient optical quantum state engineering. Phys. Rev. Lett. 103, 163602 (2009)ADSCrossRefGoogle Scholar
  36. 36.
    B. Glebov, J. Fan, A. Migdall, Deterministic generation of single photons via multiplexing repetitive parametric downconversions. Appl. Phys. Lett. 103, 031115 (2013)ADSCrossRefGoogle Scholar
  37. 37.
    J. Mower, D. Englund, Efficient generation of single and entangled photons on a silicon photonic integrated chip. Phys. Rev. A 84, 052326 (2011)ADSCrossRefGoogle Scholar
  38. 38.
    G.J. Mendoza, R. Santagati, J. Munns et al., Active temporal multiplexing of photons. Optica. 3, 127–132 (2016)CrossRefGoogle Scholar
  39. 39.
    C.T. Schmiegelow, M.A. Larotonda, Multiplexing photons with a binary division strategry. Appl. Phys. B 74, 902 (2013)Google Scholar
  40. 40.
    F. Kaneda, B.G. Christensen, J.J. Wong et al., Time-multiplexed heralded single-photon source. Optica 2, 1010–1013 (2015)CrossRefGoogle Scholar
  41. 41.
    K.T. McCusker, Efficient quantum optical state engineering and applications. Ph.D. thesis (University of Illinois at Urbana-Champaign, 2012)Google Scholar
  42. 42.
    A.I. Lvovsky, B.C. Sanders, W. Tittel, Optical quantum memory. Nat. Photonics 3, 706–714 (2009)ADSCrossRefGoogle Scholar
  43. 43.
    C. Robert, Simple, stable, and compact multiple-reflection optical cell for very long optical paths. Appl. Opt. 46, 5408–5418 (2007)ADSCrossRefGoogle Scholar
  44. 44.
    A. Christ, K. Laiho, A. Eckstein et al., Probing multimode squeezing with correlation functions. New J. Phys. 13, 033027 (2011)ADSCrossRefGoogle Scholar
  45. 45.
    R. Loudon, The Quantum Theory of Light, vol. 3, (Oxford University Press, 2000)Google Scholar
  46. 46.
    C.R. Myers, R. Laflamme, Linear optics quantum computation: an overview. arXiv:0512104 (2005)
  47. 47.
    M.A. Nielsen, Cluster-state quantum computation. Rep. Math. Phys. 47, 147–161 (2006)ADSMathSciNetzbMATHCrossRefGoogle Scholar
  48. 48.
    P. Kok, S.L. Braunstein, J.P. Dowling, Quantum lithography, entanglement and Heisenberg-limited parameter estimation. J. Opt. B 13, 033027 (2011)Google Scholar
  49. 49.
    P.C. Humphreys, B.J. Metcalf, J.B. Spring et al., Linear optical quantum computing in a single spatial mode. Phys. Rev. Lett. 111, 150501 (2013)ADSCrossRefGoogle Scholar
  50. 50.
    S. Aaronson, A. Arkhipov, The computation complexity of linear optics, in Proceedings of the 43rd Annual ACM Symposium on Theory of Computing (2011), pp. 333–342Google Scholar
  51. 51.
    L. Valiant, The complexity of computing the permanent. Theor. Comput. Sci. 8, 189–201 (1979)MathSciNetzbMATHCrossRefGoogle Scholar
  52. 52.
    J.P. Buhler, H.W. Lenstra Jr., C. Pomerance, Factoring integers with the number field sieve, in The Development of the Number Field Sieve (1993), pp. 50–94Google Scholar
  53. 53.
    M.A. Broome, A. Fedrizzi, S. Rahimi-Keshari et al., Photonic Boson sampling in a tunable circuit. Science 339, 794–798 (2013)ADSCrossRefGoogle Scholar
  54. 54.
    J.B. Spring, B.J. Metcalf, P.C. Humphreys et al., Boson sampling on a photonic chip. Science 339, 798–801 (2013)ADSCrossRefGoogle Scholar
  55. 55.
    M. Tillmann, B. Dakić, R. Heilmann et al., Experimental Boson sampling. Nat. Photonics 7, 540–544 (2013)ADSCrossRefGoogle Scholar
  56. 56.
    N. Spagnolo, C. Vitelli, M. Bentivegna et al., Experimental validation of photonic Boson sampling. Nat. Photonics 8, 615–620 (2014)ADSCrossRefGoogle Scholar
  57. 57.
    M. Bentivegna, N. Spagnolo, C. Vitelli et al., Experimental scattershot Boson sampling. Sci. Adv. 1, e1400255 (2015)ADSCrossRefGoogle Scholar
  58. 58.
    A. Dantan, J. Ciklinski, M. Pinard, Ph Grangier, Dynamics of a pulsed continuous-variable quantum memory. Phys. Rev. A 73, 032338 (2006)ADSCrossRefGoogle Scholar
  59. 59.
    J. Jin, E. Saglamyurek, M. Ií, G. Puigibert et al., Telecom-wavelength atomic quantum memory in optical fiber for heralded polarization qubits. Phys. Rev. Lett. 115, 140501 (2015)ADSCrossRefGoogle Scholar
  60. 60.
    J. Appel, E. Figueroa, D. Korystove et al., Quantum memory for squeezed light. Phys. Rev. Lett. 100, 093602 (2008)ADSCrossRefGoogle Scholar
  61. 61.
    M. Gündoğan, P.M. Ledingham, K. Kutluer et al., Solid state spin-wave quantum memory for time-bin qubits. Phys. Rev. Lett. 114, 230501 (2015)ADSCrossRefGoogle Scholar
  62. 62.
    V. Parigi, V. D’Ambrosio, C. Arnold et al., Storage and retrieval of vector beams of light in a multiple-degree-of-freedom quantum memory. Nat. Commun. 6, 7706 (2015)CrossRefGoogle Scholar
  63. 63.
    A. Sennaroglu, J. Fujimoto, Design criteria for Herriott-type multi-pass cavities for ultrashort pulse lasers. Opt. Express 11, 1106–1113 (2003)ADSCrossRefGoogle Scholar
  64. 64.
    G.G. Ball, W.H. Glenn, W.W. Morey, Programmable fiber optic delay line. IEEE Photonics Technol. Lett. 6, 741–743 (1994)ADSCrossRefGoogle Scholar
  65. 65.
    E. Saglamyurek, A quantum memory for orbital angular momentum photonic qubits. Nat. Photonics 8, 234–238 (2014)CrossRefGoogle Scholar
  66. 66.
    Y. Soudagar, F. Bussiéres, G. Berlin, S. Lacroix, J. Fernandez, Cluster-state quantum computing in optical fibers. J. Opt. Soc. Am. B 24, 226–230 (2007)ADSMathSciNetCrossRefGoogle Scholar
  67. 67.
    J. Altepeter, E. Jeffrey, P. Kwiat, Photonic state tomography. Adv. At. Mol. Opt. Phys. 52, 105–159 (2005)ADSCrossRefGoogle Scholar
  68. 68.
    D.V. James, P. Kwiat, W. Munro, A. White, Measurement of qubits. Phys. Rev. A 64, 052312 (2001)ADSCrossRefGoogle Scholar
  69. 69.
    A. Tiranov et al., Storage of hyperentanglement in a solid-state quantum memory. Optica 2, 287–297 (2015)CrossRefGoogle Scholar
  70. 70.
    K. Makino, Y. Hashimoto, J.-I. Yoshikawa, H. Ohdan, T. Toyama, P. vanLoock, A. Furusawa, Synchronization of optical photons for quantum information processing. Sci. Adv. 2, e150177 (2016)ADSCrossRefGoogle Scholar
  71. 71.
    J.-I. Yoshikawa, K. Makino, S. Kurata et al., Creation, storage, and on-demand release of optical quantum states with a negative wigner function. Phys. Rev. X 3, 041028 (2013)Google Scholar
  72. 72.
    M.J. Fitch, B.C. Jacobs, T.B. Pittman, J.D. Franson, Photon-number resolution using time-multiplexed single-photon detectors. Phys. Rev. A 68, 043814 (2003)ADSCrossRefGoogle Scholar
  73. 73.
    D. Achilles, C. Silberhorn, C. Śliwa, K. Banaszek, I.A. Walmsley, Fiber-assisted detection with photon number resolution. Opt. Lett. 28, 2387–2389 (2003)ADSCrossRefGoogle Scholar
  74. 74.
    J. Brendel, N. Gisin, W. Tittel, H. Zbinden, Pulsed energy-time entangled twin-photon source for quantum communication. Phys. Rev. Lett. 82, 2594–2597 (1999)ADSCrossRefGoogle Scholar
  75. 75.
    H. Jayakumar, A. Predojević, T. Kauten, T. Huber, G.S. Solomon, G. Weihs, Time-bin entangled photons from a quantum dot. Nat. Commun. 5, 4251 (2014)ADSCrossRefGoogle Scholar
  76. 76.
    M.A.M. Versteegh, M.E. Reimer, A.A. vanden Berg et al., Single pairs of time-bin-entangled photons. Phys. Rev. A 92, 033802 (2015)ADSCrossRefGoogle Scholar
  77. 77.
    S. Etcheverry, G. Cañas, E.S. Gómez et al., Quantum key distribution session with 16-dimensional photonic states. Sci. Rep. 3, 02316 (2013)CrossRefGoogle Scholar
  78. 78.
    M. Malik, M. O’Sullivan, B. Rodenburg et al., Influence of atmospheric turbulence on optical communications using orbital angular momentum for encoding. Opt. Exp. 20, 13195–13200 (2012)ADSCrossRefGoogle Scholar
  79. 79.
    M. Mafu, A. Dudley, S. Goyal et al., Higher-dimensional orbital-angular-momentum-based quantum key distribution with mutually unbiased bases. Phys. Rev. A 88, 032305 (2013)ADSCrossRefGoogle Scholar
  80. 80.
    J. Jin, S. Agne, J. -P. Bourgoin, Y. Zhang, T. Jennewein et al., Demonstration of analyzers for multimode photonic time-bin qubits. Phys. Rev. A97, 043847 (2018)Google Scholar
  81. 81.
    B. Christensen, K. McCusker, D. Gauthier, D. Kumor, V. Chandar, P. Kwiat, Higher-dimensional quantum cryptography. OSA Tech. Dig. 3, 2316 (2013)Google Scholar
  82. 82.
    T. Zhong, H. Zhou, R.D. Horansky et al., Photon-efficient quantum key distribution using time-energy entanglement with high-dimensional encoding. New J. Phys. 17, 022002 (2015)ADSCrossRefGoogle Scholar
  83. 83.
    D. Bunandar, Z. Zhang, J. Shapiro, D. Englund, Practical high-dimensional quantum key distribution with decoy states. Phys. Rev. A 91, 022336 (2015)ADSCrossRefGoogle Scholar
  84. 84.
    T. Brougham, S. Barnett, K. McCusker, P.G. Kwiat, D. Gauthier, Security of high-dimensional quantum key distribution protocols using Franson interferometers. J. Phys. B: At. Mol. Opt. Phys. 46, 104010 (2013)ADSCrossRefGoogle Scholar
  85. 85.
    T. Brougham, S. Barnett, Mutually unbiased measurements for high-dimensional time-bin-based photonic states. EPL 104, 30003 (2013)ADSCrossRefGoogle Scholar
  86. 86.
    Z. Zhang, J. Mower, D. Englund, F. Wong, J. Shapiro, Unconditional security of time-energy entanglement quantum key distribution using dual-basis interferometry. Phys. Rev. Lett. 112, 12 (2014)Google Scholar
  87. 87.
    D. Simon, A. Sergienko, High-capacity quantum key distribution via hyperentangled degrees of freedom. New J. Phys. 16, 063052 (2014)ADSCrossRefGoogle Scholar
  88. 88.
    T. Zhong, Photon-efficient quantum cryptography with pulse-position modulation. New J. Phys. 16, 063052 (2014)CrossRefGoogle Scholar
  89. 89.
    Y. Noguchi, H. Takesue, Implementation of quantum state tomography for time-bin entangled photon pairs. Opt. Exp. 17, 10976–10989 (2009)CrossRefGoogle Scholar
  90. 90.
    K.M. Rosfjord, J.K.W. Yang, E.A. Dauler et al., Nanowire single-photon detector with an integrated optical cavity and anti-reflection coating. Opt. Exp. 14, 527–534 (2006)ADSCrossRefGoogle Scholar
  91. 91.
    J.M. Donohue, M. Agnew, J. Lavoie, K.J. Resch, Coherent ultrafast measurement of time-bin encoded photons. Phys. Rev. Lett. 111, 153602 (2013)ADSCrossRefGoogle Scholar
  92. 92.
    F. Bussieres, Y. Soudagar, G. Berlin, S. Lacroix, N. Godbout, Manipulating time-bin qubits with fiber optics components, in 2006 Digest of the LEOS Summer Topical Meetings (2006), pp. 22–23Google Scholar
  93. 93.
    A. Schreiber, K.N. Cassemiro, V. Poto\(\breve{\rm c}\)ek et al., Photons walking the line: a quantum walk with adjustable coin operations. Phys. Rev. Lett. 104, 00502 (2010)Google Scholar
  94. 94.
    M. Szegedy, Quantum speed-up of Markov chain based algorithms, in Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science (2004), pp. 32–41Google Scholar
  95. 95.
    A. Childs, Universal computation by quantum walk. Phys. Rev. Lett. 102, 180501 (2008)MathSciNetCrossRefGoogle Scholar
  96. 96.
    A. Peruzzo et al., Quantum walks of correlated photons. Science 329, 1500–1503 (2010)ADSCrossRefGoogle Scholar
  97. 97.
    J.O. Owens, M.A. Broome, D.N. Biggerstaff et al., Two-photon quantum walks in an elliptical direct-write waveguide array. New J. Phys. 13, 075003 (2011)ADSCrossRefGoogle Scholar
  98. 98.
    A. Schreiber, A.G abris, P.P. Rohde et al., A 2D quantum walk simulation of two-particle dynamics. Sci. Mag. 336, 55–58 (2012)ADSCrossRefGoogle Scholar
  99. 99.
    N. Gisin, G. Ribordy, W. Tittel, H. Zbinden, Quantum cryptography. Rev. Mod. Phys. 74, 145–195 (2002)ADSzbMATHCrossRefGoogle Scholar
  100. 100.
    M. Horodecki, M. Piani, On quantum advantage in dense coding. J. Phys. A 45, 105305 (2012)ADSMathSciNetzbMATHCrossRefGoogle Scholar
  101. 101.
    C.H. Bennett, S.J. Wiesner, Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states. Phys. Rev. Lett. 69, 2881–2884 (1992)ADSMathSciNetzbMATHCrossRefGoogle Scholar
  102. 102.
    T. Das, R. Prabhu, A. Sen(De), U. Sen, Distributed quantum dense coding with two receivers in noisy environments. Phys. Rev. A 92, 052330 (2015)ADSCrossRefGoogle Scholar
  103. 103.
    H. Buhrman, R. Cleve, J. Watrous, R. de Wolf, Quantum fingerprinting. Phys. Rev. Lett. 87, 167902 (2001)ADSCrossRefGoogle Scholar
  104. 104.
    D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibel, A. Zeilinger, Experimental quantum teleportation. Nature 390, 575–579 (1997)ADSzbMATHCrossRefGoogle Scholar
  105. 105.
    K. Azuma, K. Tamaki, H.-K. Lo, All-photonic quantum repeaters. Nat. Commun. 6, 6787 (2015)Google Scholar
  106. 106.
    T. Li, F. -G. Deng, Heralded high-efficiency quantum repeater with atomic ensembles assisted by faithful single-photon transmission. Sci. Rep. 5, 15610 (2015)Google Scholar
  107. 107.
    N. Sangouard, C. Simon, H. de Riedmatten, N. Gisin, Quantum repeaters based on atomic ensembles and linear optics. Rev. Mod. Phys. 83, 33–80 (2011)ADSCrossRefGoogle Scholar
  108. 108.
    H.-J. Briegel, W. Dür, J.I. Ciract, P. Zoller, Quantum repeaters: the role of imperfect local operations in quantum communication. Phys. Rev. Lett. 81, 5932–5935 (1998)ADSCrossRefGoogle Scholar
  109. 109.
    M. Zukowski, A. Zeilinger, M.A. Horne, A.K. Ekert, “Event-ready-detectors” bell experiment via entanglement swapping. Phys. Rev. Lett. 71, 4287–4290 (1993)ADSCrossRefGoogle Scholar
  110. 110.
    J.-W. Pan, D. Bouwmeester, H. Weinfurter, A. Zeilinger, Experimental entanglement swapping: entangling photons that never interacted. Phys. Rev. Lett. 80, 3891 (1998)ADSMathSciNetzbMATHCrossRefGoogle Scholar
  111. 111.
    E. Megidish, A. Halevy, T. Shacham, T. Dvir, L. Dovrat, H.S. Eisenberg, Entanglement swapping between Photons that have never coexisted. Phys. Rev. Lett. 110, 210403 (2013)ADSCrossRefGoogle Scholar
  112. 112.
    A.M. Goebel, C. Wagenknecht, Q. Zhang et al., Multistage entanglement swapping. Phys. Rev. Lett. 101, 080403 (2008)ADSCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of PhysicsUniversity of Illinois at Urbana-ChampaignUrbanaUSA
  2. 2.Frontier Research Institute for Interdisciplinary SciencesTohoku UniversitySendaiJapan
  3. 3.Bergmann Messgeraete Entwicklung KGMurnauGermany
  4. 4.DSO National LaboratoriesSingaporeSingapore
  5. 5.The Institute of OpticsUniversity of RochesterRochesterUSA

Personalised recommendations