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Introduction and Essential Physics

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Complexity and Control in Quantum Photonics

Part of the book series: Springer Theses ((Springer Theses))

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Abstract

Over the past century, it has become increasingly apparent that Nature, at its most fundamental level, resists analogy with human experience. Quantum theory predicts behaviour which is not explained by any classical model. As a result, we have come to understand that certain intuitive beliefs concerning the potential capability of machines do not hold.

Krazy:“Why is Lenguage, Ignatz?”

Ignatz: “Language is that we may understand one another.”

Krazy: “Can you unda-stend a Finn, or a Leplender, or a Oshkosher, huh?”

Ignatz: “No,”

Krazy: “Can a Finn, or a Leplender, or a Oshkosher unda-stend you?”

Ignatz: “No,”

Krazy: “Then I would say lenguage is that that we may mis-unda-stend each udda.”

George Herriman, Krazy Kat

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Notes

  1. 1.

    Experimentalists can use LOCC operations to selectively throw away states coming from some partially entangled source, thus producing a postselected state with greater entanglement than the source itself. However, the entanglement of the system as a whole, including those systems that were thrown away, does not increase under LOCC operations.

  2. 2.

    In terms of computational complexity, Deutsch-Josza provides an oracle relative to which EQP (the class of problems exactly soluble by a quantum computer in polynomial time) is distinguishable from \({{\textsf {\textsc {P}}}}\) (decision problems soluble in poly-time by a deterministic Turing machine). However, we do not expect that a Deutsch-Josza machine would have direct “economically significant” implications!

  3. 3.

    Assuming a perfect experimental implementation, see Ref. [34].

  4. 4.

    After V.A. Fock, whose name is also given to the Hartree-Fock method described in Sect. 5.3.2.

  5. 5.

    The Canada balsam fir, Abies balsamea.

  6. 6.

    This implies that numerical methods identical to the Reck-Zeilinger decomposition are provided in almost any numerical linear-algebra package capable of QR decomposition (e.g. LAPACK). Your home router probably knowns how to build Reck schemes.

References

  1. M.A. Nielsen, I.L. Chuang, in Quantum Computation and Quantum Information (Cambridge Series on Information and the Natural Sciences), 1st edn. (Cambridge University Press, 2004)

    Google Scholar 

  2. J. Preskill, in Quantum Information Lecture Notes (Chapter 1)

    Google Scholar 

  3. P.A.M. Dirac, The Principles of Quantum Mechanics, 4th edn. (Oxford University Press, New York, 1982)

    Google Scholar 

  4. K. Hannabuss, in An Introduction to Quantum Theory (Oxford University Press, 1997)

    Google Scholar 

  5. S. Aaronson, in Quantum Computing since Democritus (Cambridge University Press, 2013)

    Google Scholar 

  6. A. Einstein, B. Podolsky, N. Rosen, Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. Online Arch. (Prola) 47, 777–780 (1935)

    MATH  ADS  Google Scholar 

  7. M.B. Plenio, S. Virmani, An introduction to entanglement measures. Quantum Inf. Comput. 7, 1–51 (2006)

    Google Scholar 

  8. D.M. Greenberger, M.A. Horne, A. Shimony, A. Zeilinger, Bell’s theorem without inequalities. Am. J. Phys. 58(12) (1990)

    Google Scholar 

  9. C.H. Bennett, S. Popescu, B. Schumacher, Concentrating partial entanglement by local operations. Phys. Rev. A 53(4), 2046–2052 (1996)

    Google Scholar 

  10. N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, S. Wehner, Bell nonlocality (2013). arXiv

    Google Scholar 

  11. J.S. Bell, On the Einstein Podolsky Rosen Paradox. Physics 1(3), 195–200 (1964)

    Google Scholar 

  12. John F. Clauser, Michael A. Horne, Abner Shimony, Richard A. Holt, Proposed experiment to test local hidden-variable theories. Phys. Rev. Lett. 23, 880–884 (1969)

    Article  ADS  Google Scholar 

  13. S. Popescu, D. Rohrlich, Quantum nonlocality as an axiom. Found. Phys. 24(3), 379–385 (1994)

    Article  MathSciNet  ADS  Google Scholar 

  14. B.S. Tsirelson, Some results and problems on quantum bell-type inequalities. Hadronic J. Suppl. 8, 329–345 (1993)

    MATH  MathSciNet  Google Scholar 

  15. Alain Aspect, Jean Dalibard, Gérard Roger, Experimental test of Bell’s inequalities using time—varying analyzers. Phys. Rev. Lett. 49(25), 1804–1807 (1982)

    Article  MathSciNet  ADS  Google Scholar 

  16. M. Giustina, A. Mech, S. Ramelow, B. Wittmann, J. Kofler, J. Beyer, A. Lita, B. Calkins, T. Gerrits, S.W. Nam, R. Ursin, A. Zeilinger, Bell violation using entangled photons without the fair-sampling assumption. Nature 497, 227–230 (2013)

    Article  ADS  Google Scholar 

  17. T. Scheidl, R. Ursin, J. Kofler, S. Ramelow, X.-S. Ma, T. Herbst, L. Ratschbacher, A. Fedrizzi, N.K. Langford, T. Jennewein, A. Zeilinger, Violation of local realism with freedom of choice. P. Natl. Acad. Sci. U.S.A. 107(46), 19708–19713 (2010)

    Google Scholar 

  18. R.F. Werner, Quantum states with einstein-podolsky-rosen correlations admitting a hidden-variable model. Phys. Rev. A 40, 4277–4281 (1989)

    Article  ADS  Google Scholar 

  19. D. Deutsch, Quantum theory, the Church-turing principle and the universal quantum computer. Proc. Roy. Soc. Lond. A 400, 97–117 (1985)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  20. R.P. Feynman, Simulating physics with computers. Int. J. Theor. Phy. Theor. Phy. 21, 467–488 (1982)

    Article  MathSciNet  Google Scholar 

  21. R.P. Feynman, Quantum mechanical computers. Found. Phys. 16(6), 507–531 (1986)

    Google Scholar 

  22. P.W. Shor, Algorithms for quantum computation: discrete logarithms and factoring. In SFCS ’94: Proceedings of the 35th Annual Symposium on Foundations of Computer Science, vol. 0 (IEEE Computer Society, Washington, 1994), pp. 124–134

    Google Scholar 

  23. D.P. DiVincenzo, Quantum computation. Science 270(5234), 255–261 (1995)

    Google Scholar 

  24. A. Barenco, C.H. Bennett, R. Cleve, D.P. DiVincenzo, N. Margolus, P. Shor, T. Sleator, J.A. Smolin, H. Weinfurter, Elementary gates for quantum computation. Phys. Rev. A 52, 3457–3467 (1995)

    Article  ADS  Google Scholar 

  25. S. Lloyd, Almost any quantum logic gate is universal. Phys. Rev. Lett. 75, 346–349 (1995)

    Article  ADS  Google Scholar 

  26. P.O. Boykin, T. Mor, M. Pulver, V. Roychowdhury, F. Vatan, On universal and fault-tolerant quantum computing: a novel basis and a new constructive proof of universality for shor’s basis. In Foundations of Computer Science, 1999. 40th Annual Symposium on (1999), pp. 486–494

    Google Scholar 

  27. D.P. DiVincenzo, The physical implementation of quantum computation. Fortschr. Phys. 48, 771–783 (2000)

    Article  MATH  Google Scholar 

  28. R. Raussendorf, H.J. Briegel, A one-way quantum computer. Phys. Rev. Lett. 86 (2001)

    Google Scholar 

  29. R. Raussendorf, D. Browne, H. Briegel, Measurement-based quantum computation on cluster states. Phys. Rev. A 68(2) (2003)

    Google Scholar 

  30. P.W. Shor, Scheme for reducing decoherence in quantum memory. Phys. Rev. A 52, 3457–3467 (1995)

    Article  ADS  Google Scholar 

  31. S.J. Devitt, K. Nemoto, Programming a topological quantum computer (2012). ArXiv e-prints

    Google Scholar 

  32. D. Gottesman, An introduction to quantum error correction and Fault-Tolerant quantum computation (2009). ArXiv e-prints

    Google Scholar 

  33. C. Bennett, G. Brassard, Quantum cryptography: Public key distribution and coin tossing. Proc. IEEE Int. (1984)

    Google Scholar 

  34. L. Lydersen, C. Wiechers, C. Wittmann, D. Elser, J. Skaar, V. Makarov, Hacking commercial quantum cryptography systems by tailored bright illumination. Nat. Photonics 4, 686–689 (2010)

    Article  ADS  Google Scholar 

  35. S. Pironio, A. Acín, N. Brunner, N. Gisin, S. Massar, V. Scarani, Device-independent quantum key distribution secure against collective attacks. New J. Phys. 11(4), 045021 (2009)

    Article  ADS  Google Scholar 

  36. V. Giovannetti, S. Lloyd, L. Maccone, Quantum-enhanced measurements: beating the standard quantum limit. Science 306, 1330–1336 (2004)

    Article  ADS  Google Scholar 

  37. V. Giovannetti, S. Lloyd, L. Maccone, Advances in quantum metrology. Nat. Photonics 5, 222–229 (2011)

    Article  ADS  Google Scholar 

  38. J.C.F. Matthews, X.-Q. Zhou, H. Cable, P.J. Shadbolt, D.J. Saunders, G.A. Durkin, G.J. Pryde, J.L. O’Brien, Practical quantum metrology (2013). ArXiv e-prints

    Google Scholar 

  39. H. Cable, G.A. Durkin, Parameter estimation with entangled photons produced by parametric down-conversion. Phys. Rev. Lett. 105, 013603 (2010)

    Article  ADS  Google Scholar 

  40. P.S. Venkataram, Electromagnetic field quantization and applications to the casimir effect. MIT. Edu. (2013)

    Google Scholar 

  41. http://www.photond.com/products/fimmwave.htm

  42. http://www.phoenixbv.com

  43. R.J. Glauber, Coherent and incoherent states of the radiation field. Phys. Rev. 131, 2766–2788 (1963)

    Article  MathSciNet  ADS  Google Scholar 

  44. R.H. Brown, R.Q. Twiss, A test of a new type of stellar interferometer on Sirius. Nature 178, 1046–1048 (1956)

    Google Scholar 

  45. K.P. Zetie, S.F. Adams, R.M. Tocknell, How does a mach-zehnder interferometer work? Phys. Educ. 35(1), 46 (2000)

    Article  ADS  Google Scholar 

  46. P. Grangier, G. Roger, A. Aspect, Experimental evidence for a photon anticorrelation effect on a beam splitter: A new light on single-photon interferences. EPL (Europhys. Lett.) 1(4), 173 (1986)

    Article  ADS  Google Scholar 

  47. S.M. Tan, D.F. Walls, M.J. Collett, Nonlocality of a single photon. Phys. Rev. Lett. 66, 252–255 (1991)

    Article  ADS  Google Scholar 

  48. 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)

    Article  ADS  Google Scholar 

  49. J. Rarity, P. Tapster, R. Loudon, Non-classical interference between independent sources (1997). arXiv:quant-ph/9702032

  50. S. Scheel, Permanents in linear optical networks (2004). arXiv:quant-ph/0406127

  51. E.R. Caianiello, On quantum field theory, 1: explicit solution of dyson’s equation in electrodynamics without use of feynman graphs. Nuovo Cimento 10 (1953)

    Google Scholar 

  52. L.G. Valiant, The complexity of computing the permanent. Theor. Comput. Sci. 8, 189–201 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  53. T. Tilma, E.C.G. Sudarshan, Generalized Euler angle parametrization for SU(N). J. Phys. Math. Gen. 35, 10467–10501 (2002)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  54. E. Martín-López, A. Laing, T. Lawson, R. Alvarez, X.-Q. Zhou, J.L. O’Brien, Experimental realization of Shor’s quantum factoring algorithm using qubit recycling. Nat. Photonics 6, 773–776 (2012)

    Article  ADS  Google Scholar 

  55. J.L. O’Brien, G.J. Pryde, A.G. White, T.C. Ralph, D. Branning, Demonstration of an all-optical quantum controlled-NOT gate. Nature 426, 264–267 (2003)

    Google Scholar 

  56. J. Silverstone, D. Bonneau, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, R. Hadfield, G.D. Marshall, V. Zwiller, J. Rarity, J. OBrien, M. Thompson, On-chip quantum interference between two silicon waveguide sources (2013). arXiv:1304.1490

  57. M. Reck, A. Zeilinger, H.J. Bernstein, P. Bertani, Experimental realization of any discrete unitary operator. Phys. Rev. Lett. 73, 58–61 (1994)

    Article  ADS  Google Scholar 

  58. S. Aaronson, A. Arkhipov, The computational complexity of linear optics (2010). arXiv

    Google Scholar 

  59. N. Russell, E.M. López, A. Laing, In preparation

    Google Scholar 

  60. M.R. Geller, J.M. Martinis, A.T. Sornborger, P.C. Stancil, E.J. Pritchett, A. Galiautdinov, Universal quantum simulation with pre-threshold superconducting qubits: Single-excitation subspace method (2012). arXiv:1210.5260

  61. R. Blatt, D. Wineland, Entangled states of trapped atomic ions. Nature 453, 1008–1015 (2008)

    Article  ADS  Google Scholar 

  62. B.P. Lanyon, P. Jurcevic, M. Zwerger, C. Hempel, E.A. Martinez, W. Dür, H.J. Briegel, R. Blatt, C.F. Roos, Measurement-based quantum computation with trapped ions. Phys. Rev. Lett. 111, 210501 (2013)

    Article  ADS  Google Scholar 

  63. M.H. Devoret, R.J. Schoelkopf, Superconducting circuits for quantum information: An outlook. Science 339(6124), 1169–1174 (2013)

    Article  MathSciNet  ADS  Google Scholar 

  64. L. Robledo, L. Childress, H. Bernien, B. Hensen, P.F.A. Alkemade, R. Hanson, High-fidelity projective read-out of a solid-state spin quantum register. Nature 477, 574–578 (2011)

    Article  ADS  Google Scholar 

  65. B.E. Kane, A silicon-based nuclear spin quantum computer. Nature 393(6681), 133–137 (1998)

    Article  ADS  Google Scholar 

  66. T.F. Rønnow, Z. Wang, J. Job, S. Boixo, S.V. Isakov, D. Wecker, J.M. Martinis, D.A. Lidar, M. Troyer, Defining and detecting quantum speedup (2014). ArXiv e-prints

    Google Scholar 

  67. A.B. U’Ren, C. Silberhorn, K. Banaszek, I.A. Walmsley, Efficient conditional preparation of high-fidelity single photon states for fiber-optic quantum networks. Phys. Rev. Lett. 93(9), 093601 (2004)

    Article  ADS  Google Scholar 

  68. G.I. Taylor, Interference fringes with feeble light. Proc. Camb. Philos. Soc. 15, 114–115 (1909)

    Google Scholar 

  69. X.-C. Yao, T.-X. Wang, X. Ping, L. He, G.-S. Pan, X.-H. Bao, C.-Z. Peng, L. Chao-Yang, Y.-A. Chen, J.-W. Pan, Observation of eight-photon entanglement. Nat. Photonics 6(4), 225–228 (2012)

    Article  ADS  Google Scholar 

  70. A.R. Dixon, Z.L. Yuan, J.F. Dynes, A.W. Sharpe, A.J. Shields, Gigahertz decoy quantum key distribution with 1 mbit/s secure key rate. Opt. Express 16(23), 18790–18979 (2008)

    Article  ADS  Google Scholar 

  71. J.G. Rarity, P.R. Tapster, E. Jakeman, T. Larchuk, R.A. Campos, M.C. Teich, B.E.A. Saleh, Two-photon interference in a mach-zehnder interferometer. Phys. Rev. Lett. 65, 1348–1351 (1990)

    Article  ADS  Google Scholar 

  72. L. Chao-Yang, D.E. Browne, T. Yang, J.-W. Pan, Demonstration of a compiled version of shor’s quantum factoring algorithm using photonic qubits. Phys. Rev. Lett. 99, 250504 (2007)

    Article  Google Scholar 

  73. B.P. Lanyon, T.J. Weinhold, N.K. Langford, M. Barbieri, D.F.V. James, A. Gilchrist, A.G. White, Experimental demonstration of a compiled version of shor’s algorithm with quantum entanglement. Phys. Rev. Lett. 99, 250505+ (2007)

    Google Scholar 

  74. A. Politi, J.C.F. Matthews, J.L. O’Brien, Shor’s quantum factoring algorithm on a photonic chip. Science 325, 1221+ (2009)

    Google Scholar 

  75. S. Barz, R. Vasconcelos, C. Greganti, M. Zwerger, W. Dür, H.J. Briegel, P. Walther, Demonstrating an element of measurement-based quantum error correction (2013). ArXiv e-prints

    Google Scholar 

  76. X. Cai, J. Wang, M.J. Strain, B. Johnson-Morris, J. Zhu, M. Sorel, J.L. O’Brien, M.G. Thompson, Y. Siyuan, Integrated compact optical vortex beam emitters. Science 338(6105), 363–366 (2012)

    Article  ADS  Google Scholar 

  77. P. Kok, W.J. Munro, K. Nemoto, T.C. Ralph, J.P. Dowling, G.J. Milburn, Linear optical quantum computing (2005). arXiv, Review article

    Google Scholar 

  78. S.J. Devitt, A.D. Greentree, R. Ionicioiu, J.L. O’Brien, W.J. Munro, L.C.L. Hollenberg, Photonic module: An on-demand resource for photonic entanglement. Phys. Rev. A 76(5), 052312 (2007)

    Article  ADS  Google Scholar 

  79. E. Knill, R. Laflamme, G.J. Milburn, A scheme for efficient quantum computation with linear optics. Nature 409, 46–52 (2001)

    Article  ADS  Google Scholar 

  80. P. Kok, S.L. Braunstein, Limitations on the creation of maximal entanglement. Phys. Rev. A 62(6), 064301 (2000)

    Article  MathSciNet  ADS  Google Scholar 

  81. J.L. O’Brien, A. Furusawa, J. Vuckovic, Photonic quantum technologies. Nat. Photon. 3, 687–695 (2009)

    Google Scholar 

  82. S. Gasparoni, J.W. Pan, P. Walther, T. Rudolph, A. Zeilinger, Realization of a photonic controlled-NOT gate sufficient for quantum computation. Phys. Rev. Lett. 93, 020504+ (2004)

    Google Scholar 

  83. M.A. Nielsen, Optical quantum computation using cluster states. arXiv (4) (2004)

    Google Scholar 

  84. D.E. Browne, T. Rudolph, Resource-efficient linear optical quantum computation. Phys. Rev. Lett. 95(1) (2005)

    Google Scholar 

  85. P. Walther, K.J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, M. Aspelmeyer, A. Zeilinger, Experimental one-way quantum computing. arXiv (2005)

    Google Scholar 

  86. R. Prevedel, P. Walther, F. Tiefenbacher, P. Bohi, R. Kaltenbaek, T. Jennewein, A. Zeilinger, High-speed linear optics quantum computing using active feed-forward. Nature 445, 65–69 (2007)

    Article  ADS  Google Scholar 

  87. R. Ceccarelli, G. Vallone, F. De Martini, P. Mataloni, A. Cabello, Experimental entanglement and nonlocality of a Two-Photon Six-Qubit cluster state. Phys. Rev. Lett. 103, 160401+ (2009)

    Google Scholar 

  88. T. Horikiri, H. Sasaki, H. Wang, T. Kobayashi, Security and gain improvement of a practical quantum key distribution using a gated single-photon source and probabilistic photon-number resolution. Phys. Rev. A 72, 012312 (2005)

    Article  ADS  Google Scholar 

  89. M.D. Eisaman, J. Fan, A. Migdall, S.V. Polyakov, Invited review article: Single-photon sources and detectors. Rev. Sci. Instrum. 82(7) (2011)

    Google Scholar 

  90. M.J. Collins, C. Xiong, I.H. Rey, T.D. Vo, J. He, S. Shahnia, C. Reardon, T.F. Krauss, M.J. Steel, A.S. Clark, B.J. Eggleton, Integrated spatial multiplexing of heralded single-photon sources. Nat. Commun. 4 (2013)

    Google Scholar 

  91. E. Jeffrey, N.A. Peters, P.G. Kwiat, Towards a periodic deterministic source of arbitrary single-photon states. New J. Phys. 6(1), 100 (2004)

    Google Scholar 

  92. L. Mandel, E. Wolf, in Optical coherence and quantum Optics (Cambridge University Press, 1995)

    Google Scholar 

  93. P.G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A.V. Sergienko, Y. Shih, New high-intensity source of polarization-entangled photon pairs. Phys. Rev. Lett. 75, 4337–4341 (1995)

    Google Scholar 

  94. A. Politi, M.J. Cryan, J.G. Rarity, Y. Siyuan, J.L. O’Brien, Silica-on-Silicon waveguide quantum circuits. Science 320, 646–649 (2008)

    Google Scholar 

  95. A. Laing, A. Peruzzo, A. Politi, M.R. Verde, M. Halder, T.C. Ralph, M.G. Thompson, J.L. O’Brien, High-fidelity operation of quantum photonic circuits. Appl. Phys. Lett. 97, 211109+ (2010)

    Google Scholar 

  96. J.C.F. Matthews, A. Politi, A. Stefanov, J.L. O’Brien, Manipulation of multiphoton entanglement in waveguide quantum circuits. Nat. Photon. 3, 346–350 (2009)

    Google Scholar 

  97. A. Peruzzo, M. Lobino, J.C.F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M.G. Thompson, J.L. OBrien, Quantum walks of correlated photons. Science 329, 1500–1503 (2010)

    Google Scholar 

  98. A. Peruzzo, A. Laing, A. Politi, T. Rudolph, J.L. O’Brien, Multimode quantum interference of photons in multiport integrated devices. Nat. Commun. 2, 224+ (2011)

    Google Scholar 

  99. N. Matsuda, H. Le Jeannic, H. Fukuda, T. Tsuchizawa, W.J. Munro, K. Shimizu, K. Yamada, Y. Tokura, H. Takesue, A monolithically integrated polarization entangled photon pair source on a silicon chip. Sci. Rep. 2 (2012)

    Google Scholar 

  100. W. Sohler, H. Hui, R. Ricken, V. Quiring, C. Vannahme, H. Herrmann, D. Büchter, S. Reza, W. Grundkötter, S. Orlov, H. Suche, R. Nouroozi, Y. Min, Integrated optical devices in lithium niobate. Opt. Photon. News 19(1), 24–31 (2008)

    Google Scholar 

  101. B. Calkins, P.L. Mennea, A.E. Lita, B.J. Metcalf, W.S. Kolthammer, A. Lamas-Linares, J.B. Spring, P.C. Humphreys, R.P. Mirin, J.C. Gates, P.G.R. Smith, I.A. Walmsley, T. Gerrits, S.W. Nam, High quantum-efficiency photon-number-resolving detector for photonic on-chip information processing. Opt. Express 21, 22657 (2013)

    Article  ADS  Google Scholar 

  102. N. Spagnolo, C. Vitelli, L. Sansoni, E. Maiorino, P. Mataloni, F. Sciarrino, D.J. Brod, E.F. Galvao, A. Crespi, R. Ramponi, R. Osellame, General rules for bosonic bunching in multimode interferometers. Phys. Rev. Lett. 111(13), 130503 (2013)

    Article  ADS  Google Scholar 

  103. A. Crespi, R. Ramponi, R. Osellame, L. Sansoni, I. Bongioanni, F. Sciarrino, G. Vallone, P. Mataloni, Integrated photonic quantum gates for polarization qubits. Nat. Commun. 2, 566 (2011)

    Google Scholar 

  104. M. Tillmann, B. Dakić, R. Heilmann, S. Nolte, A. Szameit, P. Walther, Experimental Boson sampling. Nat. Photonics 7(7), 540–544 (2013)

    Google Scholar 

  105. D.G. Marshall, A. Politi, J.C.F. Matthews, P. Dekker, M. Ams, M.J. Withford, J.L. O’Brien, Laser written waveguide photonic quantum circuits. Opt. Express 17, 12546–12554 (2009)

    Google Scholar 

  106. K. Poulios, R. Keil, D. Fry, J.D.A. Meinecke, J.C.F. Matthews, A. Politi, M. Lobino, M. Gräfe, M. Heinrich, S. Nolte, A. Szameit, J.L. O’Brien, Quantum walks of correlated photon pairs in two-dimensional waveguide arrays (2013). arXiv:1308.2554

  107. M.C. Rechtsman, J.M. Zeuner, A. Tünnermann, S. Nolte, M. Segev, A. Szameit, Strain-induced pseudomagnetic field and photonic Landau levels in dielectric structures. Nat. Photonics 7, 153–158 (2013)

    Article  ADS  Google Scholar 

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    Peter Shadbolt

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Shadbolt, P. (2016). Introduction and Essential Physics. In: Complexity and Control in Quantum Photonics. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-21518-1_1

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