Introduction to Quantum Information

  • Martin RingbauerEmail author
Part of the Springer Theses book series (Springer Theses)


Quantum information science views quantum mechanics as a theory that is fundamentally about information and information processing.


  1. 1.
    Helstrom, C.W.: Quantum detection and estimation theory. J. Stat. Phys. 1, 231–252 (1969)ADSMathSciNetCrossRefGoogle Scholar
  2. 2.
    Bertlmann, R.A., Krammer, P.: Bloch vectors for qudits. J. Phys. A 41, 235303 (2008)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Goyal, S.K., Simon, B.N., Singh, R., Simon, S.: Geometry of the generalized Bloch sphere for qutrits. J. Phys. A 49, 165203 (2016)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Braunstein, S.L., van Loock, P.: Quantum information with continuous variables. Rev. Mod. Phys. 77, 513 (2005)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Wigner, E.: On the quantum correction for thermodynamic equil. Phys. Rev. 40, 749–759 (1932)ADSCrossRefzbMATHGoogle Scholar
  6. 6.
    Moyal, J.E., Bartlett, M.S.: Quantum mechanics as a statistical theory. In: Mathematical Proceedings of the Cambridge Philosophical Society, vol. 99 (1949)Google Scholar
  7. 7.
    Hillery, M., O’Connell, R., Scully, M., Wigner, E.: Distribution functions in physics: fundamentals. Phys. Rep. 106, 121–167 (1984)ADSMathSciNetCrossRefGoogle Scholar
  8. 8.
    Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press (2000)Google Scholar
  9. 9.
    Jozsa, R.: Fidelity for mixed quantum states. J. Mod. Opt. 41, 2315–2323 (1994)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Gilchrist, A., Langford, N.K., Nielsen, M.A.: Distance measures to compare real and ideal quantum processes. Phys. Rev. A 71, 062310 (2005)ADSCrossRefGoogle Scholar
  11. 11.
    Branciard, C., Brunner, N., Gisin, N., Kurtsiefer, C., Lamas-Linares, A., Ling, A., Scarani, V.: Testing quantum correlations versus single-particle properties within Leggett’s model and beyond. Nat. Phys. 4, 681–685 (2008)CrossRefGoogle Scholar
  12. 12.
    Schrödinger, E.: Die gegenwärtige Situation in der Quantenmechanik. Die Naturwissenschaften 23, 807–849 (1935)ADSCrossRefzbMATHGoogle Scholar
  13. 13.
    Gurvits, L.: Classical deterministic complexity of Edmonds’ Problem and quantum entanglement. In: Proceedings of the Thirty-Fifth ACM symposium on Theory of Computing—STOC ’03. ACM Press (2003)Google Scholar
  14. 14.
    Horodecki, R., Horodecki, M., Horodecki, K.: Quantum entanglement. Rev. Mod. Phys. 81, 865–942 (2009)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Langford, N.K.: Encoding, manipulating and measuring quantum information in optics. Ph.D. The University of Queensland (2007)Google Scholar
  16. 16.
    Cavalcanti, E.G., Menicucci, N.C., Pienaar, J.L.: The preparation problem in nonlinear extensions of quantum theory. arXiv:1206.2725 (2012)
  17. 17.
    Ringbauer, M., Broome, M.A., Myers, C.R., White, A.G., Ralph, T.C.: Experimental simulation of closed timelike curves. Nat. Commun. 5, 4145 (2014)Google Scholar
  18. 18.
    Shahandeh, F., Ringbauer, M., Loredo, J.C., Ralph, T.C.: Ultrafine entanglement witnessing. Phys. Rev. Lett. 118, 110502 (2017)ADSCrossRefGoogle Scholar
  19. 19.
    Tóth, G., Wieczorek, W., Krischek, R., Kiesel, N., Michelberger, P., Weinfurter, H.: Practical methods for witnessing genuine multi-qubit entanglement in the vicinity of symmetric states. New J. Phys., 083002 (2009)Google Scholar
  20. 20.
    Dür, W., Vidal, G., Cirac, J.I.: Three qubits can be entangled in two inequivalent ways. Phys. Rev. A 62, 062314 (2000)ADSMathSciNetCrossRefGoogle Scholar
  21. 21.
    Hill, S., Wootters, W.K.: Entanglement of a pair of quantum bits. Phys. Rev. Lett. 78, 5022–5025 (1997)ADSCrossRefGoogle Scholar
  22. 22.
    Wootters, W.K.: Entanglement of formation of an arbitrary state of two qubits. Phys. Rev. Lett. 80, 2245–2248 (1998)ADSCrossRefzbMATHGoogle Scholar
  23. 23.
    Coffman, V., Kundu, J., Wootters, W.K.: Distributed entanglement. Phys. Rev. A 61, 052306 (2000)ADSCrossRefGoogle Scholar
  24. 24.
    Cao, K., Zhou, Z.-W., Guo, G.-C., He, L.: Efficient numerical method to calculate the three-tangle of mixed states. Phys. Rev. A 81, 034302 (2010)ADSCrossRefGoogle Scholar
  25. 25.
    Miyake, A.: Classification of multipartite entangled states by multidimensional determinants. Phys. Rev. A 67, 012108 (2003)ADSMathSciNetCrossRefGoogle Scholar
  26. 26.
    Wood, C.: Non-completely positive maps: properties and applications. Ph.D. thesis, Macquarie University (2009)Google Scholar
  27. 27.
    Ringbauer, M., Wood, C.J., Modi, K., Gilchrist, A., White, A.G., Fedrizzi, A.: Characterizing quantum dynamics with initial system-environment correlations. Phys. Rev. Lett. 114, 090402 (2015)ADSCrossRefGoogle Scholar
  28. 28.
    Wood, C.J., Biamonte, J.D., Cory, D.G.: Tensor networks and graphical calculus for open quantum systems. Quantum Inf. Comput. 15, 0759–0811 (2011)MathSciNetGoogle Scholar
  29. 29.
    Stinespring, W.F.: Positive functions on C*-algebras. Proc. Am. Math. Soc. 6, 211–211 (1955)MathSciNetzbMATHGoogle Scholar
  30. 30.
    Schumacher, B.: Sending quantum entanglement through noisy channels. Phys. Rev. A 54, 2614 (1996)ADSCrossRefGoogle Scholar
  31. 31.
    Choi, M.-D.: Completely positive linear maps on complex matrices. Linear Algebra Appl. 10, 285–290 (1975)MathSciNetCrossRefzbMATHGoogle Scholar
  32. 32.
    Jamiołkowski, A.: Linear transformations which preserve trace and positive semidefiniteness of operators. Rep. Math. Phys. 3, 275–278 (1972)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  33. 33.
    Wood, C.J.: Initialization and characterization of open quantum systems. Ph.D. thesis, University of Waterloo (2015)Google Scholar
  34. 34.
    Born, M.: On the quantum mechanics of collisions. Zeitschrift für Physik 38, 803–827 (1926)ADSCrossRefGoogle Scholar
  35. 35.
    Fuchs, C.A.: QBism, the perimeter of quantum Bayesianism. arXiv:1003.5209 (2010)
  36. 36.
    Aerts, D.: A possible explanation for the probabilities of quantum mechanics. J. Math. Phys. 27, 202–210 (1986)ADSMathSciNetCrossRefGoogle Scholar
  37. 37.
    Gleason, A.: Measures on the closed subspaces of a hilbert space. Indiana Univ. Math. J. 6, 885–893 (1957)MathSciNetCrossRefzbMATHGoogle Scholar
  38. 38.
    Carroll, S.M.: Why probability in quantum mechanics is given by the wave function squared. Sean Carroll’s Blog (2014)Google Scholar
  39. 39.
    Davies. E.B., Lewis, J.T.: An operational approach to quantum probabillity. Commun. Math. Phys. 17, 239–260 (1970)Google Scholar
  40. 40.
    Naimark, M.: Spectral functions of a symmetric operator. Izv. Akad. Nauk SSSR Ser. Mat. 4, 277–318 (1940)MathSciNetzbMATHGoogle Scholar
  41. 41.
    Kwiat, P.G., Englert, B.-G.: Quantum-erasing the nature of reality, or perhaps, the reality of nature? In: Barrow, J.D., Davies, P.C.W., L., H.C. (eds.) Science and Ultimate Reality: Quantum Theory, Cosmology, and Complexity. Cambridge University Press (2004)Google Scholar
  42. 42.
    Pusey, M.F., Leifer, M.S.: Logical pre- and post-selection paradoxes are proofs of contextuality. Electron. Notes Theor. Comput. Sci. 195, 295–306 (2015)CrossRefGoogle Scholar
  43. 43.
    Kocsis, S., Braverman, B., Ravets, S., Stevens, M.J., Mirin, R.P., Shalm, L.K., Steinberg, A.M.: Observing the average trajectories of single photons in a two-slit interferometer. Science 332, 1170–1173 (2011)ADSCrossRefzbMATHGoogle Scholar
  44. 44.
    Bliokh, K.Y., Bekshaev, A.Y., Kofman, A.G., Nori, F.: Photon trajectories, anomalous velocities and weak measurements: a classical interpretation. New J. Phys. 15, 073022 (2013)ADSCrossRefGoogle Scholar
  45. 45.
    Dressel, J.: Weak values as interference phenomena. Phys. Rev. A 91, 032116 (2015)ADSCrossRefGoogle Scholar
  46. 46.
    Dressel, J., Jordan, A.N.: Contextual-value approach to the generalized measurement of observables. Phys. Rev. A 85, 022123 (2012)Google Scholar
  47. 47.
    Grangier, P., Levenson, J.A., Poizat, J.-P.: Characterization of quantum non-demolition measurements in optics. Nature 396, 537–542 (1998)ADSCrossRefGoogle Scholar
  48. 48.
    Ralph, T.C., Bartlett, S.D., O’Brien, J.L., Pryde, G.J., Wiseman, H.M.: Quantum nondemolition measurements for quantum information. Phys. Rev. A 73, 012113 (2006)ADSCrossRefGoogle Scholar
  49. 49.
    Monroe, C.: Demolishing quantum nondemolition. Phys. Today 64, 8 (2011)ADSCrossRefGoogle Scholar
  50. 50.
    Brune, M., Haroche, S., Raimond, J.M., Davidovich, L., Zagury, N.: Manipulation of photons in a cavity by dispersive atom-field coupling: quantum-nondemolition measurements and generation of "Schrödinger cat" states. Phys. Rev. A 45, 5193–5214 (1992)ADSCrossRefGoogle Scholar
  51. 51.
    Knill, E., Laflamme, R., Milburn, G.J.: A scheme for efficient quantum computation with linear optics. Nature 409, 46–52 (2001)ADSCrossRefzbMATHGoogle Scholar
  52. 52.
    Carolan, J., et al.: Universal linear optics. Science 349, 711–716 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  53. 53.
    Molina-Terriza, G., Torres, J.P., Torner, L.: Twisted photons. Nat. Phys. 3, 305–310 (2007)CrossRefGoogle Scholar
  54. 54.
    Fernandez-Corbaton, I., Molina-Terriza, G.: Role of duality symmetry in transformation optics. Phys. Rev. B 88, 085111 (2013)ADSCrossRefGoogle Scholar
  55. 55.
    Nagali, E., Sciarrino, F.: Manipulation of photonic orbital angular momentum for quantum information processing. In: Advanced Photonic Sciences (InTech, 2012)Google Scholar
  56. 56.
    Andersen, M., Ryu, C., Cladé, P., Natarajan, V., Vaziri, A., Helmerson, K., Phillips, W.: Quantized rotation of atoms from photons with orbital angular momentum. Phys. Rev. Lett. 97, 170406 (2006)ADSCrossRefGoogle Scholar
  57. 57.
    Fickler, R.: Quantum entanglement of complex structures of photons. Ph.D. thesis, University of Vienna (2015)Google Scholar
  58. 58.
    Hou, Z., Xiang, G., Dong, D., Li, C.-F., Guo, G.-C.: Realization of mutually unbiased bases for a qubit with only one wave plate: theory and experiment. Opt. Express 23, 10018 (2015)ADSCrossRefGoogle Scholar
  59. 59.
    Logofatu, P.C.: Simple method for determining the fast axis of a wave plate. Opt. Eng. 41, 3316 (2002)ADSCrossRefGoogle Scholar
  60. 60.
    Volz, J., Scheucher, M., Junge, C., Rauschenbeutel, A.: Nonlinear \(\pi \) phase shift for single fibre-guided photons interacting with a single resonator-enhanced atom. Nat. Phot. 8, 965–970 (2014)CrossRefGoogle Scholar
  61. 61.
    Holbrow, C.H., Galvez, E., Parks, M.E.: Photon quantum mechanics and beam splitters. Am. J. Phys. 70, 260 (2002)ADSCrossRefGoogle Scholar
  62. 62.
    Hong, C.K., Ou, Z.Y., Mandel, L.: Measurement of subpicosecond time intervals between two photons by interference. Phys. Rev. Lett. 59, 2044–2046 (1987)ADSCrossRefGoogle Scholar
  63. 63.
    Kim, Y.-H., Grice, W.P.: Quantum interference with distinguishable photons through indistinguishable pathways, vol. 6. arXiv:quant-ph/0304086 (2003)
  64. 64.
    Ralph, T.: Scaling of multiple postselected quantum gates in optics. Phys. Rev. A 70, 012312 (2004)ADSCrossRefGoogle Scholar
  65. 65.
    Loredo, J.C.: Enabling multi-photon experiments with solid-state emitters: a farewell to downconversion. Ph.D. thesis, The University of Queensland (2016)Google Scholar
  66. 66.
    Kok, P., Lovett, B.W.: Optical Quantum Information Processing. Cambridge University Press (2010)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.School of Mathematics and PhysicsThe University of QueenslandQueenslandAustralia

Personalised recommendations