Russian Microelectronics

, Volume 40, Issue 4, pp 225–236 | Cite as

Quantum computers: Achievements, implementation difficulties, and prospects

Quantum Information Science

Abstract

A review of the principles of operation of quantum computers and their elements is presented. The radical advantage of quantum algorithms for processing information over the classical ones is discussed, quantum entanglement is considered as the basic resource of quantum computations, and the most promising and interesting proposals on realization of quantum computers on the basis of trapped ions, nuclear spins, quantum dots, superconducting structures, and others are described. This review reflects the materials of the report presented at the scientific session of the Department of Nanotechnologies and Information Technologies of the Russian Academy of Sciences on February 25, 2010.

Keywords

Quantum Computer RUSSIAN Microelectronics CNOT Gate Bloch Sphere Toffoli Gate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Valiev, K.A. and Kokin, A.A., Kvantovye Komp’yutery: Nadezhda i Real’nost’. (Quantum Computers: Hopes and Reality), Izhevsk: RKhD, 2001.Google Scholar
  2. 2.
    Valiev, K.A., Quantum Computers and Quantum Computations, Usp. Fiz. Nauk, 2005, vol. 175, no. 1, pp. 3–39 [Phys.-Usp. (Engl. Transl.), 2005, vol. 48, no. 1, pp. 1–36]..CrossRefMathSciNetGoogle Scholar
  3. 3.
    Nilsen, M. and Chuang, I., Quantum Computation and Quantum Information, Cambridge: University Press, 2004.Google Scholar
  4. 4.
    Preskill, J., Lecture Notes for Physics 229, Quantum Information and Computation, California Institute of Technology, 1998.Google Scholar
  5. 5.
    The Physics of Quantum Information. Quantum Cryptography. Quantum Teleportation. Quantum Computation, Bouwmeester, D., Ekert, A., and Zeilinger, A., Eds., Berlin: Springer, 2001.Google Scholar
  6. 6.
    Holevo, A.S., Vvedenie v kvantovuyu teoriyu informatsii (Introduction to Quantum Inforamtion Theory), Moscow: MTsNMO, 2002.Google Scholar
  7. 7.
    Kitaev, A., Shen’, A., and Vyalyi, M., Klassicheskie i kvantovye vychisleniya (Classical and Quantum Computation), Graduate Studies in Mathematics. Vol. 47. Providence, RI: AMS, American Mathematical Society, xiii, 257 p. (2002).Google Scholar
  8. 8.
    Shor, P., Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer //arXiv: quant-ph/9508027, 1995, 28 p.Google Scholar
  9. 9.
    Feynman, R., Simulating Physics with Computers, Int. J. Theor. Phys., 1982., vol. 21, no. 6/7, pp. 467–488.CrossRefMathSciNetGoogle Scholar
  10. 10.
    Feynman, R., Quantum Mechanical Computers, Found. of Phys., 1986, vol.16, no. 6, pp. 507–531.CrossRefMathSciNetGoogle Scholar
  11. 11.
    Manin, Yu.I., Vychislimoe i nevychislimoe (Calculable and Noncalculable), Moscow: Sovetskoe Radio, 1980, 128 p.MATHGoogle Scholar
  12. 12.
    Barenco, A., Bennett, C.H., Cleve, C., DiVincenzo, D.P., Margolus, N., Shor, P., Sleater, T., Smolin, J.A., and Weinfurter, H., Elementary Gates for Quantum Computation, Phys. Rev. A, 1995, vol. 52, no. 5, pp. 3457–3467.CrossRefGoogle Scholar
  13. 13.
    DiVincenzo, D.P., The Physical Implementation of Quantum Computation, Fortschr. der Phys., 2000, vol. 48, nos. 9–11, pp. 771–783; arXiv: quant-ph/0002077.MATHCrossRefGoogle Scholar
  14. 14.
    Farhi, E., Goldstone, J., Gutmann, S., and Sipser, M., Quantum Computation by Adiabatic Evolution //arXiv: quant-ph/0001106.Google Scholar
  15. 15.
    Raussendorf, R. and Briegel, H.J., A One-Way Quantum Computer, Phys. Rev. Lett., 2001, vol. 86, pp. 5188–5191.CrossRefGoogle Scholar
  16. 16.
    Raussendorf, R., Browne, D.E., and Briegel, H.J., Measurement-Based Quantum Computation on Cluster States, Phys. Rev. A, 2003, vol. 68, 022312.CrossRefGoogle Scholar
  17. 17.
    Walther, P., Resch, K.J., Rudolph, T., Schenck, E., Weinfurter, H., Vedral, V., Aspelmeyer, M., and Zeilinger, A., Experimental One-Way Quantum Computing, Nature, 2005, vol. 434, pp. 169–176.CrossRefGoogle Scholar
  18. 18.
    Mizel, A., Lidar, D.A., and Mitchell, M., Simple Proof of Equivalence Between Adiabatic Quantum Computation and the Circuit Model, Phys. Rev. Lett., 2007, vol. 99, 070502.CrossRefGoogle Scholar
  19. 19.
    Cirac, J.I. and Zoller, P., Quantum Computation with Cold Trapped Ions, Phys. Rev. Lett., 1995, vol. 74, no. 20, pp. 4094–4097.CrossRefGoogle Scholar
  20. 20.
    Monroe, C., Meerkhof, D.M., King, B.E., Itano, W.M., and Wineland, D., J Demonstration of a Fundamental Quantum Logic Gate, Phys. Rev. Lett., 1995, vol. 75, no. 25, pp. 4714–4717.MATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    Garcia-Ripoll, J.J., Zoller, P., and Cirac, J.I., Speed Optimized Two-Qubit Gates with Laser Coherent Control Techniques for Ion Trap Quantum Computing, Phys. Rev. Lett., 2003, vol. 91, 157901.CrossRefGoogle Scholar
  22. 22.
    Leibfried, D., Blatt, R., Monroe, C., and Wineland, D., Quantum Dynamics of Single Trapped Ions, Rev. Mod. Phys., 2003, vol. 75, pp. 281–324.CrossRefGoogle Scholar
  23. 23.
    Ospelkaus, C., Langer, C.E., Amini, J.M., Brown, K.R., Leibfried, D., and Wineland, D.J., Trapped-Ion Quantum Logic Gates Based on Oscillating Magnetic Fields, Phys. Rev. Lett., 2008, vol. 101, 090502.CrossRefGoogle Scholar
  24. 24.
    Wineland, D. and Blatt, R., Entangled States of Trapped Atomic Ions, Nature, 2008, vol. 453, pp. 1008–1014.CrossRefGoogle Scholar
  25. 25.
    Monz, T., Kim, K., Hansel, W., Riebe, M., Villar, A.S., Schindler, P., Chwalla, M., Hennrich, M., and Blatt, R., Realization of the Quantum Toffoli Gate with Trapped Ions, Phys. Rev. Lett., 2009, vol. 102, 04501.CrossRefGoogle Scholar
  26. 26.
    Olmschenk, S., Matsukevich, D.N., Maunz, P., Hayes, D., Duan, L.-M., and Monroe, C., Quantum Teleportation Between Distant Matter Qubits, Science, 2009, vol. 323, pp. 486–489.CrossRefGoogle Scholar
  27. 27.
    Blakestad, R.B. and Ospelkaus, C., VanDevender A.P., Amini J.M., Britton J., Leibfried D., and Wineland D.J., High-Fidelity Transport of Trapped-Ion Qubits Through An X-Junction Trap Array, Phys. Rev. Lett., 2009, vol. 102, 153002.CrossRefGoogle Scholar
  28. 28.
    Home, J.P., Hanneke, D., Jost, J.D., Amini, J.M., Leibfried, D., and Wineland, D.J., Complete Methods Set for Scalable Ion Trap Quantum Information Processing, Science, 2009, vol. 325, pp. 1227–1230.CrossRefMathSciNetGoogle Scholar
  29. 29.
    Ryabtsev, I.I., Tretyakov, D.B., Beterov, I.I., and Entin, V.M., Observation of the Stark-Tuned Forster Resonance Between Two Rydberg Atoms, Phys. Rev. Lett., 2010, vol. 104, 073003.CrossRefGoogle Scholar
  30. 30.
    Wilk, T., Gaetan, A., Evellin, C., Wolters, J., Miroshnichenko, Y., Grangier, P., and Browayes, A., Entanglement of Two Individual Neutral Atoms Using Rydberg Blockade, Phys. Rev. Lett., 2010, vol. 104, 010502.CrossRefGoogle Scholar
  31. 31.
    Isenhower, L., Urban, E., Zhang, X.L., Gill, A.T., Henage, T., Johnson, T.A., Walker, T.G., and Saffman, M., Demonstration of a Neutral Atom Controlled-NOT Quantum Gate, Phys. Rev. Lett., 2010, vol. 104, 010503.CrossRefGoogle Scholar
  32. 32.
    Gershenfeld, N.A. and Chuang, I.L., Bulk Spin Resonance Quantum Computation, Science, 1997, vol. 275, pp. 350–356.CrossRefMathSciNetGoogle Scholar
  33. 33.
    Vandersypen, L.M.K. and Chuang, I.L., NMR Techniques for Quantum Control and Computation, Rev. Mod. Phys., 2004, vol. 76, no. 4, pp. 1037–1069.CrossRefGoogle Scholar
  34. 34.
    Negrevergne, C., Mahesh, T.S., Ryan, C.A., Ditty, M., Cyr-Racine, F., Power, W., Boulant, N., Havel, T., Cory, D.G., and Laflamme, R., Benchmarking Quantum Control Methods on a 12-Qubit System, Phys. Rev. Lett., 2006, vol. 96, 170501.Google Scholar
  35. 35.
    Kane, B.E., A Silicon-Based Nuclear Spin Quantum Computer, Nature, 1998, vol. 393, no. 5, pp. 133–137.CrossRefGoogle Scholar
  36. 36.
    Valiev, K.A. and Kokin, A.A., Semiconductor NMR Quantum Computers with Individual and Ensemble Addressing to Qubits, Mikroelektronika, 1999, vol. 28, no. 5, pp. 326–337 [Russian Microelectronics, 1999, vol. 28, no. 5, pp. 277-286].Google Scholar
  37. 37.
    Kokin, A.A., Tverdotel’nye kvantovye komp’yutery na yadernykh spinakh (Solid-State Nuclear Spin Quantum Computers), M.-Izhevsk: IKI, 2004.Google Scholar
  38. 38.
    Valiev, K.A. and Kokin, A.A., Problems of Realization of Full-Scale Nuclear Spin Quantum Computer in a Silicon Nanostructure, Trudy FTIAN, 2005, vol. 18, pp. 19–36.Google Scholar
  39. 39.
    Fedichkin, L., Yanchenko, M., and Valiev, K.A., Coherent Charge Qubits Based on GaAs Quantum Dots with a Built-In Barrier, Nanotecnology, 2000, vol. 11, pp. 387–391.CrossRefGoogle Scholar
  40. 40.
    V’yurkov, V.V. and Gorelik, L.Y., Charge Based Quantum Computer Without Charge Transfer, Quantum Computers & Computing, 2000, no. 1, pp. 77–83; arXiv: quant-ph/0009099.Google Scholar
  41. 41.
    Tsukanov, A.V., Entanglement and Quantum State Engineering in the Optically Driven Two-Electron Double-Dot Structure, Phys. Rev. A, 2005, vol. 72, 022344.CrossRefGoogle Scholar
  42. 42.
    Valiev, K.A. and Tsukanov, A.V., Perfectly and Imperfectly Controlled Quantum Operations on a Charge Qubit, Mikroelektronika, 2007, vol. 36, no. 2, pp. 83–97 [Russian Microelectronics (Engl. Transl.), 2007, vol. 36, no. 2, pp. 67–80].Google Scholar
  43. 43.
    Tsukanov, A.V., Quantum Information Transfer Protocol via Optimized Single-Electron Transport in Semiconductor Nanostructure, Quantum Computers & Computing, 2010, vol. 10, pp. 3–19.Google Scholar
  44. 44.
    Hayashi, T., Fujisawa, T., Cheong, H.D., Jeong, Y.H., and Hirayama, Y., Coherent Manipulation of Electronic States in a Double Quantum Dot, Phys. Rev. Lett., 2003, vol. 91, 226804.CrossRefGoogle Scholar
  45. 45.
    Shinkai, G., Hayashi, T., Ota, T., and Fujisawa, T., Correlated Coherent Oscillations in Coupled Semiconductor Charge Qubits, Phys. Rev. Lett., 2009, vol. 103, 056802.CrossRefGoogle Scholar
  46. 46.
    Loss, D. and DiVincenzo, D.P., Quantum Computation with Quantum Dots, Phys. Rev. A, 1998, vol. 57, p. 120.CrossRefGoogle Scholar
  47. 47.
    Hanson, R., Kouwenhoven, L.P., Petta, J.R., Tarucha, S., and Vandersypen, L.M.K., Spins in Few-Electron Quantum Dots, Rev. Mod. Phys., 2007, vol. 79, pp. 1217–1265.CrossRefGoogle Scholar
  48. 48.
    Simmons, C.B., Thalakulam, M., Rosemeyer, B.M., van Bael, B.J., Sackmann, E.K., Savage, D.E., Lagally, M.G., Joynt, R., Friesen, M., Coppersmith, S.N., and Eriksson, M.A., Charge Sensing and Controllable Tunnel Coupling in a Si/SiGe Double Quantum Dot, Nano Lett, 2009, vol. 9, no. 9, pp. 3234–3238.CrossRefGoogle Scholar
  49. 49.
    Nakamura, Y., Pashkin, Yu.A., and Tsai, J.S., Coherent Control of Macroscopic Quantum States in a Single-Cooper-Pair Box, Nature, 1999, vol. 398, p. 679.CrossRefGoogle Scholar
  50. 50.
    Pashkin, Yu.A., Yamamoto, T., Astafiev, O.V., Nakamura, Y., Averin, D.V., and Tsai, J.S., Quantum Oscillations in Two Coupled Charge Qubits, Nature, 2003, vol. 421, p. 823.CrossRefGoogle Scholar
  51. 51.
    Yamamoto, T., Pashkin, Yu.A., Astafiev, O.V., Nakamura, Y., and Tsai, J.S., Demonstration of Conditional Operation Using Superconducting Charge Qubits, Nature, 2003, vol. 425, pp. 941–944.CrossRefGoogle Scholar
  52. 52.
    Schreier, J.A., Houck, A.A., Koch, J., Schuster, D.I., Johnson, B.R., Chow, J.M., Gambetta, J.M., Majer, J., Frunzio, L., Devoret, M.H., Girvin, S.M., and Schoelkopf, R.J., Suppressing Charge Noise Decoherence in Superconducting Charge Qubits, Phys. Rev. B, 2008, vol. 77, 180502.CrossRefGoogle Scholar
  53. 53.
    Friedman, J.R., Patel, V., Chen, W., Tolpygo, S.K., and Lurens, J.E., Quantum Superposition of Distinct Macroscopic States, Nature, 2000, vol. 406, pp. 43–46.CrossRefGoogle Scholar
  54. 54.
    Chiorescu, I., Nakamura, Y., Harmans, C.J.P.M., and Mooij, J.E., Coherent Quantum Dynamics of a Superconducting Flux Qubit, Science, 2003, vol. 299, pp. 1869–1871.CrossRefGoogle Scholar
  55. 55.
    Martinis, J.M., Nam, S., Aumentado, J., and Urbina, C., Rabi Oscillations in a Large Josephson-Junction Qubit, Phys. Rev. Lett., 2002, vol. 89, 117901.Google Scholar
  56. 56.
    Martinis, J.M., Superconducting Phase Qubits, Quantum Inf Process, 2009, vol. 8, pp. 81–103.CrossRefGoogle Scholar
  57. 57.
    Grajcar, M., Izmalkov, A., van der Ploeg, S.H.W., Linzen, S., Plecenik, T., Wagner, Th., Hübner, U., Il’ichev, E., Meyer, H.-G., Smirnov, A.Yu., Love, Peter J., van den Brink, Alec Maassen, Amin, M.H.S., Uchaikin, S., and Zagoski, A.M., Four-Qubit Device with Mixed Couplings, Phys. Rev. Lett., 2006, vol. 96, 047006.CrossRefGoogle Scholar
  58. 58.
    Wallraff, A., Schuster, D.I., Blais, A., Frunzio, L., Huang, R.-S., Majer, J., Kumar, S., Girvin, S.M., and Schoelkopf, R.J., Strong Coupling of a Single Photon To a Superconducting Qubit Using Circuit Quantum Electrodynamics, Nature, 2004, vol. 431, pp. 162–167.CrossRefGoogle Scholar
  59. 59.
    DiCarlo, L., Chow, J.M., Gambetta, J.M., Bishop, L.S., Johnson, B.R., Schuster, D.I., Majer, J., Blais, A., Frunzio, L., Girvin, S.M., and Schoelkopf, R.J., Demonstration of Two-Qubit Algorithms with a Superconducting Quantum Processor, Nature, 2009, vol. 460, pp. 240–244.CrossRefGoogle Scholar
  60. 60.
    Ansmann, M., Wang, H., Bialczak, R.C., Hofheinz, M., Lucero, E., Neeley, M., O’Connell, A.D., Sank, D., Weides, M., Wenner, J., Cleland, A.N., and Martinis, J.M., Violation of Bell’s Inequality in Josephson Phase Qubits, Nature, 2009, vol. 461, pp. 504–506.CrossRefGoogle Scholar
  61. 61.
    Bogdanov, Yu.I., Studying the Statistical Nature of the Bell Inequality, Mikroelektronika, 2008, vol. 37, no. 5, pp. 352–369 [Russian Microelectronics, 2008, vol. 37, No. 5, pp. 308–321].Google Scholar
  62. 62.
    Niskanen, A.O., Harrabi, K., Yoshihara, F., Nakamura, Y., Lloyd, S., and Tsai, J.S., Quantum Coherent Tunable Coupling of Superconducting Qubits, Science, 2007, vol. 316, pp. 723–726.CrossRefGoogle Scholar
  63. 63.
    Harris, R., Berkley, A.J., Johnson, M.W., Bunyk, P., Govorkov, S., Thom, M.C., Uchaikin, S., Wilson, A.B., Chung, J., Holtham, E., Biamonte, J.D., Smirnov, A.Yu., Amin, M.H.S., and van den Brink, A.M., Sign and Magnitude Tunable Coupler for Superconducting Flux Qubits, Phys. Rev. Lett., 2007, vol. 98, 177001.CrossRefGoogle Scholar
  64. 64.
    van der Ploeg, S.H.W., Izmalkov, A., Grajcar, M., Hübner, U., Linzen, S., Uchaikin, S., Wagner, Th., Smirnov, A.Yu., Brink, A.M., Amin, M.H.S., Zagoskin, A.M., Il’ichev, E., and Meyer, H.-G., Adiabatic quantum computation with flux qubits, first experimental results //arXiv: cond-mat/0702580.Google Scholar
  65. 65.
    Harris, R., Johansson, J., Berkley, A.J., Johnson, M.W., Lanting, T., Han, S., Bunyk, P., Ladizinsky, E., Oh, T., Perminov, I., Tolkacheva, E., Uchaikin, S., Chapple, E.M., Enderud, C., Rich, C., Thom, M., Wang, J., Wilson, B., and Rose, G., Experimental Demonstration of a Robust and Scalable Flux Qubit, Phys. Rev. B, 2010, vol. 81, 134510.CrossRefGoogle Scholar
  66. 66.
    Klyshko, D.N., Fotony i nelineinaya optika (Photons and Nonlinear Optics), Gordon and Breach Science Publishers, New York, 1988.Google Scholar
  67. 67.
    Rebic, S., Twamley, J., and Milburn, G.J., Giant Kerr Nonlinearities in Circuit Quantum Electrodynamics, Phys. Rev. Lett., 2009, vol. 103, 150503.CrossRefGoogle Scholar
  68. 68.
    Lukin, M.D. and Imamoglu, A., Controling Photons Using Electromagnetically Induced Transparency, Nature, 2001, vol. 413, pp. 273–276.CrossRefGoogle Scholar
  69. 69.
    Duan, L.M. and Kimble, H.J., Scalable Photonic Quantum Computation Through Cavity-Assisted Interactions, Phys. Rev. Lett., 2004, vol. 92, 127902.CrossRefGoogle Scholar
  70. 70.
    Mücke, M., Figueroa, E., Bochmann, J., and Hahn, C., Electromagnetically induced transparency with single atoms in a cavity //arXiv: quant-ph/1004.2442.Google Scholar
  71. 71.
    Knill, E., Laflamme, R., and Milburn, G.J., A Scheme for Efficient Quantum Computation with Linear Optics, Nature, 2001, vol. 409, pp. 46–52.CrossRefGoogle Scholar
  72. 72.
    Politi, A., Matthews, J.C.F., and O’Brien, J.L., Shor’s Quantum Factoring Algorithm on a Photonic Chip, Science, 2009, vol. 325, p. 1221.CrossRefMathSciNetGoogle Scholar
  73. 73.
    O’Brien, J.L., Optical Quantum Computing, Science, 2007, vol. 318, pp. 1567–1570.CrossRefGoogle Scholar
  74. 74.
    Harneit, W., Fullerene-Based Electron-Spin Quantum Computer, Phys. Rev. A, 2002, vol. 65, 032322.CrossRefGoogle Scholar
  75. 75.
    Yang, W.L., Xu, Z.Y., Wei, H., Feng, M., and Suter, D., Quantum-Information-Processing Architecture with Endohedral Fullerenes in a Carbon Nanotube, Phys. Rev. A, 2010, vol. 81, 032303.CrossRefGoogle Scholar
  76. 76.
    Hu, Y.M., Yang, W.L., Feng, M., and Du, J.F., Distributed Quantum-Information Processing with Fullerene-Caged Electron Spins in Distant Nanotubes, Phys. Rev. A, 2009, vol. 80, 022322.CrossRefGoogle Scholar
  77. 77.
    Yu, Z.G., Noninvasive Electrical Detection of Electron Spin Dynamics at the N Atom in N@C60, J. Phys.: Condens. Matter, 2010, vol. 22, 295305.CrossRefGoogle Scholar
  78. 78.
    Trauzettel, B. and Loss, D., Carbon Surprises Again, Nature Phys., 2009, vol. 5, pp. 317–318.CrossRefGoogle Scholar
  79. 79.
    Trauzettel, B., Bulaev, D.V., Loss, D., and Burkard, G., Spin Qubits in Graphene Quantum Dots, Nature Phys, 2007, vol. 3, pp. 192–196.CrossRefGoogle Scholar
  80. 80.
    Lyon, S.A., Spin-Based Quantum Computing Using Electron on Liquid Helium, Phys. Rev. A, 2006, vol. 74, 052338.CrossRefGoogle Scholar
  81. 81.
    Platzman, P.M. and Dykman, M.I., Quantum Computing with Electrons Floating on Liquid Helium, Science, 1999, vol. 284, pp. 1967–1969.CrossRefGoogle Scholar
  82. 82.
    Schuster, D.I., Fragner, A., Dykman, M.I., Lyon, S.A., and Schoelkopf, R.J., Proposal for Manipulating and Detecting Spin and Orbital States of Trapped Electrons on Helium Using Cavity Quantum Electrodynamics, Phys. Rev. Lett., 2010, vol. 105, 040503.CrossRefGoogle Scholar
  83. 83.
    Kitaev, A.Yu., Fault-Tolerant Quantum Computation by Anyons //arXiv: quant-ph/970702.Google Scholar
  84. 84.
    Nayak, C., Simon, S.H., Stern, A., Freedman, M., and Sarma, S.D., Non-Abelian Anyons and Topological Quantum Computation, Rev. Mod. Phys., 2008, vol. 80, pp. 1083–1159.MATHCrossRefGoogle Scholar
  85. 85.
    Sau, J.D., Lutchyn, R.M., Tewari, S., and Sarma, S.D., Generic New Platform for Topological Quantum Computation Using Semiconductor Heterostructures, Phys. Rev. Lett., 2010, vol. 104, 040502.CrossRefGoogle Scholar
  86. 86.
    Duclos-Cianci, G. and Poulin, D., Fast Decoders for Topological Quantum Codes, Phys. Rev. Lett., 2010, vol. 104, 050504.CrossRefGoogle Scholar
  87. 87.
    Fowler, A.G., Wang, D.S., Hill, C.D., Ladd, T.D., van Meter, R., Lloyd, C.L., and Hollenberg, L.C.L., Surface Code Quantum Communication, Phys. Rev. Lett., 2010, vol. 104, 180503.CrossRefGoogle Scholar
  88. 88.
    Ibort, A., Man’ko, V.I., Marmo, G., Simoni, A., and Ventriglia, F., An Introduction To the Tomographic Picture of Quantum Mechanics, Phys. Scr., 2009, vol. 79, 065013.CrossRefGoogle Scholar
  89. 89.
    Vogel, K. and Risken, H., Determination of Quasiprobability Distributions in Terms of Probability Distributions for the Rotated Quadrature Phase, Phys. Rev. A, 1989, vol. 40, pp. 2847–2849.CrossRefGoogle Scholar
  90. 90.
    Lvovsky, A.I., Hansen, H., Aichele, T., Benson, O., Mlynek, J., and Schiller, S., Quantum State Reconstruction of the Single-Photon Fock State, Phys. Rev. Lett., 2001, vol. 87, 050402.CrossRefGoogle Scholar
  91. 91.
    James, D.F., Kwiat, P.G., Munro, W.J., and White, A.G., Measurement of Qubits, Phys. Rev. A, 2001, vol. 64, 052312, 15 p.CrossRefGoogle Scholar
  92. 92.
    Bogdanov, Yu.I., Statistical Inverse Proplem //arXiv: physics/0211109.Google Scholar
  93. 93.
    Bogdanov, Yu.I., Krivitskii, L.A., and Kulik, S.P., Statistical Reconstruction of Quantum States of Three-Level Optical Systems, Pis’ma Zh. Eksp. Teor. Fiz., 2003, vol. 78, no. 6, pp. 804–809 [JETP Letters, 2003, vol. 78, no. 6, pp. 352–357].Google Scholar
  94. 94.
    Bogdanov, Yu.I., Statistical Inverse Problem: Root Approach //arXiv: quant-ph/0312042, 2003, 17 p.Google Scholar
  95. 95.
    Bogdanov, Yu.I., Root Estimator of Quantum States, New Topics in Quantum Physics Research. Nova Science, 2006, pp. 129–162; arXiv: quant-ph/0303014.Google Scholar
  96. 96.
    Bogdanov, Yu.I., Chekhova, M.V., Krivitsky, L.A., Kulik, S.P., Penin, A.N., Zhukov, A.A.., Kwek, L.C., Oh, C.H., and Tey, M.K., Statistical Reconstruction of Qutrits, Phys. Rev. A, 2004, vol. 70, 042303.CrossRefGoogle Scholar
  97. 97.
    Bogdanov, Yu.I., Chekhova, M.V., Kulik, S.P., Maslennikov, G.A., Zhukov, A.A., Oh, C.H., and Tey, M.K., Qutrit State Engineering with Biphotons, Phys. Rev. Lett., 2004, vol. 93, 230503.CrossRefGoogle Scholar
  98. 98.
    Bogdanov, Yu.I., Multiparametric Statistical Models in Problems of Quantum Informatics, Trudy FTIAN, Moscow: Nauka, 2005, vol. 18, pp. 91–118.Google Scholar
  99. 99.
    Bogdanov, Yu.I., Moreva, E.V., Maslennikov, G.A., Galeev, R.F., Straupe, S.S., and Kulik, S.P., Polarization States of Four-Dimensional Systems Based on Biphotons, Phys. Rev. A, 2006, vol. 73, 063810.CrossRefGoogle Scholar
  100. 100.
    D’Ariano, G.M., Mataloni, P., and Sac, M.F., Generating Qudits with D = 3,4 Encoded on Two-Photon States, Phys. Rev. A, 2005, vol. 71, 062337.CrossRefGoogle Scholar
  101. 101.
    Hradil, Z., Mogilevtsev, D., and Rehacek, J., Biased Tomography Schemes: An Objective Approach, Phys. Rev. Lett., 2006, vol. 96, 230401.CrossRefGoogle Scholar
  102. 102.
    Mikami, H. and Kobayashi, T., Remote Preparation of Qutrit States with Biphotons, Phys. Rev. A, 2007, vol. 75, 022325.CrossRefGoogle Scholar
  103. 103.
    Lanyon, B.P., Weinhold, T.J., Langford, N.K., O’Brien, J.L., Resch, K.J., Gilchrist, A., and White, A.G., Manipulating Biphotonics Qutrits, Phys. Rev. Lett., 2008, vol. 100, 060504.CrossRefGoogle Scholar
  104. 104.
    Allevi, A., Andreoni, A., Bondani, M., Brida, G., Genovese, M., Gramegna, M., Traina, P., Olivares, S., Paris, M.G.A., and Zambra, G., State Reconstruction by On/Off Measurements, Phys. Rev. A:, 2009, vol. 80, 022114.CrossRefGoogle Scholar
  105. 105.
    Brida, G., Degiovanni, I.P., Florio, A., Genovese, M., Giorda, P., Meda, A., Paris, M.G.A., and Shurupov, A., Experimental Estimation of Entanglement at the Quantum Limit, Phys. Rev. Lett., 2010, vol. 104, 100501.CrossRefGoogle Scholar
  106. 106.
    Bogdanov, Yu.I., Quantum Theory as a Universal Information Model of Statistical Phenomena, in supplement to Russian translation of: Breuer, H. and Pettruccione, F. The Theory of Open Quantum Systems, Oxford: Oxford University Press, 2007.Google Scholar
  107. 107.
    Bogdanov, Yu.I., A Unified method for Statistical Reconstruction of Quantum States by Purification, Zh. Eksp. Teor. Fiz., 2009, vol. 135, no. 6, pp. 1068–1078 [JETP, 2009, vol. 108, no. 6, pp. 928–935].MathSciNetGoogle Scholar
  108. 108.
    Bogdanov, Yu.I., Brida, G., Genovese, M., Kulik, S.P., Moreva, E.V., and Shurupov, A.P., Statistical Estimation of the Efficiency of Quantum State Tomography Protocols, Phys. Rev. Lett., 2010, vol. 105, 010404, 4 p.CrossRefGoogle Scholar
  109. 109.
    Bogdanov, Yu.I., Kulik, S.P., Moreva, E.V., Tikhonov, I.V., and Gavrichenko, A.K., Optimization of the Protocol of Statistical Reconstruction of Polarization Qubits, Pis’ma Zh. Eksp. Teor. Fiz., 2010, vol. 91, no. 12, pp. 755–761 [JETP Lett., 2010, vol. 91, pp. 686–692].Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2011

Authors and Affiliations

  1. 1.Institute of Physics and TechnologyRussian Academy of SciencesMoscowRussia

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