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Adaptive quantum tomography

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Abstract

We provide a review of the experimental and theoretical research in the field of quantum tomography with an emphasis on recently developed adaptive protocols. Several statistical frameworks for adaptive experimental design are discussed. We argue in favor of the Bayesian approach, highlighting both its advantages for a statistical reconstruction of unknown quantum states and processes, and utility for adaptive experimental design. The discussion is supported by an analysis of several recent experimental implementations and numerical recipes.

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References

  1. M.-D. Choi, Linear Algebra Appl. 10, 285 (1975).

    Article  Google Scholar 

  2. A. Jamiolkowski, Rep. Math. Phys. 3, 275 (1972).

    Article  ADS  MathSciNet  Google Scholar 

  3. D. F. James, P. G. Kwiat, W. J. Munro, and A. G. White, Phys. Rev. A 64, 052312 (2001).

    Article  ADS  Google Scholar 

  4. Z. Hradil, Phys. Rev. A 55, R1561 (1997).

    Article  ADS  MathSciNet  Google Scholar 

  5. R. Blume-Kohout, New J. Phys. 12, 043034 (2010).

  6. R. Blume-Kohout, Phys. Rev. Lett. 105, 200504 (2010).

  7. Yu. I. Bogdanov, A. K. Gavrichenko, K. S. Kravtsov, S. P. Kulik, E. V. Moreva, and A. A. Soloviev, J. Exp. Theor. Phys. 113, 192 (2011).

    Article  ADS  Google Scholar 

  8. C. Ferrie, New J. Phys. 16, 093035 (2014).

    Article  ADS  MathSciNet  Google Scholar 

  9. M. Christandl and R. Renner, Phys. Rev. Lett. 109, 120403 (2012).

    Article  ADS  Google Scholar 

  10. R. Blume-Kohout, arXiv:1202.5270 (2012).

  11. M. S. Kaznady and D. F. V. James, Phys. Rev. A 79, 022109 (2009).

    Article  ADS  Google Scholar 

  12. T. Opatrný, D.-G. Welsch, and W. Vogel, Phys. Rev. A 56, 1788 (1997).

    Article  ADS  Google Scholar 

  13. B. Qi, Zh. Hou, L. Li, D. Dong, G. Xiang, and G. Guo, Sci. Rep. 3, 3496 (2013).

    ADS  Google Scholar 

  14. D. Giovannini, J. Romero, J. Leach, A. Dudley, A. Forbes, and M. J. Padgett, Phys. Rev. Lett. 110, 143601 (2013).

    Article  ADS  Google Scholar 

  15. C. Granade, J. Combes, and D. G. Cory, New J. Phys. 18, 033024 (2016).

    Article  ADS  Google Scholar 

  16. U. von Toussaint, Rev. Mod. Phys. 83, 943 (2011).

  17. J. Shang, H. K. Ng, A. Sehrawat, X. Li, and B.-G. Englert, New J. Phys. 15, 123026 (2013).

    Article  ADS  MathSciNet  Google Scholar 

  18. C. Ferrie, New J. Phys. 16, 023006 (2014).

    Article  ADS  MathSciNet  Google Scholar 

  19. D. Suess, U. Rudnicki, and D. Gross, arXiv:1608.00374 (2016).

  20. X. Li, J. Shang, H. K. Ng, and B.-G. Englert, arXiv:1602.05780 (2016).

  21. A. Doucet, N. de Freitas, and N. Gordon, Sequential Monte Carlo Methods in Practice (Springer, Berlin, 2001).

    Book  MATH  Google Scholar 

  22. F. E. Huszár, and N. M. T. Houlsby, Phys. Rev. A 85, 052120 (2012).

    Article  ADS  Google Scholar 

  23. C. Ferrie, New J. Phys. 16, 093035 (2014).

    Article  ADS  MathSciNet  Google Scholar 

  24. C. Granade, C. Ferrie, and S. T. Flammia, arXiv:1605.05039 (2016).

  25. H. S. Kravtsov, S. S. Straupe, I. V. Radchenko, N. M. T. Houlsby, F. Huszár, and S. P. Kulik, Phys. Rev. A 87, 062122 (2013).

    Article  ADS  Google Scholar 

  26. G. I. Struchalin, I. A. Pogorelov, S. S. Straupe, K. S. Kravtsov, I. V. Radchenko, and S. P. Kulik, Phys. Rev. A 93, 012103 (2016).

    Article  ADS  Google Scholar 

  27. W. K. Hastings, Biometrika 57, 97 (1970).

    Article  MathSciNet  Google Scholar 

  28. J. Liu and M. West, Combined Parameter and State Estimation in Simulation-Based Filtering (Springer, New York, 2001), p. 197.

    MATH  Google Scholar 

  29. C. E. Granade, C. Ferrie, N. Wiebe, and D. G. Cory, New J. Phys. 14, 103013 (2012).

    Article  ADS  MathSciNet  Google Scholar 

  30. J. Shang, Y.-L. Seah, H. K. Ng, J. Nott, and B.-G. Englert, New J. Phys. 17, 043017 (2015).

    Article  ADS  Google Scholar 

  31. Y.-L. Seah, J. Shang, H. K. Ng, and D. J. Nott, and B.-G. Englert, New J. Phys. 17, 043018 (2015).

    Article  ADS  Google Scholar 

  32. I. Bengtsson and K. Zyczkovsky, Geometry of Quantum States (Cambridge Univ. Press, Cambridge, 2006).

    Book  Google Scholar 

  33. W. K. Wootters, Phys. Rev. D 23, 357 (1981).

    Article  ADS  MathSciNet  Google Scholar 

  34. C. A. Fuchs and C. M. Caves, Open Syst. Inform. Dyn. 3, 345 (1995).

    Article  Google Scholar 

  35. K. Zyczkowski, K. A. Penson, I. Nechita, and B. Collins, J. Math. Phys. 52, 062201 (2011).

    Article  ADS  MathSciNet  Google Scholar 

  36. F. Mezzadri, Not. AMS 54, 592 (2007).

    MathSciNet  Google Scholar 

  37. Y. S. Teo, J. Rehácek, and Z. Hradil, Quantum Meas. Quantum Metrol. 1, 57 (2013).

    ADS  Google Scholar 

  38. J. Rehácek, B.-G. Englert, and D. Kaszlikowski, Phys. Rev. A 70, 052321 (2004).

    Article  ADS  Google Scholar 

  39. A. Ling, K. P. Soh, and A. Lamas-Linares, and C. Kurtsiefer, Phys. Rev. A 74, 022309 (2006).

    Article  ADS  Google Scholar 

  40. K. Jones, Ann. Phys. 207, 140 (1991).

    Article  ADS  Google Scholar 

  41. M. D. de Burgh, N. K. Langford, A. C. Doherty, and A. Gilchrist, Phys. Rev. A 78, 052122 (2008).

    Article  ADS  Google Scholar 

  42. Yu. I. Bogdanov, G. Brida, M. Genovese, S. P. Kulik, E. V. Moreva, and A. P. Shurupov, Phys. Rev. Lett. 105, 010404 (2010).

    Article  ADS  Google Scholar 

  43. Yu. I. Bogdanov, G. Brida, I. D. Bukeev, M. Genovese, K. S. Kravtsov, S. P. Kulik, E. V. Moreva, A. A. Soloviev, and A. P. Shurupov, Phys. Rev. A 84, 042108 (2011).

    Article  ADS  Google Scholar 

  44. J. M. Renes, R. Blume-Kohout, A. J. Scott, and C. M. Caves, J. Math. Phys. 45, 2171 (2004).

    Article  ADS  MathSciNet  Google Scholar 

  45. E. Bagan, M. A. Ballester, R. D. Gill, R. Muñoz-Tapia, and O. Romero-Isart, Phys. Rev. Lett. 97, 130501 (2006).

    Article  ADS  Google Scholar 

  46. D. H. Mahler, L. A. Rozema, A. Darabi, C. Ferrie, R. Blume-Kohout, and A. M. Steinberg, Phys. Rev. Lett. 111, 183601 (2013).

    Article  ADS  Google Scholar 

  47. M. J. W. Hall, Phys. Lett. A 242, 123 (1998).

    Article  ADS  MathSciNet  Google Scholar 

  48. E. Bagan, M. Baig, R. Muñoz-Tapia, and A. Rodriguez, Phys. Rev. A 69, 010304 (2004).

    Article  ADS  Google Scholar 

  49. S. Massar and S. Popescu, Phys. Rev. Lett. 74, 1259 (1995).

    Article  ADS  MathSciNet  Google Scholar 

  50. G. Vidal, J. I. Latorre, P. Pascual, and R. Tarrach, Phys. Rev. A 60, 126 (1999).

    Article  ADS  Google Scholar 

  51. R. D. Gill and S. Massar, Phys. Rev. A 61, 042312 (2000).

    Article  ADS  Google Scholar 

  52. Z. Hou, H. Zhu, G.-Y. Xiang, C.-F. Li, and G.-C. Guo, Quantum Inform. 2, 16001 (2016).

    Article  Google Scholar 

  53. D. G. Fischer, S. H. Kienle, and M. Freyberger, Phys. Rev. A 61, 032306 (2000).

    Article  ADS  Google Scholar 

  54. A. Kalev and I. Hen, New J. Phys. 17, 093008 (2015).

    Article  ADS  Google Scholar 

  55. H. Nagaoka, in Asymptotic Theory of Quantum Statistical Inference, Ed. by M. Hayashi (World Scientific, Singapore, 2005).

  56. A. Fujiwara, J. Phys. A: Math. Gen. 39, 12489, (2006).

    Article  ADS  Google Scholar 

  57. T. Sugiyama, P. S. Turner, and M. Murao, Phys. Rev. A 85, 052107 (2012).

    Article  ADS  Google Scholar 

  58. Th. Hannemann, D. Reiss, Ch. Balzer, W. Neuhauser, P. E. Toschek, and Ch. Wunderlich, Phys. Rev. A 65, 050303 (2002).

    Article  ADS  Google Scholar 

  59. R. Okamoto, M. Iefuji, S. Oyama, K. Yamagata, H. Imai, A. Fujiwara, and S. Takeuchi, Phys. Rev. Lett. 109, 130404 (2012).

    Article  ADS  Google Scholar 

  60. S. Lerch and A. Stefanov, Opt. Lett. 39, 5399 (2014).

    Article  ADS  Google Scholar 

  61. J. T. Barreiro, N. K. Langford, N. A. Peters, and P. G. Kwiat, Phys. Rev. Lett. 95, 260501 (2005).

    Article  ADS  Google Scholar 

  62. N. Bent, H. Qassim, A. A. Tahir, D. Sych, G. Leuchs, L. L. Sánchez-Soto, E. Karimi, and R. W. Boyd, Phys. Rev. X 5, 041006 (2015).

    Google Scholar 

  63. B. Qi, Zh. Hou, Y. Wang, D. Dong, H.-S. Zhong, L. Li, G.-Y. Xiang, H. M. Wiseman, Ch.-F. Li, and G.-C. Guo, arXiv:1512.01634 (2015).

  64. C. Ferrie, Phys. Rev. Lett. 113, 190404 (2014).

    Article  ADS  Google Scholar 

  65. R. J. Chapman, C. Ferrie, and A. Peruzzo, Phys. Rev. Lett. 117, 040402 (2016).

    Article  ADS  Google Scholar 

  66. X.-C. Yao, T.-X. Wang, P. Xu, H. Lu, G.-Sh. Pan, X.-H. Bao, Ch.-Zh. Peng, Ch.-Y. Lu, Y.-A. Chen, and J.-W. Pan, Nat. Photon. 6, 225 (2012).

    Article  ADS  Google Scholar 

  67. X.-L. Wang, L.-K. Chen, W. Li, et al. (Collab.), arXiv:1605.08547 (2016).

  68. D. Gross, Y.-K. Liu, S. T. Flammia, S. Becker, and J. Eisert, Phys. Rev. Lett. 105, 150401 (2010).

    Article  ADS  Google Scholar 

  69. M. Cramer, M. B. Plenio, S. T. Flammia, R. Somma, D. Gross, S. D. Bartlett, O. Landon-Cardinal, D. Poulin, and L. Yi-Kai, Nature Commun. 1, 149 (2010).

    Article  ADS  Google Scholar 

  70. S. T. Flammia, D. Gross, Y.-K. Liu, and J. Eisert, New J. Phys. 14, 095022 (2012).

    Article  ADS  Google Scholar 

  71. J. Rehácek, D. Mogilevtsev, and Z. Hradil, Phys. Rev. Lett. 105, 010402 (2010).

    Article  ADS  Google Scholar 

  72. D. Mogilevtsev, A. Ignatenko, A. Maloshtan, B. Stoklasa, J. Rehácek, and Z. Hradil, New J. Phys. 15, 025038 (2013).

    Article  ADS  MathSciNet  Google Scholar 

  73. M. Cooper, M. Karpinski, and B. J. Smith, Nat. Commun. 5, 4332 (2014).

    ADS  Google Scholar 

  74. G. Harder, C. Silberhorn, J. Rehácek, Z. Hradil, L. Motka, B. Stoklasa, and L. L. Sánchez-Soto, Phys. Rev. A 90, 042105 (2014).

    Article  ADS  Google Scholar 

  75. A. Mikhalychev, D. Mogilevtsev, Y. S. Teo, J. Rehácek, and Z. Hradil, Phys. Rev. A 92, 052106 (2015).

    Article  ADS  Google Scholar 

  76. C. E. Granade, C. Ferrie, N. Wiebe, and D. G. Cory, New J. Phys. 14, 103013 (2012).

    Article  ADS  MathSciNet  Google Scholar 

  77. M. P. V. Stenberg, Y. R. Sanders, and F. K. Wilhelm, Phys. Rev. Lett. 113, 210404 (2014).

    Article  ADS  Google Scholar 

  78. M. P. V. Stenberg, O. Köhn, and F. K. Wilhelm, Phys. Rev. A 93, 012122 (2016).

    Article  ADS  Google Scholar 

  79. B. L. Higgins, D. W. Berry, S. D. Bartlett, H. M. Wiseman, and G. J. Pryde, Nature 450, 393 (2007).

    Article  ADS  Google Scholar 

  80. L. Pezzé, A. Smerzi, G. Khoury, J. F. Hodelin, and D. Bouwmeester, Phys. Rev. Lett. 99, 223602 (2007).

    Article  ADS  Google Scholar 

  81. A. Hentschel and B. C. Sanders, Phys. Rev. Lett. 104, 063603 (2010).

    Article  ADS  Google Scholar 

  82. M. P. Stenberg, K. Pack, and F. K. Wilhelm, arXiv:1508.04412.

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Straupe, S.S. Adaptive quantum tomography. Jetp Lett. 104, 510–522 (2016). https://doi.org/10.1134/S0021364016190024

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