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Information and Signal Exchanging in Universal Network

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The Quantum Mechanics Conundrum

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Abstract

With his notion of the fabric of reality (Sect. 3.1.2), D. Deutsch,  extending ideas that were originally proposed by R. Feynman (Sect. 4.1) and J. Wheeler (Sect. 3.2.3), has contributed to change the way in which we consider the basic elements of our universe.

L’hypothèse ainsi renversée a–t–elle donc été stérile?

Loin de là, on peut dire qu’elle a rendu plus de services qu’une hypothése vraie.

Henri Poincaré, La science et l’hypothése

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Notes

  1. 1.

    See Auletta (2011, Sects. 6.2–6.5) for a summary.

  2. 2.

    Collins (2010, pp. 16–17).  I recall also Armstrong (1978).

  3. 3.

    See e.g. Deutsch (2011, Chap. 11).

  4. 4.

    Wootters and Zurek (1982), Dieks (1982).  See also Auletta et al. (2009, Sect. 15.2).

  5. 5.

    See D’Ariano and Yuen (1996).

  6. 6.

    See Barnum et al. (1996) for details.

  7. 7.

    Pati and Braunstein (2000).

  8. 8.

    Ionicioiu and Terno (2011) , Peruzzo et al. (2012).  See also Afriat and Tarozzi (2006).

  9. 9.

    Nielsen and Chuang (1997).

  10. 10.

    Nielsen and Chuang (1997).

  11. 11.

    D’Ariano et al. (2017, Sect. 9.3).

  12. 12.

    Lo and Chau (1997), Mayers (1997).  See also Clifton et al. (2003).

  13. 13.

    Deutsch and Hayden (2000).

  14. 14.

    Timpson (2013, p. 105).

  15. 15.

    See also Timpson (2013, Sect. 5.3).

  16. 16.

    Timpson (2013, pp. 111–112). However, I do not share the negative conclusion of the author about information accessibility.

  17. 17.

    Landauer (1961) , Bennett (1982).

  18. 18.

    Cerf and Adami (1997).

  19. 19.

    Beltrametti and Maczyński (1991). For a general summary on entropic Bell inequalities see Auletta (2000, Sect. 42.7).

  20. 20.

    Schumacher (1990, 1991) .

  21. 21.

    Battail (2014, Sect. 3.1).

  22. 22.

    Singh et al. (2017).

  23. 23.

    For the following considerations see D’Ariano et al. (2017, Sects. 8.2–8.5).

  24. 24.

    See Ueda and Kitagawa (1992) .

  25. 25.

    See Imamoḡlu (1993) .

  26. 26.

    See Auletta et al. (2009, Sect. 4.4).

  27. 27.

    For what follows see Auletta et al. (2009, Sect. 15.3).

  28. 28.

    See Mabuchi and Zoller (1996).  See also Mensky (1996).

  29. 29.

    See Nielsen and Caves (1997) .

  30. 30.

    In Fuchs and Peres (1996)  the trade-off (in terms of measurement uncertainty relation) between information gain and state disturbance has been computed. See also Pfister and Wehner (2013).

  31. 31.

    D’Ariano et al. (2017, Sect. 2.10.3 and Sect. 7.7).

  32. 32.

    For this whole subsection see Auletta et al. (2009, Sects. 13.4–5 and 15.4).

  33. 33.

    See Pauli (1980, 17) .

  34. 34.

    See Prugovec̆ki (1977) .

  35. 35.

    See Yuen (1976) .

  36. 36.

    Gnedenko (1969, Chaps. 4–5).

  37. 37.

    Wigner (1932).  Note that the Wigner function is only one among a whole family of interrelated quasi-probability distributions.

  38. 38.

    See Royer (1989) .

  39. 39.

    See D’Ariano et al. (2017, Sects. 2.4.2 and 2.8.4).

  40. 40.

    Byron and Fuller (1969–70, II, Chap. 7).

  41. 41.

    See Auletta et al. (2009, Sect. 3.5.5).

  42. 42.

    Further details regarding the subject of this subsection can be found in Bjorken and Drell (1964, 78–89) Prugovec̆ki (1971, 520–42) .

  43. 43.

    See Dirac (1930, 125–30). For what follows see also Auletta et al. (2009, Sect. 10.5.2).

  44. 44.

    Feynman (1948), Feynman and Hibbs (1965).  See also Auletta et al. (2009, Sect. 10.8).

  45. 45.

    I follow here Auletta et al. (2009, Sect. 14.4).

  46. 46.

    Truly speaking, the choice of \(\hat{\mathcal{J}}\) is not unique and may well depend on how the system is thought to be monitored. This remark, however, does not alter the essence of the following argument.

  47. 47.

    Examination in Auletta (2011, Sects. 2.1–2.2).

  48. 48.

    Elitzur (1992).

  49. 49.

    Elitzur (1992).

  50. 50.

    Cohen–Tannoudji (1991, pp. 60–61).

  51. 51.

    Elitzur (1992).

  52. 52.

    Wheeler (1983, p. 194).

  53. 53.

    Lloyd and Ng (2004).

  54. 54.

    Clayden et al. (2001, pp. 137–139).

  55. 55.

    Battail (2014, p. 58).

  56. 56.

    Chibbaro et al. (2014).

  57. 57.

    Boltzmann (1896, Sect. 6).

  58. 58.

    Poincaré (1890).

  59. 59.

    Elitzur (1992).

  60. 60.

    Wiener (1948).

  61. 61.

    On this problem the reader may have a look at Auletta (2005a).

  62. 62.

    See Auletta (2011, Sect. 2.3).

  63. 63.

    Helstrom (1976).

  64. 64.

    Bayes (1763). See also Auletta (2011, Sects. 7.6.2 and 18.4.4).

  65. 65.

    There is another attempt at interpreting quantum mechanics by using Bayesian probabilities by Caves et al. (2002). It is also known as quantum Bayesianism, and clearly there are points in common with the view supported here. However, it is characterised by a strong subjectivity, according to which the state of a quantum system represents the degrees of belief an agent has about the possible outcomes of measurements.

  66. 66.

    Formulated in Auletta (2011, Sect. 2.3). See also Auletta and Wang (2014, Sect. 11.2).

  67. 67.

    Auletta (2011, Chaps. 2 and 12).

  68. 68.

    Kant (1787, p. 75).

  69. 69.

    Kant (1787).

  70. 70.

    On this see Einstein (1949, pp. 687–88).

  71. 71.

    Cohen–Tannoudji (1991, pp. 67–69).

  72. 72.

    Cohen–Tannoudji (1991, p. 59).

  73. 73.

    Cohen–Tannoudji (1991, p. 117).

  74. 74.

    Landauer (1961, 1996),  Bennett (1982), Bennett and Landauer (1985), Lloyd (2000).

  75. 75.

    Cohen–Tannoudji (1991, pp. 71–72).

  76. 76.

    Elitzur (1992).

  77. 77.

    Kuhlmann (2013).

  78. 78.

    D’Ariano et al. (2017, Sects. 3.3 and 5.2).

  79. 79.

    See D’Ariano et al. (2017, Sect. 8.6).

  80. 80.

    See D’Ariano et al. (2017, Sects. 7.5–7.6, 8.1).

  81. 81.

    See Auletta et al. (2009, Sect. 9.11.1).

  82. 82.

    D’Ariano et al. (2017, Sect. 8.6).

  83. 83.

    I follow here Auletta et al. (2009, Sect. 17.8.5). On computation and decoherence see Schlosshauer (2007, Chap. 7).

  84. 84.

    D’Ariano et al. (2017, Sect. 7.8).

  85. 85.

    See e.g. Bohm and Hiley (1993, Sects. 5.1–5.2).

  86. 86.

    See D’Ariano et al. (2017, Sect. 7.1).

  87. 87.

    See Auletta (2005b, 2006a).

  88. 88.

    For what follows see Auletta (2011, Sect. 2.3). See also Auletta and Wang (2014, Sect. 12.5).

  89. 89.

    D’Ariano et al. (2017, Sect. 2.8.1).

  90. 90.

    See e.g. Timpson (2013, Sect. 3.6).

  91. 91.

    Shannon (1948).

  92. 92.

    Quoted in Battail (2014, p. 29).

  93. 93.

    Geroch (1978, p. 3) tells us that events need to be considered as a part of the world in which we live and not as a theoretical construct.

  94. 94.

    D’Ariano (2010).

  95. 95.

    D’Ariano et al. (2017, Sect. 2.4 and Chap. 5).

  96. 96.

    D’Ariano et al. (2017, Sect. 5.4).

  97. 97.

    Poincaré (1902, p. 45 and 51–52).

  98. 98.

    D’Ariano and Tosini (2013)  D’Ariano et al. (2017, Sect. 5.1).

  99. 99.

    D’Ariano et al. (2017, Sect. 2.8.3 and Sect. 4.1).

  100. 100.

    D’Ariano et al. (2017, Sect. 5.3).

  101. 101.

    D’Ariano et al. (2017, Sect. 4.2 and Chap. 10).

  102. 102.

    D’Ariano et al. (2017, Sect. 2.4.1, Sect. 4.2, Chap. 6).

  103. 103.

    D’Ariano et al. (2017, Sect. 3.3).

  104. 104.

    D’Ariano et al. (2017, Sects. 4.3 and 8.3).

  105. 105.

    D’Ariano et al. (2017, Sect. 2.10 and Chap. 7).

  106. 106.

    D’Ariano et al. (2017, Sect. 7.11).

  107. 107.

    D’Ariano et al.  (2017, Sects. 10.2–10.3).

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  1. University of Cassino and Southern Lazio, Cassino, Frosinone, Italy

    Gennaro Auletta

  2. Pontifical Gregorian University, Rome, Italy

    Gennaro Auletta

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Auletta, G. (2019). Information and Signal Exchanging in Universal Network. In: The Quantum Mechanics Conundrum. Springer, Cham. https://doi.org/10.1007/978-3-030-16649-6_6

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