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Information, Correlations, and More

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Part of the book series: Lecture Notes in Physics ((LNP,volume 893))

Abstract

Quantum information science has experienced enormous developments during the last 30 years. I do not cover this wide and fascinating field in these notes, but shall only discuss briefly some relations with the question of the formalism. Indeed quantum information theory led to new points of view and to new uses and applications of quantum theory. This renewal is considered by some authors as a real change of paradigm, and referred to as “the second quantum revolution”.

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Notes

  1. 1.

    Slightly more general than in some presentations.

  2. 2.

    In some discussions the context may include additional parameters (not included into the hidden variables) like the details of the apparatus used, etc.

  3. 3.

    If not satisfying every minds, every times…

  4. 4.

    Well… as long as gravity is not taken into account!

  5. 5.

    as already pointed out in [105].

Bibliography

  1. A.E. Allahverdyan, R. Balian, T.M. Nieuwenhuizen, Understanding quantum measurement from the solution of dynamical models (2012)

    Google Scholar 

  2. V.I. Arnold, A. Avez, Ergodic Problems in Classical Mechanics (Benjamin, New York, 1968)

    Google Scholar 

  3. G. Auletta, Foundations and Interpretation of Quantum Mechanics (World Scientific, Singapore, 2001)

    Google Scholar 

  4. G. Bacciagaluppi, A. Valentini, Quantum Theory at the Crossroads, Reconsidering the 1927 Solvay Conference (Cambridge University Press, Cambridge, 2012), arXiv:quant-ph/0609184

    Google Scholar 

  5. J.S. Bell, On the Einstein-Podolsky-Rosen paradox. Physics 1, 195 (1964)

    Google Scholar 

  6. J.S. Bell, On the problem of hidden variables in quantum mechanics. Rev. Mod. Phys. 38, 447–452 (1966)

    Article  ADS  MATH  Google Scholar 

  7. E.G. Beltrametti, G. Cassinelli, The Logic of Quantum Mechanics. Encyclopedia of Mathematics and Its Applications, vol. 15 (Addison-Wesley, Reading, 1981)

    Google Scholar 

  8. G. Brassard, H. Buhrman, N.Linden, A.A. Méthot, A. Tapp, F. Unger, Limit on nonlocality in any world in which communication complexity is not trivial. Phys. Rev. Lett. 96, 250401 (2006)

    Google Scholar 

  9. C. Brukner, Questioning the rules of the game. Physics 4, 55 (2011)

    Article  Google Scholar 

  10. J. Bub, Von Neumann’s “no hidden variables” proof: a re-appraisal. Found. Phys. 40, 1333–1340 (2010)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  11. G. Chiribella, G.M. D’Ariano, P. Perinotti, Probabilistic theories with purification. Phys. Rev. A 81, 062348 (2010)

    Article  ADS  Google Scholar 

  12. G. Chiribella, G.M. D’Ariano, P. Perinotti, Informational derivation of quantum theory. Phys. Rev. A 84, 012311 (2011)

    Article  ADS  Google Scholar 

  13. B.S. Cirel’son, Quantum generalizations of Bell’s inequality. Lett. Math. Phys. 4, 93–100 (1980). doi:10.1007/BF00417500

    Google Scholar 

  14. J.F. Clauser, M.A. Horne, A. Shimony, R.A. Holt, Proposed experiment to test local hidden-variable theories. Phys. Rev. Lett. 23, 880–884 (1969)

    Article  ADS  Google Scholar 

  15. B. Coecke, Quantum picturalism. Contemp. Phys. 51(1), 59–83 (2010)

    Article  ADS  Google Scholar 

  16. E. Crull, G. Bacciagaluppi, Translation of: W. Heisenberg, “Ist eine deterministische Ergänzung der Quantenmechanik möglich?” (2011). http://philsci-archive.pitt.edu/8590/

  17. D. Deutsch, The Fabric of Reality: The Science of Parallel Universes– and Its Implications (Allen Lane, New York, 1997)

    Google Scholar 

  18. B.S. DeWitt, R.N. Graham (eds.), The Many-Worlds Interpretation of Quantum Mechanics. Princeton Series in Physics (Princeton University Press, Princeton, 1973)

    Google Scholar 

  19. D. Dürr, S. Goldstein, N. Zanghì. Quantum equilibrium and the origin of absolute uncertainty. J. Stat. Phys. 67, 843–907 (1992)

    Article  ADS  MATH  Google Scholar 

  20. D. Dürr, S. Goldstein, N. Zanghì. Quantum equilibrium and the role of operators as observables in quantum theory. J. Stat. Phys. 116, 959–1055 (2004)

    Article  ADS  MATH  Google Scholar 

  21. C.A. Fuchs, Quantum foundations in the light of quantum information (2001)

    Google Scholar 

  22. C.A. Fuchs, Quantum mechanics as quantum information (and only a little more) (2002), arXiv:quant-ph/0205039v1

    Google Scholar 

  23. G.C. Ghirardi, A. Rimini, T. Weber, A Model for a Unified Quantum Description of Macroscopic and Microscopic Systems (Springer, Berlin, 1985)

    Google Scholar 

  24. G.C. Ghirardi, A. Rimini, T. Weber, Unified dynamics for microscopic and macroscopic systems. Phys. Rev. D34, 470 (1986)

    ADS  MathSciNet  Google Scholar 

  25. A.M. Gleason, Measures on the closed subspaces of a Hilbert space. Indiana Univ. Math. J. 6, 885–893 (1957)

    Article  MATH  MathSciNet  Google Scholar 

  26. S. Goldstein, J.L. Lebowitz, C. Mastrodano, R. Tumulka, N. Zanghi, Normal typicality and von Neumann’s quantum ergodic theorem. Proc. R. Soc. A 466, 3203–3224 (2010)

    Article  ADS  MATH  Google Scholar 

  27. R.B. Griffiths, Consistent Quantum Theory (Cambridge University Press, Cambridge, 2002)

    MATH  Google Scholar 

  28. D. Gross, M. Müller, R. Colbeck, O.C.O. Dahlsten, All reversible dynamics in maximally nonlocal theories are trivial. Phys. Rev. Lett. 104, 080402 (2010)

    Article  ADS  Google Scholar 

  29. J.J. Halliwell, J. Pérez-Mercader, W.H. Zurek (eds.), Physical Origins of Time Asymmetry (Cambridge University Press, Cambridge, 1996)

    Google Scholar 

  30. L. Hardy, Quantum theory from five reasonable axioms (2001). Perimeter Institute preprint, arXiv:quant-ph/0101012

    Google Scholar 

  31. L. Hardy, Reformulating and reconstructing quantum theory (2011). Perimeter Institute preprint, arXiv:1104.2066

    Google Scholar 

  32. D. Howard, Who invented the “Copenhagen Interpretation”? A study in mythology. Philos. Sci. 71(5), 669–682 (2004)

    Google Scholar 

  33. E. Joos, H.D. Zeh, C. Kiefer, D. Giulini, J. Kupsch, I.-O. Stamatescu, Decoherence and the Appearance of a Classical World in Quantum Theory, 2nd edn. (Springer, Berlin, 2003)

    Book  Google Scholar 

  34. S. Kochen, E.P. Specker, The problem of hidden variables in quantum mechanics. J. Math. Mech. 17, 59–87 (1967)

    MATH  MathSciNet  Google Scholar 

  35. F. Laloë, Do We Really Understand Quantum Mechanics? (Cambridge University Press, Cambridge, 2012)

    Book  Google Scholar 

  36. A.J. Lichtenberg, M.A. Lieberman, Regular and Chaotic Dynamics. Applied Mathematical Sciences (Springer, Berlin, 1992)

    Book  MATH  Google Scholar 

  37. O. Lombardi, D. Dieks, Modal interpretations of quantum mechanics, in The Stanford Encyclopedia of Philosophy, ed. by E.N. Zalta, spring 2014 edition (2014), http://plato.stanford.edu/entries/qm-modal/

  38. G. Ludwig, Foundations of Quantum Mechanics (Springer, New York, 1985)

    Book  MATH  Google Scholar 

  39. L. Masanes, M. Mueller, A derivation of quantum theory from physical requirements. New J. Phys. 13, 063001 (2011)

    Article  ADS  Google Scholar 

  40. N.F. Mott, The wave mechanics of α-ray tracks. Proc. R. Soc. Lond. A 129, 79–84 (1929)

    Article  ADS  Google Scholar 

  41. E. Nelson, Derivation of the Schrödinger equation from Newtonian mechanics. Phys. Rev. 150, 079–1085 (1966)

    Article  ADS  Google Scholar 

  42. M.A. Nielsen, I.L. Chuang, Quantum Computation and Quantum Information, 10th anniversary edition (Cambridge University Press, Cambridge, 2010)

    Google Scholar 

  43. M. Pawlowski, T. Paterek, D. Kaszlikowski, V. Scarani, A. Winter, M. Zukowski, Information causality as a physical principle. Nature 461, 1101–1104 (2009)

    Article  ADS  Google Scholar 

  44. A. Peres, Unperformed experiments have no results. Am. J. Phys. 46(7), 745 (1978)

    Google Scholar 

  45. A. Peres, Quantum Theory: Concepts and Methods (Springer, Berlin, 1995)

    MATH  Google Scholar 

  46. S. Popescu, D. Rohrlich, Quantum nonlocality as an axiom. Found. Phys. 24, 379–385 (1994). doi:10.1007/BF02058098

    Article  ADS  MathSciNet  Google Scholar 

  47. B. Saunders, J. Barrett, A. Kent, D. Wallace (eds.), Many worlds? Everett, Quantum Theory and Reality (Oxford University Press, Oxford, 2010)

    MATH  Google Scholar 

  48. M.A. Schlosshauer, Decoherence and the Quantum-to-Classical Transition (Springer, Berlin, 2007)

    Google Scholar 

  49. R.F. Streater, Lost Causes in and Beyond Physics (Springer, Berlin, 2007)

    MATH  Google Scholar 

  50. G. ’t Hooft, A mathematical theory for deterministic quantum mechanics. J. Phys. Conf. Ser. 67(1), 012015 (2007)

    Google Scholar 

  51. A. Valentini, Signal-locality, uncertainty, and the sub-quantum h-theorem, I. Phys. Lett. A 156(5) (1991)

    Google Scholar 

  52. A. Valentini, Signal-locality, uncertainty, and the sub-quantum h-theorem, II. Phys. Lett. A 158(1) (1991)

    Google Scholar 

  53. W. van Dam, Implausible consequences of superstrong nonlocality (2005). arXiv:quant-ph/0501159. Natural Computing, March 2013, vol. 12, issue 1, pp. 9–12

    Google Scholar 

  54. J. von Neumann, Beweis des Ergodensatzes und des H-theorems in der neuen Mechanik. Z. Phys. 57, 30–70 (1929)

    Article  ADS  MATH  Google Scholar 

  55. J. von Neumann, Mathematische Grundlagen der Quantenmechanik. Grundlehren der mathematischen Wissenschaften, volume Bd. 38. (Springer, Berlin, 1932)

    Google Scholar 

  56. J. von Neumann, Mathematical Foundations of Quantum Mechanics. Investigations in Physics, vol. 2. (Princeton University Press, Princeton, 1955)

    Google Scholar 

  57. J. von Neumann, Proof of the ergodic theorem and the H-theorem in quantum mechanics. Eur. Phys. J. H 35, 201–237 (2010). doi:10.1140/epjh/e2010-00008-5

    Article  Google Scholar 

  58. J.A. Wheeler, W. Zurek, Quantum Theory and Measurement. Princeton Series in Physics (Princeton University Press, Princeton, 1983)

    Google Scholar 

  59. W.H. Zurek (ed.), Complexity, entropy, and the physics of information, in Santa Fe Institute Studies in the Sciences of Complexity, vol. 8 (Addison-Wesley, Redwood City, 1990)

    Google Scholar 

  60. W.H. Zurek, Decoherence and the transition from quantum to classical – revisited (2003), arXiv:quant-ph/0306072v1

    Google Scholar 

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David, F. (2015). Information, Correlations, and More. In: The Formalisms of Quantum Mechanics. Lecture Notes in Physics, vol 893. Springer, Cham. https://doi.org/10.1007/978-3-319-10539-0_5

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