Quantum theory and beyond: Is entanglement special?

Deep Beauty: Understanding the Quantum World Through Mathematical Innovation

Volumn , Issue , 2011, Pages 365-392

  Dakić, Borivoje ^a   Brukner, Časlav ^a  

^a UNIVERSITY OF VIENNA   (Austria)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84926950265     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1017/CBO9780511976971.011     Document Type: Chapter

References (69)

1. S. Kochen and E. P. Specker. The problem of hidden variables in quantum mechanics. Journal of Mathematics Mechanics 17 (1967), 59.
2. J. S. Bell. Speakable and Unspeakable in Quantum Mechanics. Cambridge: Cambridge University Press, 1987.
3. A. J. Leggett. Nonlocal hidden-variable theories and quantum mechanics: An incompatibility theorem. Foundations of Physics 33 (2003), 1469.
4. S. Gröblacher, T. Paterek, R. Kaltenbaek, et al. An experimental test of non-local realism. Nature 446 (2007), 871.
5. I. Biaynicki-Birula and J. Mycielski. Nonlinear wave mechanics. Annals of Physics 100 (1976), 62.
6. A. Shimony. Proposed neutron interferometer test of some nonlinear variants of wave mechanics. Physical Review A 20 (1979), 394.
7. C. G. Shull, D. K. Atwood, J. Arthur, et al. Search for a nonlinear variant of the Schrodinger equation by neutron interferometry. Physical Review Letters 44 (1980), 765.
8. R. Gähler, A. G. Klein, and A. Zeilinger. Neutron optical tests of nonlinear wave mechanics. Physical Review A 23 (1981), 1611.
9. G. C. Ghirardi, A. Rimini, and T. Weber. Unified dynamics for microscopic and macroscopic systems. Physical Review D 34 (1986), 470.
10. F. Károlyházy. Nuovo Cimento 42 (1966), 390.
11. F. Károlyházy. Gravitation and quantum mechanics of macroscopic bodies (Thesis, in Hungarian). Magyar Fizikai Folyóirat 22 (1974), 23.
12. L. Diosi. Models for universal reduction of macroscopic quantum fluctuations. Physical Review A 40 (1989), 1165.
13. R. Penrose. On gravity’s role in quantum state reduction. General Relativity and Gravitation 28 (1996), 581.
14. P. Pearle. Reduction of the state vector by a nonlinear Schrödinger equation. Physical Review D 13 (1976), 857.
15. H. Barnum, J. Barrett, M. Leifer, et al. Cloning and broadcasting in generic probabilistic models (2006). arXiv:quant-ph/061129.
16. H. Barnum, J. Barrett, M. Leifer, et al. A general no-cloning theorem. Physical Review Letters 99 (2007), 240501.
17. J. Barrett. Information processing in general probabilistic theories. Physical Review A. 75 (2007), 032304.
18. S. Popescu and D. Rohrlich. Quantum nonlocality as an axiom. Foundations of Physics 24 (1994), 379.
19. G. W. Mackey. Quantum mechanics and Hilbert space. American Mathematical Monthly 64 (1957), 45.
20. L. Hardy. Quantum theory from five reasonable axioms (2001). arXiv:quant-ph/0101012.
21. G. M. Dariano. Probabilistic theories: What is special about quantum mechanics? In Philosophy of Quantum Information and Entanglement, eds. A. Bokulich and G. Jaeger. Cambridge: Cambridge University Press, 2010.
22. P. Goyal, K. H. Knuth, and J. Skilling. Origin of complex quantum amplitudes and Feynman’s rules (2009). arXiv:quant-ph/0907.0909.
23. C. Rovelli. Relational quantum mechanics. International Journal of Theoretical Physics 35 (1996), 1637.
24. A. Zeilinger. A foundational principle for quantum mechanics. Foundations of Physics 29 (1999), 631.
25. Č. Brukner and A. Zeilinger. Information and fundamental elements of the structure of quantum theory. In Time, Quantum, Information, eds. L. Castell and O. Ischebeck. Springer, 2003.
26. Č. Brukner and A. Zeilinger. Information invariance and quantum probabilities. Foundations of Physics 39 (2009), 677.
27. R. Clifton, J. Bub, and H. Halvorson. Characterizing quantum theory in terms of information-theoretic constraints. Foundations of Physics 33(11) (2003), 1561.
28. A. Grinbaum. Elements of information-theoretic derivation of the formalism of quantum theory. International Jouranal Quantum Information 1(3) (2003), 289.
29. W. K. Wootters. Statistical distance and Hilbert space. Physical Review D 23 (1981), 357.
30. D. I. Fivel. How interference effects in mixtures determine the rules of quantum mechanics. Physical Review A 59 (1994), 2108.
31. J. Summhammer. Maximum predictive power and the superposition principle. International Journal of Theoretical Physics 33 (1994), 171.
32. J. Summhammer. Quantum theory as efficient representation of probabilistic information (2007). arXiv:quant-ph/0701181.
33. A. Bohr and O. Ulfbeck. Primary manifestation of symmetry: Origin of quantal indeterminacy. Reviews of Modern Physics 67 (1995), 1.
34. A. Caticha. Consistency, amplitudes and probabilities in quantum theory. Physical Review A 57 (1998), 1572.
35. C. A. Fuchs. Quantum mechanics as quantum information (and only a little more). In Quantum Theory: Reconstruction of Foundations, ed. A. Khrenikov. Växjo: Växjo, Sweden University Press, 2002.
36. C. A. Fuchs and R. Schack. Quantum-Bayesian coherence (2009). arXiv:quant-ph/0906.2187.
37. P. Grangier. Contextual objectivity: A realistic interpretation of quantum mechanics. European Journal of Physics 23 (2002), 331.
38. P. Grangier. Contextual objectivity and the quantum formalism. International Journal Quantum Information 3 (2005), 17–22.
39. S. Luo. Maximum Shannon entropy, minimum Fisher information, and an elementary game. Foundations of Physics 32 (2002), 1757.
40. R. Spekkens. Evidence for the epistemic view of quantum states: A toy theory. Physical Review A 75 (2007), 032110.
41. P. Goyal. Information-geometric reconstruction of quantum theory. Physical Review A 78 (2008), 052120.
42. W. van Dam. Implausible consequences of superstrong nonlocality (2005). arXiv:quant-ph/0501159.
43. G. Brassard, H. Buhrman, N. Linden, et al. A limit on nonlocality in any world in which communication complexity is not trivial. Physical Review Letters 96 (2006), 250401.
44. M. Pawlowski, T. Paterek, D. Kaszlikowski, et al. A new physical principle: Information causality. Nature 461 (2009), 1101.
45. M. Navascues and H. Wunderlich. A glance beyond the quantum model. Proceedings of the Royal Society A 466 (2009), 2115.
46. K. Zyczkowski. Quartic quantum theory: An extension of the standard quantum mechanics. Journal of Physics A 41 (2008), 355302.
47. T. Paterek, B. Dakić, and Č. Brukner. Theories of systems with limited information content. New Journal of Physics 12 (2010), 053037.
48. A. Peres. Proposed test for complex versus quaternion quantum theory. Physical Review Letters 42 (1979), 683.
49. H. Kaiser, E. A. George, and S. A. Werner. Neutron interferometric search for quaternions in quantum mechanics. Physical Review A 29 (1984), 2276.
50. A. Peres. Quaternionic quantum interferometry. In Quantum Interferometry, eds. F. De Martini et al. VCH Publication, 1996, pp 431–437.
51. R. D. Sorkin. Quantum mechanics as quantum measure theory. Modern Physics Letters A 9 (1994), 3119.
52. U. Sinha, C. Couteau, Z. Medendorp, et al. Testing Born’s Rule in quantum mechanics with a triple slit experiment. AIP Conference Proceedings 1101 (2009), 200–207.
53. A. Grinbaum. Reconstruction of quantum theory. British Journal for the Philosophy of Science 8 (2007), 387.
54. D. Gross, M. Mueller, R. Colbeck, et al. All reversible dynamics in maximally non-local theories are trivial (2009). arXiv:quant-ph/0910.1840.
55. C. F. von Weizsäcker. Aufbau der Physik. Carl Hanser, Munchen, 1958.
56. J. A. Wheeler. Law without law in quantum theory and measurement. In Quantum Theory and Measurement, eds. J. A. Wheeler and W. H. Zurek. Princeton, NJ: Princeton University Press, 1983, p. 182.
57. H. Barnum and A. Wilce. Information processing in convex operational theories. arXiv:quant-ph/0908.2352.
58. S. Abramsky and B. Coecke. A categorical semantics of quantum protocols. Logic in Computer Science, Symposium on 0 (2004), 415–25.
59. [59] J. Ambjorn, J. Jurkiewicz, and R. Loll. Reconstructing the universe. Physical Review D 72 (2005), 064014.
60. H. Boerner. Representations of groups. Amsterdam: North-Holland Publishing Company, 1963.
61. W. K. Wooters and B.D. Fields. Optimal state-determination by mutually unbiased measurements. Annals of Physics (N.Y.) 191 (1989), 363.
62. I. D. Ivanovic. Geometrical description of quantal state determination. Journal of Physics A 14 (1981), 3241.
63. D. Bohm. A suggested interpretation of the quantum theory in terms of “hidden variables” I. Physical Review 85 (1952), 166.
64. D. Bohm. A suggested interpretation of the quantum theory in terms of “hidden variables” II. Physical Review 85 (1952), 180.
65. L. Hardy. Quantum ontological excess baggage. Studies in History and Philosophy of Modern Physics 35 (2004), 267.
66. A. Montina. Exponential complexity and ontological theories of quantum mechanics. Physical Review A 77 (2008), 022104.
67. B. Dakić, M. Suvakov, T. Paterek, et al. efficient hidden-variable simulation of measurements in quantum experiments. Physical Review Letters 101 (2008), 190402.
68. Č. Brukner and A. Zeilinger. Young’s experiment and the finiteness of information. Philosophical Transactions of the Royal Society of London A 360 (2002), 1061.
69. E. Schrödinger. Discussion of probability relations between separated systems, Proceedings of the Cambridge Philosophical Society 31 (1935), 555–63; 32 (1936), 446–51.