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Three Slit Experiments and the Structure of Quantum Theory


In spite of the interference manifested in the double-slit experiment, quantum theory predicts that a measure of interference defined by Sorkin and involving various outcome probabilities from an experiment with three slits, is identically zero. We adapt Sorkin’s measure into a general operational probabilistic framework for physical theories, and then study its relationship to the structure of quantum theory. In particular, we characterize the class of probabilistic theories for which the interference measure is zero as ones in which it is possible to fully determine the state of a system via specific sets of ‘two-slit’ experiments.

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  1. 1.

    Feynman, R.P., Leighton, R.B., Sands, M.: The Feynman Lectures on Physics. Addison-Wesley, Reading (1965)

  2. 2.

    Sorkin, R.: Mod. Phys. Lett. A 9, 3119 (1994)

  3. 3.

    Sinha, U., et al.: In: Accardi, L., et al. (eds.) Foundations of Probability and Physics—5, Vaxjo, August, 2008, American Institute of Physics, Ser. Conference Proceedings, vol. 1101, pp. 200–207. Melville, NY (2009)

  4. 4.

    Gale, W., Guth, E., Trammell, G.T.: Phys. Rev. 165(5), 1434 (1968)

  5. 5.

    Ballentine, L.E.: In: Greenberger, D.M. (ed.) New Techniques and Ideas in Quantum Mechanics. Annals of the New York Academy of Sciences, vol. 480, pp. 382–392. New York Academy of Sciences, New York (1986)

  6. 6.

    Jaynes, E.: Probability Theory: The Logic of Science. Cambridge University Press, Cambridge (2003)

  7. 7.

    Mackey, G.: Mathematical Foundations of Quantum Mechanics. Addison-Wesley, Reading (1963)

  8. 8.

    Holevo, A.: Probabilistic and Statistical Aspects of Quantum Mechanics. North-Holland, Amsterdam (1983)

  9. 9.

    Gudder, S.: Int. J. Theor. Phys. 28(12), 3179 (1999)

  10. 10.

    Hardy, L.: Quantum theory from five reasonable axioms. ArXiv:quant-ph/0101012 (2001)

  11. 11.

    Mana, P.: Why can states and measurement outcomes be represented as vectors? ArXiv:quant-ph/0305117v3 (2003)

  12. 12.

    Barnum, H., Barrett, J., Leifer, M., Wilce, A.: Cloning and broadcasting in generalized probabilistic models. ArXiv:quant-ph/0611295 (2006)

  13. 13.

    Alfsen, E., Shultz, F.: Geometry of State Spaces of Operator Algebras. Birkhauser, Basel (2003)

  14. 14.

    Araki, H.: Commun. Math. Phys. 75, 1 (1980)

  15. 15.

    Ludwig, G.: An Axiomatic Basis of Quantum Mechanics, vol. I. Springer, Berlin (1985)

  16. 16.

    Ludwig, G.: An Axiomatic Basis of Quantum Mechanics, vol. II. Springer, Berlin (1987)

  17. 17.

    Mielnik, B.: Comm. Math. Phys. 15(1), 1 (1969)

  18. 18.

    Beltrametti, E., Cassinelli, J.: The Logic of Quantum Mechanics. Addison-Wesley, Reading (1981)

  19. 19.

    Ududec, C., Barnum, H., Emerson, J.: Probabilistic interference in operational models. Forthcoming

  20. 20.

    Jordan, P., von Neumann, J., Wigner, E.: Ann. Math. 35, 29 (1934)

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Correspondence to Cozmin Ududec.

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Ududec, C., Barnum, H. & Emerson, J. Three Slit Experiments and the Structure of Quantum Theory. Found Phys 41, 396–405 (2011).

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  • Quantum theory
  • Interference
  • Three slit experiment
  • Operational models
  • Tomography