Advertisement

Foundations of Physics

, Volume 41, Issue 3, pp 396–405 | Cite as

Three Slit Experiments and the Structure of Quantum Theory

  • Cozmin Ududec
  • Howard Barnum
  • Joseph Emerson
Article

Abstract

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.

Keywords

Quantum theory Interference Three slit experiment Operational models Tomography 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Feynman, R.P., Leighton, R.B., Sands, M.: The Feynman Lectures on Physics. Addison-Wesley, Reading (1965) MATHGoogle Scholar
  2. 2.
    Sorkin, R.: Mod. Phys. Lett. A 9, 3119 (1994) MATHCrossRefMathSciNetADSGoogle Scholar
  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) Google Scholar
  4. 4.
    Gale, W., Guth, E., Trammell, G.T.: Phys. Rev. 165(5), 1434 (1968) CrossRefADSGoogle Scholar
  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) Google Scholar
  6. 6.
    Jaynes, E.: Probability Theory: The Logic of Science. Cambridge University Press, Cambridge (2003) MATHCrossRefGoogle Scholar
  7. 7.
    Mackey, G.: Mathematical Foundations of Quantum Mechanics. Addison-Wesley, Reading (1963) MATHGoogle Scholar
  8. 8.
    Holevo, A.: Probabilistic and Statistical Aspects of Quantum Mechanics. North-Holland, Amsterdam (1983) Google Scholar
  9. 9.
    Gudder, S.: Int. J. Theor. Phys. 28(12), 3179 (1999) CrossRefMathSciNetGoogle Scholar
  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) MATHCrossRefGoogle Scholar
  14. 14.
    Araki, H.: Commun. Math. Phys. 75, 1 (1980) MATHCrossRefMathSciNetADSGoogle Scholar
  15. 15.
    Ludwig, G.: An Axiomatic Basis of Quantum Mechanics, vol. I. Springer, Berlin (1985) MATHCrossRefGoogle Scholar
  16. 16.
    Ludwig, G.: An Axiomatic Basis of Quantum Mechanics, vol. II. Springer, Berlin (1987) CrossRefGoogle Scholar
  17. 17.
    Mielnik, B.: Comm. Math. Phys. 15(1), 1 (1969) MATHCrossRefMathSciNetADSGoogle Scholar
  18. 18.
    Beltrametti, E., Cassinelli, J.: The Logic of Quantum Mechanics. Addison-Wesley, Reading (1981) MATHGoogle Scholar
  19. 19.
    Ududec, C., Barnum, H., Emerson, J.: Probabilistic interference in operational models. Forthcoming Google Scholar
  20. 20.
    Jordan, P., von Neumann, J., Wigner, E.: Ann. Math. 35, 29 (1934) CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Institute for Quantum ComputingUniversity of WaterlooWaterlooCanada
  2. 2.Perimeter Institute for Theoretical PhysicsWaterlooCanada

Personalised recommendations