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Foundations of Physics

, Volume 21, Issue 8, pp 931–945 | Cite as

“Special” states in quantum measurement apparatus: Structural requirements for the recovery of standard probabilities

  • L. S. Schulman
Article

Abstract

In a recently proposed quantum measurement theory the definiteness of quantum measurements is achieved by means of “special” states. The recovery of the usual quantum probabilities is related to the relative abundance of particular classes of “special” states. In the present article we consider two-state discrimination, and model the apparatus modes that could provide the “special” states. We find that there are structural features which, if generally present in apparatus, will provide universal recovery of standard probabilities. These structural features relate to the distribution of certain Hamiltonian matrix elements or interaction times. In particular, those quantities must be asymptotically (x → ∞) distributed according to the Cauchy law, Ca(x)=a/π(x 2 +a 2 ).

Keywords

Matrix Element Structural Feature Relative Abundance Present Article Interaction Time 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    L. S. Schulman,J. Stat. Phys. 42, 689 (1986);Phys. Lett. A 102, 396 (1984);Phys. Lett. A 130, 194 (1988);Ann. Phys. (N.Y.) 183, 320 (1988);Found. Phys. Lett. 2, 515 (1989); inPath Integrals from meV to MeV, V. Sa-Yakanitet al., eds. (World Scientific, Singapore, 1989), p. 35.Google Scholar
  2. 2.
    B. Gaveau and L. S. Schulman,J. Stat. Phys. 58, 1209 (1990).Google Scholar
  3. 3.
    L. S. Schulman, C. R. Doering, and B. Gaveau, “Quantum decay in multi-level systems,”J. Phys. A 24, 2053 (1991).Google Scholar
  4. 4.
    L. S. Schulman, “Definite quantum measurements,”Ann. Phys. (N.Y.), to appear (1991).Google Scholar
  5. 5.
    M. Born, “Zur Quantenmechanik der Stossvorgänge,”Z. Phys. 37, 863 (1926); translation printed in J. A. Wheeler and W. H. Zurek,Quantum Theory and Measurement (Princeton University Press, Princeton, 1983).Google Scholar
  6. 6.
    M. F. Shlesinger,Physica D 38, 304 (1989); B. D. Hughes, E. W. Montroll, and M. F. Shlesinger,J. Stat. Phys. 28, 111 (1982); E. W. Montroll and B. J. West, inFluctuation Phenomena, E. W. Montroll and J. L. Lebowitz, eds., 2nd edn. (North-Holland, Amsterdam, 1987).Google Scholar
  7. 7.
    W. Feller,An Introduction to Probability Theory and Its Applications, Vol. II (Wiley, New York, 1971).Google Scholar
  8. 8.
    E. P. Wigner,Z. Phys. 131, 101 (1952); H. Araki and M. Yanase,Phys. Rev. 120, 622 (1960); M. Yanase,Phys. Rev. 123, 666 (1961).Google Scholar
  9. 9.
    T. L. Bell, U. Frisch, and H. Frisch,Phys. Rev. A 17, 1049 (1978).Google Scholar
  10. 10.
    J. E. Avron, G. Roepstorff, and L. S. Schulman, “Ground state degeneracy and ferromagnetism in a spin glass,”J. Stat. Phys. 26, 25 (1981).Google Scholar
  11. 11.
    H. Scher, M. F. Shlesinger, and J. T. Bendler, “Time-scale invariance in transport and relaxation,”Phys. Today 44(1), 26 (1991).Google Scholar

Copyright information

© Plenum Publishing Corporation 1991

Authors and Affiliations

  • L. S. Schulman
    • 1
    • 2
  1. 1.Institute for Theoretical PhysicsState University of UtrechtUtrechtThe Netherlands
  2. 2.Physics DepartmentClarkson UniversityPotsdam

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