The Action Uncertainty Principle for Continuous Quantum Measurements

  • Michael B. Mensky
Part of the NATO ASI Series book series (NSSB, volume 282)


The path-integral approach to quantum theory of continuous measurements has been developed in preceding works of the author. According to this approach the measurement amplitude determining probabilities of different outputs of the measurement can be evaluated in the form of a restricted path integral (a path integral “in finite limits”). Given the measurement amplitude, the maximum deviation of the measurement outputs from the classical one can be easily determined The aim of the present paper is to express this variance in a more simple and transparent form of an inequality of the type of the uncertainty principle. Symbolically it can be written as
$$\Delta (Equation)\Delta (Path) \lesssim \hbar .$$


Continuous Measurement Measurement Output Uncertainty Principle Quantum Measurement Fine Measurement 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    C.M. Caves, in: Quantum Optics, Experimental Gravity and Measurement Theory, P. Meystre and M.O. Scully, eds., Plenum, New York (1983), p.567.CrossRefGoogle Scholar
  2. 2.
    V.B. Braginsky, in: Topics in Theoretical and Experimental Gravitation Physics, V. DeSabbata and J. Weber, eds., Plenum, New York (1977), p.105.Google Scholar
  3. 3.
    W.H. Zurek, Phys. Rev. D24: 1516 (1981).MathSciNetGoogle Scholar
  4. 4.
    W.H. Zurek, Phys. Rev. D26: 1862 (1982).MathSciNetGoogle Scholar
  5. 5.
    C.B. Chiu, E.C.G. Sudarshan and B. Misra, Phys. Rev. D16: 520 (1977).MathSciNetGoogle Scholar
  6. 6.
    A. Peres, Amer. J. Phys. 48: 931 (1980).MathSciNetCrossRefGoogle Scholar
  7. 7.
    W.M. Itano, D.J. Heinzen, J.J. Bollinger and D.J. Wineland, Phys. Rev. A41: 2295 (1990).Google Scholar
  8. 8.
    M.B. Mensky, Phys. Rev. D20: 384 (1979).Google Scholar
  9. 9.
    M.B. Mensky, Soy. Phys.-JETP 50: 667 (1979).Google Scholar
  10. 10.
    M.B. Mensky, The Path Group: Measurements, Fields,Particles, Nauka, Moscow (1983) (in Russian; Japan translation: Yosioka, Kyoto (1988)).Google Scholar
  11. 11.
    R.Ya. Khalili, Vestnik Mosk. Universiteta Ser. 3, Phys., Astr., 22: 37 (1981).Google Scholar
  12. 12.
    A. Barchielli, L. Lanz and G.M. Prosperi, Nuovo Cimento B72: 79 (1982).MathSciNetGoogle Scholar
  13. 13.
    C.M. Caves, Phys. Rev. D33: 1643 (1986).MathSciNetGoogle Scholar
  14. 14.
    C.M. Caves, Phys. Rev. D35: 1815 (1987).MathSciNetGoogle Scholar
  15. 15.
    V.B. Braginsky, Yu.I. Vorontsov and R.Ya. Khalili, Zh. Eksp. Teor. Fiz. 73: 1340 (1977).Google Scholar
  16. 16.
    W.G. Unruh, Phys. Rev. D19: 2888 (1979).Google Scholar
  17. 17.
    C.M. Caves, K.S. Thorne, R.W.P. Drever et al, Rev. Mod. Phys. 52: 341 (1980).CrossRefGoogle Scholar
  18. 18.
    G.A. Golubtsova and M.B. Mensky, Intern. J. Modern Phys. A4: 2733 (1989).CrossRefGoogle Scholar
  19. 19.
    M.B.Mensky, Continuous quantum nondemolition measurements and measurability of electromagnetic field from path integrals, in: Proceed. Intern. Workshop on Gravitational Wave Signal Analysis and Processing, Amalfi, Italy, 1–5 July, 1988, World Scientific, Singapore, to be published.Google Scholar
  20. 20.
    P.A.M. Dirac, Fields and Quanta, 3: 139 (1972).Google Scholar
  21. 21.
    R.P. Feynman and A.R. Hibbs, Quantum Mechanics and Path Integrals,McGraw-Hill, New York (1965).zbMATHGoogle Scholar
  22. 22.
    R.P. Feynman, Reviews of Modern Physics, 20: 367 (1948).MathSciNetCrossRefGoogle Scholar
  23. 23.
    M.B. Mensky, Lett. Phys., A150: 331 (1990).Google Scholar

Copyright information

© Springer Science+Business Media New York 1992

Authors and Affiliations

  • Michael B. Mensky
    • 1
  1. 1.P.N.Lebedev Physical InstituteMoscowUSSR

Personalised recommendations