International Journal of Theoretical Physics

, Volume 37, Issue 5, pp 1491–1509 | Cite as

Concept of Experimental Accuracy and Simultaneous Measurements of Position and Momentum

  • D. M. Appleby


The concept of experimental accuracy isinvestigated in the context of the unbiased jointmeasurement processes defined by Arthurs and Kelly. Adistinction is made between the errors of retrodictionand prediction. Four error-disturbancerelationships are derived, analogous to the singleerror-disturbance relationship derived by Braginsky andKhalili in the context of single measurements ofposition only. A retrodictive and a predictive error-errorrelationship are also derived. The connection betweenthese relationships and the extended uncertaintyprinciple of Arthurs and Kelly is discussed. Thesimilarities and differences between the quantum mechanicaland classical concepts of experimental accuracy areexplored. It is argued that these relationships providegrounds for questioning Uffink's conclusion that the concept of a simultaneous measurement ofnoncommuting observables is not fruitful.


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  1. Arthurs, E., and Goodman, M. S. (1988). Physical Review Letters, 60, 2447.Google Scholar
  2. Arthurs, E., and Kelly, J. L., Jr. (1965). Bell System Technical Journal, 44, 725.Google Scholar
  3. Ballentine, L. F. (1970). Reviews of Modern Physics, 42, 358.Google Scholar
  4. Bohm, D. (1951). Quantum Theory, Prentice-Hall, New York.Google Scholar
  5. Braginsky, V. B., and Khalili, F. Ya (1992). Quantum Measurement, K. S. Thorne, ed., Cambridge University Press, Cambridge.Google Scholar
  6. Braunstein, S. L., Caves, C. M., and Milburn, G. J. (1991). Physical Review A, 43, 1153.Google Scholar
  7. Busch, P., and Lahti, P. J. (1984). Physical Review D, 29, 1634.Google Scholar
  8. de Muynck, W. M., De Baere, W., and Martens, H. (1994). Foundations of Physics, 24, 1589.Google Scholar
  9. Heisenberg, W. (1927). Zeitschrift für Physik, 43, 172, [Reprinted in Wheeler, J. A., and Zurek, W. H., eds. (1983). Quantum Theory and Measurement, Princeton University Press, Princeton, New Jersey.]Google Scholar
  10. Heisenberg, W. (1930). The Physical Principles of the Quantum Theory, University of Chicago Press, Chicago.Google Scholar
  11. Hilgevoord, J., and Uffink, J. (1990). In Sixty-Two Years of Uncertainty, A. I. Miller, ed., Plenum Press, New York.Google Scholar
  12. Holevo, A. S. (1982). Probabilistic and Statistical Aspects of Quantum Theory, North-Holland, Amsterdam.Google Scholar
  13. Kadison, R. V., and Ringrose, J. R. (1983). Fundamentals of the Theory of Operator Algebras, Academic Press, New York.Google Scholar
  14. Kennard, E. H. (1927). Zeitschrift für Physik, 44, 326.Google Scholar
  15. Leonhardt, U., and Paul, H. (1993). Journal of Modern Optics, 40, 1745.Google Scholar
  16. Leonhardt, U., Böhmer, B., and Paul, H. (1995). Optics Communications, 119, 296.Google Scholar
  17. Martens, H., and de Muynck, W. M. (1992). Journal of Physics A, 25, 4887.Google Scholar
  18. Prugovečki, E. (1973). Foundations of Physics, 3, 3.Google Scholar
  19. Prugovečki, E. (1975). Foundations of Physics, 5, 557.Google Scholar
  20. Prugovečki, E. (1984). Stochastic Quantum Mechanics and Quantum Spacetime, Reidel, Dordrecht.Google Scholar
  21. Raymer, M. G. (1994). American Journal of Physics, 62, 986.Google Scholar
  22. Stenholm, S. (1992). Annals of Physics, 218, 233.Google Scholar
  23. Törma, P., Stenholm, S., and Jex, I. (1995). Physical Review A, 52, 4812.Google Scholar
  24. Uffink, J. (1994). International Journal of Theoretical Physics, 33, 199.Google Scholar
  25. Wódkiewicz, K. (1987). Physics Letters A, 124, 207.Google Scholar

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© Plenum Publishing Corporation 1998

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  • D. M. Appleby

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