Skip to main content
Log in

Informationally complete sets of physical quantities

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

Abstract

The notion of informational completeness is formulated within the convex state (or operational) approach to statistical physical theories and employed to introduce a type of statistical metrics. Further, a criterion for a set of physical quantities to be informationally complete is proven. Some applications of this result are given within the algebraic and Hilbert space formulations of quantum theory.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Abbati, M. C., and Mania, A. (1981).Annales de l'Institut Henri Poincaré,XXXV, 259–285.

    Google Scholar 

  • Alfsen, E. M. (1971).Compact Convex Sets and Boundary Integrals, Springer, Berlin.

    Google Scholar 

  • Ali, S. T. (1985).Nuovo Cimento,8, 1–128.

    Google Scholar 

  • Ali, S. T., and Doebner, H. D. (1976).Journal of Mathematical Physics,17, 1105–1111.

    Google Scholar 

  • Ali, S. T., and Prugovecki, E. (1977a).Journal of Mathematical Physics,18, 219–228.

    Google Scholar 

  • Ali, S. T., and Prugovecki, E. (1977b).Physica,89A, 501–521.

    Google Scholar 

  • Busch, P. (1987a). Unsharp reality and the question of quantum systems, inSymposium on the Foundations of Modem Physics 1987, P. Lahti and P. Mittelstaedt, eds., World Scientific, Singapore, pp. 105–125.

    Google Scholar 

  • Busch, P. (1987b).Foundations of Physics,17, 905–937.

    Google Scholar 

  • Busch, P., and Lahti, P. J. (1989).Foundations of Physics,19, 633–678.

    Google Scholar 

  • Busch, P., and Schroeck, F. E., Jr. (1989).Foundations of Physics,19, 807–872.

    Google Scholar 

  • Busch, P., Cassinelli, G., and Lahti, P. J. (1990). Sigma-convex structures and classical embeddings of quantum mechanical state spaces, in preparation.

  • Busch, P., Grabowski, M., and Lahti, P. J. (1989).Foundations of Physics Letters,2, 331–345.

    Google Scholar 

  • Davies, E. B. (1976).Quantum Theory of Open Systems, Academic Press, New York.

    Google Scholar 

  • De Muynck, W. M., and Martens, H. (1990). Nonideal quantum measurements, simultaneous measurements of noncommuting observables, and the Bell inequalities, inFoundations of Quantum Mechanics in the Light of New Technology, Physical Society of Japan.

  • Grabowski, M. (1991). Quantum measurement scheme and new examples of generalized observables, inSymposium on the Foundations of Modern Physics 1990, P. Lahti and P. Mittelstaedt, eds., World Scientific, Singapore, pp. 124–137.

    Google Scholar 

  • Gudder, S. P. (1973).Communications in Mathematical Physics,29, 249–264.

    Google Scholar 

  • Hadjisavvas, N. (1981).Annales de l'Institut Henri Poincaré,XXXV, 287–309.

    Google Scholar 

  • Healy, D. M., and Schroeck, F. E., Jr. (1988). Application of stochastic quantum mechanics and coherent state methodologies to signal processing, Florida Atlantic University Preprint.

  • Jauch, J. M., Misra, B., and Gibson, A. G. (1968). On the asymptotic condition of scattering theory,Helvetica Physica Acta,41, 513–527.

    Google Scholar 

  • Ludwig, G. (1983).Foundations of Quantum Mechanics, Vol. 1 (Springer, Berlin).

    Google Scholar 

  • Ludwig, G. (1987).An Axiomatic Basis for Quantum Mechanics, Vol. 2:Quantum Mechanics and Macrosystems (Springer, Berlin).

    Google Scholar 

  • Ozawa, M. (1984).Journal of Mathematical Physics,25, 79–87.

    Google Scholar 

  • Prugovecki, E. (1977).International Journal of Theoretical Physics,16, 321–331.

    Google Scholar 

  • Prugovecki, E. (1986).Stochastic Quantum Mechanics and Quantum Spacetime, 2nd ed., Reidel, Dordrecht.

    Google Scholar 

  • Rudin, W. (1973).Functional Analysis, McGraw-Hill, New York.

    Google Scholar 

  • Schroeck, F. E., Jr. (1981).Journal of Mathematical Physics,22, 2562–2572.

    Google Scholar 

  • Schroeck, F. E., Jr. (1988). On integration with respect to a positive operator valued measure, Florida Atlantic University Preprint.

  • Schroeck, F. E., Jr. (1989).International Journal of Theoretical Physics,28, 247–262.

    Google Scholar 

  • Schroeck, F. E., Jr. (1990).Quantum Mechanics on Phase Space, Monograph in preparation.

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Busch, P. Informationally complete sets of physical quantities. Int J Theor Phys 30, 1217–1227 (1991). https://doi.org/10.1007/BF00671008

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00671008

Keywords

Navigation