Skip to main content
SpringerLink
Log in

Map for Simultaneous Measurements for a Quantum Logic

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

Abstract

In this paper we will study a function of simultaneous measurements for quantum events (s-map) which will be compared with the conditional states on an orthomodular lattice as a basic structure for quantum logic. We will show the connection between s-map and a conditional state. On the basis of the Rényi approach to the conditioning, conditional states, and the independence of events with respect to a state are discussed. Observe that their relation of independence of events is not more symmetric contrary to the standard probabilistic case. Some illustrative examples are included.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Aerts, D. (2001). Disjunction. Preprint.

  • Cassinelli, G. and Beltrameti, E. (1975). Idea, first-kind measurement in propositional state structure. Communications in Mathematical Physics 40, 7-13.

    Google Scholar 

  • Cassinelli, G. and Truini, P. (1984). Conditional probabilities on orthomodular lattices. Reports on Mathematical Physics 20, 41-52.

    Google Scholar 

  • Cassinelli, G. and Zanghí, N. (1983). Conditional probabilities in quantum mechanics I. II Nuovo Cimento 738, 237-245.

    Google Scholar 

  • Cassinelli, G. and Zanghí, N. (1984). Conditional probabilities in quantum mechanics II. II Nuovo Cimento 798, 141-154.

    Google Scholar 

  • Catlin, D. E. (1968). Spectral theory in quantum logic. International Journal of Theoretical Physics 1, 3-16.

    Google Scholar 

  • Dvurečenskij, A. and Pulmannová, S. (1984). Connection between distribution and compatibility. Reports on Mathematical Physics 19, 349-355.

    Google Scholar 

  • Dvurečenskij, A. and Pulmannová, S. (2000). New Trends in Quantum Structures, Kluwer Academic, Norwell, MA.

    Google Scholar 

  • Greechie, R. J., Foulis, D. J., and Pulmannová, S. (1995). The center of an effect algebra. Order 12, 91-106.

    Google Scholar 

  • Gudder, S. P. (1965). Spectral methods for a generalized probability theory. AMS 119, 428-442.

    Google Scholar 

  • Gudder, S. P. (1966). Uniqueness and existence properties of bounded observables. Pacific Journal of Mathematics 19, 81-93.

    Google Scholar 

  • Gudder, S. P. (1967). Hilbert space, independence, and generalized probability. Math. Analys. Applic. 20, 48-61.

    Google Scholar 

  • Gudder, S. P. (1968). Joint distribution of observables. Journal of Mathematical Mechanics 15, 325-335.

    Google Scholar 

  • Gudder, S. P. (1969). Quantum probability spaces. AMS 21, 296-302.

    Google Scholar 

  • Gudder, S. P. (1984). An extension of classical measure theory. Soc. for Ind. and Appl. Math. 26, 71-89.

    Google Scholar 

  • Gudder, S. P. and Mullikin, H. C. (1984). Measure theoretic convergences of observables and operators. Journal of Mathematics and Physics 14, 71-89.

    Google Scholar 

  • Gudder, S. P. and Piron, C. (1971). Observables and the field in quantum mechanics. Journal of Mathematics and Physics 12, 1583-1588.

    Google Scholar 

  • Guz, W. (1982). Conditional probability and the axiomatic structure of quantum mechanics. Fortschritt der Physik 29 345-379.

    Google Scholar 

  • Kolmogoroff, A. N. (1933). Grundbegriffe der Wahrscheikchkeitsrechnung Springer, Berlin.

    Google Scholar 

  • Nánásiová, O. and Pulmannová, S. (1985). Relative conditional expectations on a quantum logic. Aplikace Matematiky 30, 47-64.

    Google Scholar 

  • Nánásiová, O. (1987a). Ordering of observables and characterization of conditional expectation on a quantum logic. Mathematica Slovaca 37, 323-340.

    Google Scholar 

  • Nánásiová, O. (1987b). On conditional probabilities on quantum logic. International Journal of Theoretical Physics 25, 155-162.

    Google Scholar 

  • Nánásiová, O. (1993a). Observables and expectation on the Pták sum. Tatra Mount. Publ. Math. 3, 65-76.

    Google Scholar 

  • Nánásiová, O. (1993b). States and homomorphism on the Pták sum. International Journal of Theoretical Physics 32, 1957-1964.

    Google Scholar 

  • Nánásiová, O. (1998). A note on the independent events on aquantum logic. Busefal 76, 53-57.

    Google Scholar 

  • Nánásiová, O. (2001). Principle conditioning. Preprint.

  • Pták, P. and Pulmannová, S. (1991). Quantum Logics, Kluwer Academic, Bratislava.

    Google Scholar 

  • Renyi, A. (1947). On conditional probabilities spaces generated by a dimensionally ordered set of measures. Teorija verojatnostej i jejo primene nija 1, 930-948.

    Google Scholar 

  • Riečan B., Neubrun T., Measure theory.

  • Varadarajan, V. (1968). Geometry of Quantum Theory, D. Van Nostrand, Princeton, NJ.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Slovak University of Technology, Radlinského 11, 813 68, Bratislava, Slovakia

    Olga Nánásiová

Authors
  1. Olga Nánásiová
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nánásiová, O. Map for Simultaneous Measurements for a Quantum Logic. International Journal of Theoretical Physics 42, 1889–1903 (2003). https://doi.org/10.1023/A:1027384132753

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1027384132753

Search

Navigation