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Quantum Logics and Instruments

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Abstract

In a combined quantum logic and convexityapproach, an abstract notion of an instrument (statetransformer) is introduced to describe quantummeasurements. Some important classes of instruments(first kind, repeatable, ideal, Luders) and relations amongthem are investigated.

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REFERENCES

  • Abbati, M., and Manià, A. (1984). Quantum logic and operational quantum mechanics, Reports on Mathematical Physics, 19, 383–406.

    Google Scholar 

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

    Google Scholar 

  • Alfsen, E. M., and Shultz, F. W. (1976). Non-commutative spectral theory, Memoirs of the American Mathematical Society, 6, No.172.

    Google Scholar 

  • Berberian, S. (1966). Notes on Spectral Theory, Van Nostrand, Princeton, New Jersey.

    Google Scholar 

  • Bennett, M. K., and Foulis, D. J. (1996). Interval and scale effect algebras, Advances in Appl. Math 19, 200–215.

    Google Scholar 

  • Busch, P., Lahti, P., and Mittelstaedt, P. (1991). Quantum Theory of Measurement, Springer-Verlag, Berlin.

    Google Scholar 

  • Busch, P., Lahti, P., and Mittelstaedt, P. (1996). Quantum Theory of Measurement, 2nd ed., Springer-Verlag, Berlin.

    Google Scholar 

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

    Google Scholar 

  • Edwards, C. M., and Rüttimann, G. T. (1990). On conditional probability in GL spaces, Foundations of Physics, 20, 859–872.

    Google Scholar 

  • Lahti, P., Busch, P., and Mittelstaedt, P. (1991). Some important classes of measurements and their information gain, Journal of Mathematical Physics, 32, 2770–2775.

    Google Scholar 

  • Luczak, A. (n.d.). On ideal measurements and their corresponding instruments on von Neumann algebras, preprint.

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

    Google Scholar 

  • Pták, P., and Pulmannová, S. (1991). Orthomodular Structures as Quantum Logics, Kluwer, Dordrecht.

    Google Scholar 

  • Pulmannová, S. (1980). Semiobservables on quantum logics, Mathematica Slovaca, 30, 419–432.

    Google Scholar 

  • Pulmannová, S. (1993). Boolean powers and quantum measurement, Reports on Mathematical Physics, 32, 235–250.

    Google Scholar 

  • Pulmannová, S. (1994). Quantum measurements and quantum logics, Journal of Mathematical Physics, 35, 1555–1572.

    Google Scholar 

  • Pulmannová, S. (1995). A quantum logics description of some ideal measurements, in Quantum Communication s and Measurement, V. P. Belavkin, O. Hirota, and R. L. Hudson, eds., Plenum Press, New York.

    Google Scholar 

  • Pulmannová, S. (n.d.). Quantum logics and convex spaces, preprint.

  • Rüttimann, G. T. (1985). Expectation functionals of observables and counters, Reports on Mathematical Physics, 21, 213–222.

    Google Scholar 

  • Varadarajan, V. S. (1985). Geometry of Quantum Theory, Springer-Verlag, Berlin.

    Google Scholar 

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Pulmannova, S. Quantum Logics and Instruments. International Journal of Theoretical Physics 37, 163–174 (1998). https://doi.org/10.1023/A:1026685811240

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  • DOI: https://doi.org/10.1023/A:1026685811240

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