Abstract
Various axiomatic models for unsharp quantum measurements are investigated. These include effect spaces (E-spaces), effect test spaces (E-test spaces), effect algebras, and test groups. It is shown that a test group G is the universal group of an E-test space if and only if G is strongly atomistic. It follows that if G is strongly atomistic, then G is an interpolation group. We then demonstrate that if G is an interpolation group, then G is the universal group of an E-space. Finally, it is shown that an E-space is isomorphic to an E-test space if and only if it is strongly atomistic.
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REFERENCES
M. K. Bennett and D. Foulis, Found. Phys. 25, 1699–1722 (1995).
P. Busch, P. Lahti and P. Mittlestaedt, The Quantum Theory of Measurements (Springer, Berlin, 1991).
G. Cattaneo and F. Laudisa, Found. Phys. 24, 631–681 (1994).
M. L. Dalla Chiara and R. Giuntini, Found. Phys. 24, 1161–1177 (1994).
A. Dvure?enskij, Trans. Am. Soc. 147, 1043–1057 (1995).
A. Dvure?enskij and S. Pulmannová, Rep. Math. Phys. 34, 151–170 (1994).
D. Foulis and M. K. Bennett, Found. Phys. 24, 1331–1352 (1994).
D. Foulis, M. K. Bennet, and R. Greechie, in press.
R. Giuntini and H. Greuling, Found. Phys. 19, 931–945 (1989).
K. Goodearl, Partially Ordered Abelian Groups (Am. Math. Soc., Providence, RI, 1986).
R. Greechie and D. Foulis, Int. J. Theor. Phys. 34, 1–14 (1995).
S. Gudder, Effect test spaces and effect algebras, Found. Phys. 27, 287–304 (1997).
S. Gudder, Int. J. Theor. Phys. 36, 2681–2705 (1997).
F. Kôpka, Tatra Mt. Math. Publ. 1, 83–87 (1992).
F. Kôpka and F. Chovanec, Math. Slovaca 44, 21–34 (1994).
K. Kraus, States, Effects, and Operations (Springer, Berlin, 1983).
G. Ludwig, Foundations of Quantum Mechanics. Vols. I and II (Springer, Berlin, 1983/ 1985).
S. Pulmannová and A. Wilce, Int. J. Theor. Phys. 34, 1689–1696 (1995).
A. Wilce, Int. J. Theor. Phys. ( in press).
A. Wilce, in press.
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Gudder, S. Universal Groups of Effect Spaces. Foundations of Physics 29, 409–422 (1999). https://doi.org/10.1023/A:1018818915935
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DOI: https://doi.org/10.1023/A:1018818915935