Abstract
We reconsider the description for property transitions due to perfect measurements,viewing them as a special case of general transitions that are due to an externallyimposed change. We propose a corresponding syntax involving operationalquantum logic and a fragment of noncommutative linear logic.
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REFERENCES
Birkhoff, G., and von Neumann, J. (1936). Ann. Math. 37, 823.
Husimi, K. (1937). Proc. Physicomath. Soc. Japan 19, 766.
Sasaki, U. (1954). J. Sci. Hiroshima Univ. A17, 293.
Foulis, D. J. (1960). Proc. AMS 11, 648.
Jauch, J. M. (1968). Foundations of Quantum Mechanics, Addison-Wesley, Reading, Massachussetts.
Jauch, J. M., and Piron, C. (1969). Helv. Phys. Acta 42, 842.
Piron, C. (1964). Helv. Phys. Acta 37, 439.
Pool, J. C. T. (1968). Comm. Math. Phys. 9, 118.
Piron, C. (1976). Foundations of Quantum Physics, Benjamin, New York.
Piron, C. (1977). J. Phil. Logic 6, 481.
Gisin, N., and Piron, C. (1981). Lett. Math. Phys. 5, 379.
Aerts, D. (1982). Found. Phys. 12, 1131.
Foulis, D. J., Randall, C. H., and Piron, C. (1983). Found. Phys. 13, 813.
Foulis, D. J., and Randall, C. H. (1984). Found. Phys. 14, 65.
Kalmbach, G. (1983). Orthomodular Lattices, Academic Press, New York.
Mulvey, C. J. (1986). Rend. Circ. Math. Palermo 12, 99.
Girard, J. Y. (1987). Theor. Comp. Sci. 50, 1.
Girard, J. Y. (1989). Contemp. Math. 92, 69.
Abrusci, V. M. (1990). Z. Math. Logik Grundl. Math. 36, 297.
Abrusci, V. M. (1991). J. Symbolic Logic 56, 1403.
Faure, C.-A., Moore, D. J., and Piron, C. (1995). Helv. Phys. Acta 68, 150.
Moore, D. J. (1995). Helv. Phys. Acta 68, 658.
Piron, C. (1995). Int. J. Theor. Phys. 34, 1681.
Amira, H., Coecke, B., and Stubbe, I. (1998). Helv. Phys. Acta 71, 554.
Coecke, B., and Stubbe, I. (1999). Found. Phys. Lett 13, (2).
Coecke, B., and Stubbe, I. (1999). State transitions as morphisms for complete lattices, Int. J. Theor. Phys., this issue.
Moore, D. J. (1999). On state spaces and property lattices, Stud. Hist. Phil. Mod. Phys., to appear.
Coecke, B., and Smets, S. (n.d.). Combining quantum and linear logic for propagating physical properties, in preparation.
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Coecke, B., Smets, S. A Logical Description for Perfect Measurements. International Journal of Theoretical Physics 39, 595–603 (2000). https://doi.org/10.1023/A:1003629502815
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DOI: https://doi.org/10.1023/A:1003629502815