A note to a common cause in quantum logic

A. Al-Adilee

doi:10.2478/v10189-010-0019-z

Abstract

We study the notion of a common cause in quantum logics as a type of causal relations (see [13]). We review maps like conditional state, s-map as basic tools of our constructions. Finally, we show some properties of such notions in quantum logics.

References

Dvurečenskij, A., Pulmannová, S. (2000): New trends in quantum structures, Kluwer/Dordt & Ister/Bratislava.10.1007/978-94-017-2422-7
Search in Google Scholar
Greechie, R. (1971): Orthogonal lattices admitting no states, J. Combin. Theory Ser. A10, 119 - 132.10.1016/0097-3165(71)90015-X
Search in Google Scholar
Garola, C. Sozzo, S. (2009): The ESR model: A proposal for a noncontextual and local Hilbert space extension of QM, EPL., ISSN, 86 2, 0295 - 5075.
Search in Google Scholar
Khrennikov, A. (2009): Contextual Aproach to Quantum Formaliism, Springer.10.1007/978-1-4020-9593-1
Search in Google Scholar
Khrennikov, A., Nánásiová, O. (2006): Representation theorem for observables on a quantum system, Int. Journ. of Theor. Phys, 45, 481 - 494.
Search in Google Scholar
Kolmogorov, A. N. (1956): Foundations of the theory of probability, New York: Chelsea.
Search in Google Scholar
Nánásiová, O. (2004): Principle Conditioning, Int. Jour. of Theo. Phys., 43, 1757-1767(11).10.1023/B:IJTP.0000048818.23615.28
Search in Google Scholar
Nánásiová, O. (2003): Map for simultaneous measurements for a quantum logic, Int. Journ. of Theor. Phys., 42, 1889 - 1903.
Search in Google Scholar
Nánásiová, O., Khrennikov, A. (2005): Compatibility and Marginality, Int. Jour. of Theor. Phys., 46, 1083 - 1095.
Search in Google Scholar
Nánásiová, O., Pulmannova, S. (2009): S-map and tracial states, Info. Sci., 179: 5, 515 - 520.
Search in Google Scholar
Navara, M. (1994): An orthomodular lattice admitting no group-valued measure, Proc. of the Amer. Math. Soc., 122, 7 - 12.
Search in Google Scholar
Pták, P., Pulmannová, S. (1991): Quantum logics, Kluwer Acad. Press, Bratislava.
Search in Google Scholar
Reichenbach, H. (1956): The direction of time, University of California Press, Berkeley, 2, 3, 5.
Search in Google Scholar
Rédei, M. (1997): Reichenbach's common cause principle and quantum field theory, Int. Jour. of Theo. Phys., 27, 1309 - 1321.
Search in Google Scholar
Rédei, M., Summers, S.J. (2002): Local primitive causality and the common cause principle in quantum field theory, Int. Jour. of Theo. Phys, 32, 335 - 355.
Search in 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.
Search in Google Scholar
Varadarajan, V. (1968): Geometry of quantum theory, Princeton, N. J., D. Van Nostrand, 1, 193.
Search in Google Scholar

A note to a common cause in quantum logic

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