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ArticleOriginal scientific text

Title

Quantum logics with classically determined states

Authors 1, 2

Affiliations

  1. Università degli Studi di Napoli 'Federico II', Dipartimento di Matematica e Applicazioni, Complesso Universitario, Monte S. Angelo, Via Cintia, 80126 Napoli, Italy
  2. Technical University of Prague, Faculty of Electrical Engineering, Department of Mathematics, Technická 2, 166 27 Praha 6, Czech Republic

Keywords

ENG
quantum logic (= orthomodular poset), Boolean algebra, state (= probability measure)

Bibliography

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  2. L. Bunce, M. Navara, P. Pták and J. D. M. Wright, Quantum logics with Jauch-Piron states, Quart. J. Math. Oxford 36 (1985), 261-271.
  3. R. Greechie, Orthomodular lattices admitting no states, J. Combin. Theory Ser. A 10 (1971), 119-132.
  4. S. Gudder, Stochastic Methods of Quantum Mechanics, North-Holland, Amsterdam, 1979.
  5. P. de Lucia and P. Morales, A non-commutative version of the Alexandroff decomposition theorem in ordered topological groups, Pubblicazioni del Dipartimento di Matematica e Applicazioni 'R. Caccioppoli', Università degli Studi di Napoli 'Federico II', 1993, 1-21.
  6. P. de Lucia and P. Pták, Quantum probability spaces that are nearly classical, Bull. Polish Acad. Sci. Math. 40 (1992), 163-173.
  7. V. Müller, Jauch-Piron states on concrete quantum logics, Internat. J. Theoret. Phys. 32 (1993), 433-442.
  8. M. Navara and P. Pták, Almost Boolean orthomodular posets, J. Pure Appl. Algebra 60 (1989), 105-111.
  9. P. Pták, Exotic logics, Colloq. Math. 54 (1987), 1-7.
  10. P. Pták and S. Pulmannová, Orthomodular Structures as Quantum Logics, Kluwer, Dordrecht, 1991.
  11. G. Rüttimann, Jauch-Piron states, J. Math. Phys. 18 (1977), 189-193.
  12. R. Sikorski, Boolean Algebras, Springer, Berlin, 1964.
  13. R. M. Solovay, Real-valued measurable cardinals, in: Axiomatic Set Theory, Proc. Sympos. Pure Math. 13, Part I, Amer. Math. Soc., Providence, R.I., 1971, 397-428.
  14. J. Tkadlec, Partially additive measures and set representations of orthoposets, J. Pure Appl. Algebra 86 (1993), 79-94.
Colloquium Mathematicum
1999/80/1
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Pages:
147-154
Main language of publication
English
Received
1997-05-28
Accepted
1998-10-26
Published
1999
Exact and natural sciences