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Greechie diagrams, nonexistence of measures in quantum logics, and Kochen–Specker-type constructions

J. Math. Phys. 37, 5380 (1996); doi:10.1063/1.531710

Issue Date: November 1996

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K. Svozil
Institut für Theoretische Physik, University of Technology—Vienna, Wiedner Hauptstrasse 8-10/136, A-1040 Vienna, Austria

J. Tkadlec
Department of Mathematics, Faculty of Electrical Engineering, Czech Technical University, CZ-166 27 Prague, Czech Republic
We use Greechie diagrams to construct finite orthomodular lattices ``realizable'' in the orthomodular lattice of subspaces in a three-dimensional Hilbert space such that the set of two-valued states is not ``large'' (i.e., full, separating, unital, nonempty, resp.). We discuss the number of elements of such orthomodular lattices, of their sets of (ortho)generators and of their subsets that do not admit a ``large'' set of two-valued states. We show connections with other results of this type. ©1996 American Institute of Physics.
History: Received 4 December 1995; accepted 2 April 1996
Permalink: http://link.aip.org/link/?JMAPAQ/37/5380/1
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KEYWORDS and PACS

Keywords
PACS
  • 03.65.Bz
    Classical and quantum physics: mechanics and fields Quantum mechanics Foundations, theory of measurement, miscellaneous theories (including AharonovBohm effect, Bell inequalities, Berry's phase)
  • 02.10.-v
    Mathematical methods in physics Logic, set theory, and algebra
  • 02.40.-k
    Mathematical methods in physics Geometry, differential geometry, and topology
  • YEAR: 1996

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ISSN:
0022-2488 (print)   1089-7658 (online)
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REFERENCES (32)
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