Greechie diagrams, nonexistence of measures in quantum logics, and Kochen{endash}Specker-type constructions

Journal Article · Fri Nov 01 04:00:00 EST 1996 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.531710· OSTI ID:388187

Svozil, K ^[1]; Tkadlec, J ^[2]

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1. Institut fuer Theoretische Physik, University of Technology---Vienna, Wiedner Hauptstrasse 8-10/136, A-1040 Vienna (Austria)
2. 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 {open_quote}{open_quote}realizable{close_quote}{close_quote} in the orthomodular lattice of subspaces in a three-dimensional Hilbert space such that the set of two-valued states is not {open_quote}{open_quote}large{close_quote}{close_quote} (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 {open_quote}{open_quote}large{close_quote}{close_quote} set of two-valued states. We show connections with other results of this type. {copyright} {ital 1996 American Institute of Physics.}

• OSTI ID: 388187
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 11 Vol. 37; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
99 GENERAL AND MISCELLANEOUS
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HILBERT SPACE
MATHEMATICAL LOGIC
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QUANTUM OPERATORS