Small quantum structures with small state spaces

DOI10.1007/S10773-007-9415-1zbMATH Open1147.81004OpenAlexW2000481961MaRDI QIDQ2426159

Mirko Navara

Publication date: 21 April 2008

Published in: International Journal of Theoretical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10773-007-9415-1

zbMATH Keywords

orthomodular posetorthomodular latticeprobability measureeffect algebraorthoalgebragroup-valued measure

Mathematics Subject Classification ID

Vector-valued set functions, measures and integrals (28B05) Complemented lattices, orthocomplemented lattices and posets (06C15) Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects) (81P10) Logical aspects of Boolean algebras (03G05)

Cites Work

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• On states on the product of logics
• Orthomodular structures as quantum logics. Transl. from the Slovak
• Independence of automorphism group, center, and state space of quantum logics
• A characterization of state spaces of orthomodular lattices
• There are orthomodular lattices without non-trivial group-valued states: A computer-based construction
• Generalization of blocks for \(D\)-lattices and lattice-ordered effect algebras
• Two descriptions of state spaces of orthomodular structures
• Enlargements of quantum logics
• Smearings of states defined on sharp elements onto effect algebras
• States on orthoalgebras
• Orthomodular lattices admitting no states
• Exotic logics
• CONSTRUCTION OF ORTHOMODULAR LATTICES WITH GIVEN STATE SPACES
• An Orthomodular Lattice Admitting No Group-Valued Measure
• Quantum measure theory
• Embeddings into orthomodular lattices with given centers, state spaces and automorphism groups
• Proper effect algebras admitting no states

Related Items (6)

Characterization of spaces of filtering states ⋮ Hilbert lattice equations ⋮ Quantum structures without group-valued measures ⋮ Exhaustive generation of orthomodular lattices with exactly one nonquantum state ⋮ Existence of states on quantum structures ⋮ Graph approach to quantum systems

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