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Dvurečenskij, Anatolij; Pulmannová, Sylvia

Difference posets, effects, and quantum measurements. (English) Zbl 0806.03040

Int. J. Theor. Phys. 33, No. 4, 819-850 (1994).
The authors recall definitions and basic properties of structures important in quantum theories (such as orthomodular poset, orthoalgebra, set of effects, difference poset) and connections between them. They state when a subset of a difference poset is orthomodular by means of triangle closedness and give several characterizations of observables with a Boolean range. This generalizes results of P. Lahti and M. Maczyński [J. Math. Phys. 33, 4133-4138 (1992; Zbl 0769.60101)].
They study Boolean powers (bounded, resp.) of difference posets: show that it is a difference poset and investigate properties of the embedding of a difference poset into its Boolean power and the existence and properties of product states on Boolean powers. Since a Boolean power is a special kind of a tensor product, its connection with quantum measurement is discussed.
Reviewer: J.Tkadlec (Praha)

Cited in 38 Documents

MSC:

03G12 Quantum logic
06C15 Complemented lattices, orthocomplemented lattices and posets
81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects)

Keywords:

orthomodular poset; difference poset; observables; Boolean power; tensor product; quantum measurement

Citations:

Zbl 0769.60101
PDFBibTeX XMLCite
\textit{A. Dvurečenskij} and \textit{S. Pulmannová}, Int. J. Theor. Phys. 33, No. 4, 819--850 (1994; Zbl 0806.03040)
Full Text: DOI

References:

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