Constructions of quantum structures

Navara, Mirko

doi:10.1016/b978-044452870-4/50030-3

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Cited by 16 publications

(10 citation statements)

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“…Beside OMLs, more general posets were proposed as mathematical structures describing quantum mechanical systems. (We refer to [3,9] for the respective definitions.) The smallest OMP has a Greechie diagram of the form of a rectangular 3 Â 4 grid.…”

Section: Discussionmentioning

confidence: 99%

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Existence of states on quantum structures

Navara

2009

Information Sciences

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Section: Discussionmentioning

confidence: 99%

“…Thus the event structure (orthomodular lattice) can be viewed as a union of Boolean algebras. We refer to [3,5,9] for details about the notions used throughout this paper. We just recall that an orthomodular lattice (OML) is a partially ordered set L with bounds 0 and 1 and an antitone unary operation 0 : L !…”

Section: Introductionmentioning

confidence: 99%

Existence of states on quantum structures

Navara

2009

Information Sciences

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“…In the sequel, we shall refer to some constructions with OMLs, in particular the horizontal sum (see [4,7,12]) and the substitution of an atom with an OML (see [8]). …”

Section: Lemmamentioning

confidence: 99%

Characterization of Spaces of Filtering States

Navara

2009

Int J Theor Phys

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Filtering states on orthomodular lattices have been introduced by G.T. Rüttimann as an "opposite" of completely additive states. He proved that they form a face of the state space. The question which faces can be the sets of filtering states remained open. Here we prove that, for any semi-exposed face F of a compact convex set C, there is an orthomodular lattice L and an affine homeomorphism ϕ of C onto the state space of L such that ϕ(F ) is the space of filtering states.

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“…In [13], Navara formulated sufficient and necessary conditions under which a pasting of a family of Boolean algebras is an orthoalgebra. For more details we refer the reader to Navara [14] and the references given there.…”

Section: Introductionmentioning

confidence: 99%

“…Thereafter many authors have tried to use another pasting techniques in order to construct various types of difference posets (effect algebras) (see [18], [11], [14], [19]). …”

Section: Introductionmentioning

confidence: 99%