Quantum logics and hilbert space

Pulmannová, Sylvia

doi:10.1007/bf02283040

Cited by 4 publications

(3 citation statements)

References 22 publications

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“…The following simple form will be sufficient. It remains to specify the nature of the division ring D. We need axioms which make D one of the classical division rings R, C, or H. In Pulmannov~ (1994) two of Wilbur's (1977) axioms are used which make L a so-called probabilistic logic. These two axioms express minimal conditions which are necessary to consider vectors in V as sources of states.…”

Section: A5 (Superposition Principle) To Every P Q E P P ~ Q Thermentioning

confidence: 99%

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Axiomatization of quantum logics

Pulmannová

1996

Int J Theor Phys

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Starting with a quantum logic (a tr-orthomodular poset) L, a set of probabilistically motivated axioms is suggested to identify L with a standard quantum logic L(H) of all closed linear subspaces of a complex, separable, infinite-dimensional Hilbert space. Attention is paid to recent results in this field.In the framework of the axiomatic approach known as the "quantum logic approach" it is usually assumed that a "quantum logic," that is, a mathematical representation of the set of all experimentally verifiable propositions about a physical system (equivalently, the set of all random events of a physical experiment), is a tr-orthomodular poset with a full set of states (i.e., generalized probability measures). Let us introduce the corresponding definitions.Definition 1. A tr-orthomodular poset (tr-OMP) is a partially ordered set (L, <--) with a smallest element 0 and a greatest element 1 with the following properties:(1) L carries a bijective map a ~ a' such that for every a, b e L, a" =a,a--b',ava' = l, aAa' = 0 (in the sense that the join a v a' and the meet a A a' both exist and have the value indicated).

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Section: A5 (Superposition Principle) To Every P Q E P P ~ Q Thermentioning

confidence: 99%

“…Although in Mackey's axioms the existence of pure states is not explicitly required, pure states play an important role in quantum mechanics, and hence we will assume that there is a set P of pure states (extreme points of 5e), subject to the following requirements. We follow essentially Pulmannov~ (1994).…”

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confidence: 99%

Axiomatization of quantum logics

Pulmannová

1996

Int J Theor Phys

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“…Then Hans Keller constructed a non classical orthomodular space [22], and recently Maria Pia Solèr proved that any orthomodular space that contains an infinite orthonormal sequence is a real, complex or quaternionic Hilbert space [23,24]. It is under investigation in which way this result of Solèr can be used to formulate new physically plausible axioms [24,25,26,27].…”

Section: Introductionmentioning

confidence: 99%

Representation of state property systems

Aerts

Pulmannová

2006

Journal of Mathematical Physics

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A 'state property system' is the mathematical structure which models an arbitrary physical system by means of its set of states, its set of properties, and a relation of 'actuality of a certain property for a certain state'. We work out a new axiomatization for standard quantum mechanics, starting with the basic notion of state property system, and making use of a generalization of the standard quantum mechanical notion of 'superposition' for state property systems.

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Equations and Hilbert lattices

Mayet¹

2007

Handbook of Quantum Logic and Quantum Structures

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Quantum logics and hilbert space

Abstract: Starthrg with a quantum logic ( a rr-orthomodular poser) L. a set of probabilisticall.v motivated axioms is suggested to identify L with a standard quantum logic L( H ) of all closed I#~ear subspaces of a complex, separable, h~finite-dimensionalHilbert space.

Cited by 4 publications

References 22 publications

Axiomatization of quantum logics

Axiomatization of quantum logics

Representation of state property systems

Equations and Hilbert lattices

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