Displaying similar documents to “Ring-like structures with unique symmetric difference related to quantum logic”

Effect algebras and ring-like structures

Enrico G. Beltrametti, Maciej J. Maczyński (2003)

Discussiones Mathematicae - General Algebra and Applications

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The dichotomic physical quantities, also called propositions, can be naturally associated to maps of the set of states into the real interval [0,1]. We show that the structure of effect algebra associated to such maps can be represented by quasiring structures, which are a generalization of Boolean rings, in such a way that the ring operation of addition can be non-associative and the ring multiplication non-distributive with respect to addition. By some natural assumption on the effect...

On joint distribution in quantum logics. I. Compatible observables

Anatolij Dvurečenskij (1987)

Aplikace matematiky

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The notion of a joint distribution in σ -finite measures of observables of a quantum logic defined on some system of σ -independent Boolean sub- σ -algebras of a Boolean σ -algebra is studied. In the present first part of the paper the author studies a joint distribution of compatible observables. It is shown that it may exists, although a joint obsevable of compatible observables need not exist.

Relatively additive states on quantum logics

Pavel Pták, Hans Weber (2005)

Commentationes Mathematicae Universitatis Carolinae

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In this paper we carry on the investigation of partially additive states on quantum logics (see [2], [5], [7], [8], [11], [12], [15], [18], etc.). We study a variant of weak states — the states which are additive with respect to a given Boolean subalgebra. In the first result we show that there are many quantum logics which do not possess any 2-additive central states (any logic possesses an abundance of 1-additive central state — see [12]). In the second result we construct a finite...

Quantum logics and bivariable functions

Eva Drobná, Oľga Nánásiová, Ľubica Valášková (2010)

Kybernetika

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New approach to characterization of orthomodular lattices by means of special types of bivariable functions G is suggested. Under special marginal conditions a bivariable function G can operate as, for example, infimum measure, supremum measure or symmetric difference measure for two elements of an orthomodular lattice.