Editorial: Quantum structures, states and related topics
Effect algebra counterexamples
Effect algebras and ring-like structures
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 algebra,...
Ein Beitrag zur Theorie der Orthogonalität auf Mengen
Entanglement of Grassmannian coherent states for multi-partite -level systems.
Entropy generation in a model of reversible computation
We present a model in which, due to the quantum nature of the signals controlling the implementation time of successive unitary computational steps, physical irreversibility appears in the execution of a logically reversible computation.
Equivalent norms in some spaces of analytic functions and the uncertainty principle
The main object of this work is to describe such weight functions w(t) that for all elements the estimate is valid with a constant K(Ω), which does not depend on f and it grows to infinity when the domain Ω shrinks, i.e. deforms into a lower dimensional convex set . In one-dimensional case means that as σ → 0. It should be noted that in the framework of the signal transmission problem such estimates describe a signal’s behavior under the influence of detection and amplification. This work...
Errata to the article ``Topologies on quantum logics induced by measures''
Euclidean quantum mechanics : analytical approach
Every uniformly Archimedean atomic MV-effect algebra is sharply dominating
Following the study of sharp domination in effect algebras, in particular, in atomic Archimedean MV-effect algebras it is proved that if an atomic MV-effect algebra is uniformly Archimedean then it is sharply dominating.
Explicit formulas for correlation functions of ground states of the 1 dimensional XY model
Extending Coarse-Grained Measures
In [4] it is proved that a measure on a finite coarse-grained space extends, as a signed measure, over the entire power algebra. In [7] this result is reproved and further improved. Both the articles [4] and [7] use the proof techniques of linear spaces (i.e. they use multiplication by real scalars). In this note we show that all the results cited above can be relatively easily obtained by the Horn-Tarski extension technique in a purely combinatorial manner. We also characterize the pure measures...
Extension theorems (vector measures on quantum logics)
Extensions of partially ordered partial abelian monoids
The notion of a partially ordered partial abelian monoid is introduced and extensions of partially ordered abelian monoids by partially ordered abelian groups are studied. Conditions for the extensions to exist are found. The cases when both the above mentioned structures have the Riesz decomposition property, or are lattice ordered, are treated. Some applications to effect algebras and MV-algebras are shown.
Extremal quantum states in coupled systems