Order properties of splitting subspaces in an inner product space
Ordering of observables and characterization of conditional expectation
Orthocomplemented difference lattices with few generators
The algebraic theory of quantum logics overlaps in places with certain areas of cybernetics, notably with the field of artificial intelligence (see, e. g., [19, 20]). Recently an effort has been exercised to advance with logics that possess a symmetric difference ([13, 14]) - with so called orthocomplemented difference lattices (ODLs). This paper further contributes to this effort. In [13] the author constructs an ODL that is not set-representable. This example is quite elaborate. A main result...
Orthogonal vector measures on projection lattices in a Hilbert space
Orthogonality spaces and atomistic orthocomplemented lattices
Orthomodular lattices with state-separated noncompatible pairs
In the logico-algebraic foundation of quantum mechanics one often deals with the orthomodular lattices (OML) which enjoy state-separating properties of noncompatible pairs (see e.g. , and ). These properties usually guarantee reasonable “richness” of the state space—an assumption needed in developing the theory of quantum logics. In this note we consider these classes of OMLs from the universal algebra standpoint, showing, as the main result, that these classes form quasivarieties. We also illustrate...
Orthomodular ordered sets and orthogonal closure spaces
Perspectivity and congruence in partial abelian semigroups
Perturbation approach for nuclear magnetic resonance solid-state quantum computation.
Positive projections as generators of -projections of type (B).
Principle of superposition and interference of diffusion processes
Projection and covering in a set with orthogonality
Projection postulate and superposition principle in non-lattice quantum logics
Pure states on Jordan algebras
We prove that a pure state on a -algebras or a JB algebra is a unique extension of some pure state on a singly generated subalgebra if and only if its left kernel has a countable approximative unit. In particular, any pure state on a separable JB algebra is uniquely determined by some singly generated subalgebra. By contrast, only normal pure states on JBW algebras are determined by singly generated subalgebras, which provides a new characterization of normal pure states. As an application we contribute...
Quantum computational structures
Quantum logics representable as kernels of measures
Quantum logics with classically determined states
Regularly full logics and the uniqueness problem for observables
Relatively additive states on quantum logics
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 3-homogeneous...
Remarks on effect-tribes
We show that an effect tribe of fuzzy sets with the property that every is -measurable, where is the family of subsets of whose characteristic functions are central elements in , is a tribe. Moreover, a monotone -complete effect algebra with RDP with a Loomis-Sikorski representation , where the tribe has the property that every is -measurable, is a -MV-algebra.