Modularity, atomicity and states in Archimedean lattice effect algebras.
Morphisms and pasting of orthoalgebras
Moyennes et mesures en mécanique quantique et en mécanique classique
Multipartite separability of Laplacian matrices of graphs.
Natural quantum operational semantics with predicates
A general definition of a quantum predicate and quantum labelled transition systems for finite quantum computation systems is presented. The notion of a quantum predicate as a positive operator-valued measure is developed. The main results of this paper are a theorem about the existence of generalised predicates for quantum programs defined as completely positive maps and a theorem about the existence of a GSOS format for quantum labelled transition systems. The first theorem is a slight generalisation...
New operations on partial Abelian monoids defined by preideals
We consider partial abelian monoids, in particular generalized effect algebras. From the given structures, we construct new ones by introducing a new operation , which is given by restriction of the original partial operation + with respect to a special subset called preideal. We bring some derived properties and characterizations of these new built structures, supporting the results by illustrative examples.
Noise effects in the quantum search algorithm from the viewpoint of computational complexity
We analyse the resilience of the quantum search algorithm in the presence of quantum noise modelled as trace preserving completely positive maps. We study the influence of noise on the computational complexity of the quantum search algorithm. We show that it is only for small amounts of noise that the quantum search algorithm is still more efficient than any classical algorithm.
Nonatomic states
Non-commutative probability limit theorems
Nonlinear Dirac equations.
Note on a construction of unbounded measures on a nonseparable Hilbert space quantum logic
Notes on the essential system to acquire information.
Observables on -MV algebras and -lattice effect algebras
Effect algebras were introduced as abstract models of the set of quantum effects which represent sharp and unsharp properties of physical systems and play a basic role in the foundations of quantum mechanics. In the present paper, observables on lattice ordered -effect algebras and their “smearings” with respect to (weak) Markov kernels are studied. It is shown that the range of any observable is contained in a block, which is a -MV algebra, and every observable is defined by a smearing of a sharp...
On a characterization of probability measures on Boolean algebras and some orthomodular lattices
On a sum of observables in a logic
On a summability of observables in generalized measurable spaces
On centers and state spaces of logics
On complete-cocomplete subspaces of an inner product space
In this note we give a measure-theoretic criterion for the completeness of an inner product space. We show that an inner product space is complete if and only if there exists a -additive state on , the orthomodular poset of complete-cocomplete subspaces of . We then consider the problem of whether every state on , the class of splitting subspaces of , can be extended to a Hilbertian state on ; we show that for the dense hyperplane (of a separable Hilbert space) constructed by P. Pták and...
On convergences of signed states
On direct decompositions of certain orthomodular lattices.