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Mac Neille completion of centers and centers of Mac Neille completions of lattice effect algebras

Martin Kalina (2010)

Kybernetika

If element z of a lattice effect algebra ( E , ⊕ , 0 , 1 ) is central, then the interval [ 0 , z ] is a lattice effect algebra with the new top element z and with inherited partial binary operation ⊕ . It is a known fact that if the set C ( E ) of central elements of E is an atomic Boolean algebra and the supremum of all atoms of C ( E ) in E equals to the top element of E , then E is isomorphic to a subdirect product of irreducible effect algebras ([18]). This means that if there exists a MacNeille completion E ^ of E which is its extension...

Markov chains approximation of jump–diffusion stochastic master equations

Clément Pellegrini (2010)

Annales de l'I.H.P. Probabilités et statistiques

Quantum trajectories are solutions of stochastic differential equations obtained when describing the random phenomena associated to quantum continuous measurement of open quantum system. These equations, also called Belavkin equations or Stochastic Master equations, are usually of two different types: diffusive and of Poisson-type. In this article, we consider more advanced models in which jump–diffusion equations appear. These equations are obtained as a continuous time limit of martingale problems...

Matrix representation of finite effect algebras

Grzegorz Bińczak, Joanna Kaleta, Andrzej Zembrzuski (2023)

Kybernetika

In this paper we present representation of finite effect algebras by matrices. For each non-trivial finite effect algebra E we construct set of matrices M ( E ) in such a way that effect algebras E 1 and E 2 are isomorphic if and only if M ( E 1 ) = M ( E 2 ) . The paper also contains the full list of matrices representing all nontrivial finite effect algebras of cardinality at most 8 .

Möbius gyrovector spaces in quantum information and computation

Abraham A. Ungar (2008)

Commentationes Mathematicae Universitatis Carolinae

Hyperbolic vectors, called gyrovectors, share analogies with vectors in Euclidean geometry. It is emphasized that the Bloch vector of Quantum Information and Computation (QIC) is, in fact, a gyrovector related to Möbius addition rather than a vector. The decomplexification of Möbius addition in the complex open unit disc of a complex plane into an equivalent real Möbius addition in the open unit ball 𝔹 2 of a Euclidean 2-space ℝ 2 is presented. This decomplexification proves useful, enabling the resulting...

Modular atomic effect algebras and the existence of subadditive states

Zdena Riečanová (2004)

Kybernetika

Lattice effect algebras generalize orthomodular lattices and M V -algebras. We describe all complete modular atomic effect algebras. This allows us to prove the existence of ordercontinuous subadditive states (probabilities) on them. For the separable noncomplete ones we show that the existence of a faithful probability is equivalent to the condition that their MacNeille complete modular effect algebra.

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