In this paper we consider deterministic nonlinear time evolutions satisfying so called convex quasi-linearity condition. Such preserve the equivalence of ensembles and therefore are free from problems with signaling. We show that if family linear non-trace-preserving maps satisfies semigroup property then generated quasi-linear operations also possesses property. Next generalize Gorini-Kossakow...

We present quantum query and time complexity bounds for group testing problems. For a set S and a binary operation on S, we consider the decision problem whether a groupoid, semigroup or quasigroup is a group. Our quantum algorithms for these problems improve the best known classical complexity bounds. We also present upper and lower bounds for testing associativity, distributivity and commutat...

We consider hermitian dissipative mappings δ which are densely defined in unital C∗-algebras A. The identity element in A is also in the domain of δ. Completely dissipative maps δ are defined by the requirement that the induced maps, (aij) → (δ(aij)), are dissipative on the n by n complex matrices over A for all n. We establish the existence of different types of maximal extensions of completel...

The existence is proved of a class of open quantum systems that admits a linear subspace C of the space of states such that the restriction of the dynamical semigroup to the states built over C is unitary. Such subspace allows for error-avoiding (noiseless) enconding of quantum information. PACS numbers: 71.10.Ad , 05.30.Fk

We study the structure of a quantum Markov semigroup (Tt)t≥0 on a von Neumann algebra A starting from its decomposition by means of the transient and recurrent projections. The existence of invariant states and convergence to invariant state is also discussed. Applications to quantum Markov semigroups with Lindblad type infinitesimal generator are analysed.

We define a cohomology theory for topological semigroups, with seminormed cohomology groups. Our theory can be considered as a topological version of bounded cohomology of discrete semigroups. 1. Definition of the cohomology Bounded cohomology was first defined for discrete groups by F. Trauber and then for topological spaces by M. Gromov [6]. In this paper we establish a topological bounded co...