A framework to describe a broad class of physical operations (including unitary transformations, dissipation, noise, and measurement) in a quantum optics experiment is given. This framework provides a powerful tool for assessing the capabilities and limitations of performing quantum information processing tasks using current experimental techniques. The Gottesman-Knill theorem is generalized to...

A general property of relaxation rates in open quantum systems is discussed. We find an interesting constraint for that universally holds fairly large classes dynamics, e.g., weak coupling regimes, as well entropy nondecreasing evolutions. conjecture this universal, i.e., it valid all dynamical semigroups. The supported by numerical analysis. Moreover, we show the conjectured tight providing a ...

A Banach algebra is Arens-regular when all its continuous functionals are weakly almost periodic, in symbols A⁎=WAP(A). To identify the opposite behaviour, Granirer called a extremely non-Arens regular (enAr, for short) quotient A⁎/WAP(A) contains closed subspace that has A⁎ as quotient. In this paper we propose simplification and quantification of concept. We say r-enAr, with r≥1, there an iso...

It is shown that every Hausdorff locally compact semigroup topology on the extended bicyclic with adjoined zero $$ {C}_{\mathrm{\mathbb{Z}}}^0 discrete. At same time, , there exist ???? different shift-continuous topologies. In addition, we construct a unique minimal and inverse topology.

We investigate C∗-algebras associated with row-finite topological higherrank graphs with no source, which are based on product system C∗-algebras. We prove the Cuntz-Krieger uniqueness theorem, and provide the condition of simplicity and purely infiniteness of our algebras. We give examples of non-discrete topological higher-rank graphs whose C∗-algebras contain Cuntz’s ax + b-semigroup C∗-alge...

We consider, within the algebraic formalism, the time dependence of fidelity for qubits encoded into an open physical system. We relate the decay of fidelity to the evolution of correlation functions and, in the particular case of a Markovian dynamics, to the spectral gap of the generator of the semigroup. The results are applicable to the analysis of models of quantum memories.

Let K be a commutative ring with unit and S an inverse semigroup. We show that the semigroup algebra KS can be described as a convolution algebra of functions on the universal étale groupoid associated to S by Paterson. This result is a simultaneous generalization of the author’s earlier work on finite inverse semigroups and Paterson’s theorem for the universal C-algebra. It provides a convenie...

In the paper we study the endomorphim semigroup of a general quantum polynomial ring, its finite groups of automorphisms and homological properties of this ring as a module over the skew group ring of a finite group of automorphisms. Moreover properties of the division ring of fractions are considered.

The recently developed theory of partial actions of discrete groups on C-algebras is extended. A related concept of actions of inverse semigroups on C-algebras is defined, including covariant representations and crossed products. The main result is that every partial crossed product is a crossed product by a semigroup action.