Quantum Error Correction in the Presence of Initial System-Environment Correlations

Quantum error correction is studied in a framework consisting of an open quantum system and its environment, jointly subjected to a unitary action, and an interaction-free reference system. It has been shown that coherent information between the initially correlated open system and reference system is conserved in the transmission stage of any quantum communication process, provided that the tripartite input is any pure Markov state and the overall evolution preserves its form. This conservation constitutes the necessary and sufficient condition for accomplishment of perfect error correction by a recovery channel even in the presence of initial system-environment correlations. Explicit expressions of the recovery operators and examples of the joint unitary evolution preserving the form of inputs are given for all classes of pure Markov states.

Forest management units through cost

Costs minimizing and profit maximizing make the costs adjustment seems to be a vital necessity when the activity developed within the company does not assure the maintenance and stability of the necessary relation between consuming factors and costs. In such circumstances, approaching differing sides of the production cost and improving the methods of calculation has much significance in determining the most appropriate measures necessary for its adjustment and for profit increasing. The whole informational process of costs – formation, control and analysis of costs – involves a careful use the methodological concepts known under the name of classical methods and modern or complementary methods, as well as of other proceedings. Such methods and proceedings cannot be applied separately, only conjugated and integrated in a unitary methodological system, each of these methods and proceedings participating at achieving one or more objectives. Only by their unitary action they can fulfill all the system objective.

THE CROSSED PRODUCT BY A POINTWISE UNITARY ACTION ON A C*-ALGEBRA WITH CONTINUOUS TRACE

Let $G$ be a locally compact group, $A$ a continuous trace $C^*$-algebra, and $\alpha$ a pointwise unitary action of $G$ on $A$. It is a result of Olesen and Raeburn that if $A$ is separable and $G$ is second countable, then the crossed product $A\times_\alpha G$ has continuous trace. We present a new and much more elementary proof of this fact. Moreover, we do not even need the separability assumptions made on $A$ and $G$.AMS 2000 Mathematics subject classification: Primary 46L55

Future Hegemonic Rivalry Between China and the West?

Currently there is a unipolar distribution of power. The United States reigns supreme. Russia's economic power will remain insufficient to underwrite a renewed attempt to establish global leadership. While the European Community still commands sufficient resources for exercising global leadership, it lacks the political foundation for unitary action. Moreover, the European addiction to the welfare state undermines European competitiveness. Japan is too much of a "trading state" and unlikely to become a first-rate military power, before she is overtaken by China in economic size. So, count Russia, Europe and Japan out as conceivable challengers to United States hegemony. China is the only plausible candidate. Its economic growth rate is nothing less than spectacular. Moreover, the Chinese government seems capable of extracting the necessary resources for waging a hegemonic rivalry from a society that is likely to remain quite poor for at least another generation. There are a number of conceivable scenarios for the emerging American-Chinese relationship. The future will depend on the relative speed of the American decline and the rise of China as well as on the openness of the global economy. The more open the global economy, the better the prospects for rising per capita incomes in China become, the better the prospects for some mellowing or even democratization of the Chinese regime. Only if the West sticks together under American leadership and if creeping capitalism in China leads to creeping democratization later, is hegemonic rivalry likely to remain benign and peaceful.