Entanglement monotones and maximally entangled states in multipartite qubit systems

We present a method to construct entanglement measures for pure states of multipartite qubit systems. The key element of our approach is an antilinear operator that we call {\em comb} in reference to the {\em hairy-ball theorem}. For qubits (or spin 1/2) the combs are automatically invariant under SL(2,\CC). This implies that the {\em filters} obtained from the combs are entanglement monotones by construction. We give alternative formulae for the concurrence and the 3-tangle as expectation values of certain antilinear operators. As an application we discuss inequivalent types of genuine four-, five- and six-qubit entanglement.Comment: 7 pages, revtex4. Talk presented at the Workshop on "Quantum entanglement in physical and information sciences", SNS Pisa, December 14-18, 200

Accuracy and properties of German business cycle forecasts

In this paper the accuracy of a wide range of German business cycle forecasters is assessed for the past 10 years. For this purpose, a data set is used comprising forecasts published on a monthly basis by Consensus Economics. The application of several descriptive as well as statistical measures reveals that the accuracy of the 2-years forecasts is low relative to a simple na?ve forecast. This observation can mainly be explained by a systematic overestimation of the growth rates by the forecasters. Moreover, the lack of accuracy can also be explained partly by insufficient information efficiency as well as imitation behaviour. Finally, it is shown that notwithstanding the common errors which affected the accuracy of all forecasters mainly because of their systematic overestimation, they differ significantly in their forecast accuracy. --business cycle forecasting,forecast evaluation,Consensus forecasts