Optimal estimation of SU(d) using exact and approximate 2-designs

We consider the problem of estimating an SU(d) quantum operation when n copies of it are available at the same time. It is well known that, if one uses a separable state as the input for the unitaries, the optimal mean square error will decrease as 1/n. However it is shown here that, if a proper entangled state is used, the optimal mean square error will decrease at a 1/n^2 rate. It is also shown that spherical 2-designs (e.g. complete sets of mutually unbiased bases and symmetric informationally complete positive operator valued measures) can be used to design optimal input states. Although 2-designs are believed to exist for every dimension, this has not yet been proven. Therefore, we give an alternative input state based on approximate 2-designs which can be made arbitrarily close to optimal. It is shown that measurement strategies which are based on local operations and classical communication between the ancilla and the rest of the system can be optimal.Comment: 6 pages. v2: Complete rewrite, new results 11 page

European Employment Strategy and Spanish Labour Market Policies

The paper aim is to analyse the influence of the European Employment Strategy (EES) in the implementation of the Spanish labour market policies. The first part of the paper describes the evolution and content of the EES. In the second one, the definition of activation is also explained. In addition to that, the ways how the EES develops and promotes active labour market policies are examined. The evolution of labour market policies in Spain and the current configuration of both active and passive policies are studied in the next three chapters. In these parts, the paper investigates to which extent the provisions of the EES have been implemented in Spain. The paper shows that: i) activation has been rising in the European countries since the implementation of the EES; ii) this fact has also happened in relative terms (comparing the evolution of active to passive policies); iii) Spain has been one of the countries which has led these processes; iv) the EES seems to have been influencing the configuration of some parts of the Spanish labour market policies.activation; employment policies

Re-visit of HST FUV observations of hot-Jupiter system HD 209458: No Si III detection and the need for COS transit observations

The discovery of OI atoms and CII ions in the upper atmosphere of HD 209458b, made with the Hubble Space Telescope Imaging Spectrograph (STIS) using the G140L grating, showed that these heavy species fill an area comparable to the planet's Roche lobe. The derived ~10% transit absorption depths require super-thermal processes and/or supersolar abundances. From subsequent Cosmic Origins Spectrograph (COS) observations, CII absorption was reported with tentative velocity signatures, and absorption by SiIII ions was also claimed in disagreement with a negative STIS G140L detection. Here, we revisit the COS dataset showing a severe limitation in the published results from having contrasted the in-transit spectrum against a stellar spectrum averaged from separate observations, at planetary phases 0.27, 0.72, and 0.49. We find variable stellar SiIII and CII emissions that were significantly depressed not only during transit but also at phase 0.27 compared to phases 0.72 and 0.49. Their respective off-transit 7.5 and 3.1% flux variations are large compared to their reported 8.2+/-1.4% and 7.8+/-1.3% transit absorptions. Significant variations also appear in the stellar line shapes, questioning reported velocity signatures. We furthermore present archive STIS G140M transit data consistent with no SiIII absorption, with a negative result of 1.7+/-18.7 including ~15% variability. Silicon may still be present at lower ionization states, in parallel with the recent detection of extended magnesium, as MgI atoms. In this frame, the firm detection of OI and CII implying solar or supersolar abundances contradicts the recent inference of potential x20-125 subsolar metallicity for HD 209458b.Comment: Accepted for publication in Ap

Bounded Rationality

The observation of the actual behavior by economic decision makers in the lab and in the field justifies that bounded rationality has been a generally accepted assumption in many socio-economic models. The goal of this paper is to illustrate the difficulties involved in providing a correct definition of what a rational (or irrational) agent is. In this paper we describe two frameworks that employ different approaches for analyzing bounded rationality. The first is a spatial segregation set-up that encompasses two optimization methodologies: backward induction and forward induction. The main result is that, even under the same state of knowledge, rational and non-rational agents may match their actions. The second framework elaborates on the relationship between irrationality and informational restrictions. We use the beauty contest (Nagel, 1995) as a device to explain this relationship.Behavioral economics, bounded rationality, partial information