Optimal full estimation of qubit mixed states

We obtain the optimal scheme for estimating unknown qubit mixed states when an arbitrary number N of identically prepared copies is available. We discuss the case of states in the whole Bloch sphere as well as the restricted situation where these states are known to lie on the equatorial plane. For the former case we obtain that the optimal measurement does not depend on the prior probability distribution provided it is isotropic. Although the equatorial-plane case does not have this property for arbitrary N, we give a prior-independent scheme which becomes optimal in the asymptotic limit of large N. We compute the maximum mean fidelity in this asymptotic regime for the two cases. We show that within the pointwise estimation approach these limits can be obtained in a rather easy and rapid way. This derivation is based on heuristic arguments that are made rigorous by using van Trees inequalities. The interrelation between the estimation of the purity and the direction of the state is also discussed. In the general case we show that they correspond to independent estimations whereas for the equatorial-plane states this is only true asymptotically.Comment: 19 pages, no figure

Relativistic quantum clocks

The conflict between quantum theory and the theory of relativity is exemplified in their treatment of time. We examine the ways in which their conceptions differ, and describe a semiclassical clock model combining elements of both theories. The results obtained with this clock model in flat spacetime are reviewed, and the problem of generalizing the model to curved spacetime is discussed, before briefly describing an experimental setup which could be used to test of the model. Taking an operationalist view, where time is that which is measured by a clock, we discuss the conclusions that can be drawn from these results, and what clues they contain for a full quantum relativistic theory of time.Comment: 12 pages, 4 figures. Invited contribution for the proceedings for "Workshop on Time in Physics" Zurich 201

Effectiveness of intensive group and individual interventions for smoking cessation in primary health care settings: a randomized trial

<p>Abstract</p> <p>Objectives</p> <p>Primary: To compare the effectiveness of intensive group and individual interventions for smoking cessation in a primary health care setting; secondary: to identify the variables associated with smoking cessation.</p> <p>Methods</p> <p>Three-pronged clinical trial with randomisation at the individual level. We performed the following: an intensive individual intervention (III), an intensive group intervention (IGI) and a minimal intervention (MI). Included in the study were smokers who were prepared to quit smoking. Excluded from the study were individuals aged less than 18 years or with severe mental conditions or terminal illnesses. The outcome measure was continued abstinence at 12 months confirmed through CO-oximetry (CO). The analysis was based on intention to treat.</p> <p>Results</p> <p>In total, 287 smokers were recruited: 81 in the III, 111 in the IGI, and 95 in the MI. Continued abstinence at 12 months confirmed through CO was 7.4% in the III, 5.4% in the IGI, and 1% in the MI. No significant differences were noted between III and MI on the one hand, and between IGI and MI on the other [RR 7.04 (0.9-7.2) and RR 5.1 (0.6-41.9), respectively]. No differences were noted between IGI and III [RR 0.7 (0.2-2.2)]. In multivariate analysis, only overall visit length showed a statistically significant association with smoking cessation.</p> <p>Conclusions</p> <p>The effectiveness of intensive smoking interventions in this study was lower than expected. No statistically significant differences were found between the results of individual and group interventions.</p> <p>Trial registration number</p> <p>ISRCTN32323770</p

Advances in quantum metrology

The statistical error in any estimation can be reduced by repeating the measurement and averaging the results. The central limit theorem implies that the reduction is proportional to the square root of the number of repetitions. Quantum metrology is the use of quantum techniques such as entanglement to yield higher statistical precision than purely classical approaches. In this Review, we analyse some of the most promising recent developments of this research field and point out some of the new experiments. We then look at one of the major new trends of the field: analyses of the effects of noise and experimental imperfections