Quantum tomography and nonlocality

We present a tomographic approach to the study of quantum nonlocality in multipartite systems. Bell inequalities for tomograms belonging to a generic tomographic scheme are derived by exploiting tools from convex geometry. Then, possible violations of these inequalities are discussed in specific tomographic realizations providing some explicit examples.Comment: 23 pages, 2 figures, contribution to the special issue of Physica Scripta celebrating 150 years of Margarita and Vladimir I. Man'k

A connection between viscous profiles and singular ODEs

We deal with the viscous profiles for a class of mixed hyperbolic-parabolic systems. We focus, in particular, on the case of the compressible Navier Stokes equation in one space variable written in Eulerian coordinates. We describe the link between these profiles and a singular ordinary differential equation in the form $$dV / dt = F(V) / z (V) .$$ Here $V \in R^d$ and the function F takes values into $R^d$ and is smooth. The real valued function z is as well regular: the equation is singular in the sense that z (V) can attain the value 0.Comment: 6 pages, minor change

Methods for Estimating Capacities and Rates of Gaussian Quantum Channels

Optimization methods aimed at estimating the capacities of a general Gaussian channel are developed. Specifically evaluation of classical capacity as maximum of the Holevo information is pursued over all possible Gaussian encodings for the lossy bosonic channel, but extension to other capacities and other Gaussian channels seems feasible. Solutions for both memoryless and memory channels are presented. It is first dealt with single use (single-mode) channel where the capacity dependence from channel's parameters is analyzed providing a full classification of the possible cases. Then it is dealt with multiple uses (multi-mode) channel where the capacity dependence from the (multi-mode) environment state is analyzed when both total environment energy and environment purity are fixed. This allows a fair comparison among different environments, thus understanding the role of memory (inter-mode correlations) and phenomenon like superadditivity of the capacity. The developed methods are also used for deriving transmission rates with heterodyne and homodyne measurements at the channel output. Classical capacity and transmission rates are presented within a unique framework where the rates can be treated as logarithmic approximations of the capacity.Comment: 39 pages, 30 figures. New results and graphs were added. Errors and misprints were corrected. To appear in IEEE Trans. Inf. T

POSSIBLE FUTURE SCENARIOS FOR SICILIAN CEREAL CROPPING IN THE LIGHT OF CURRENT TRENDS IN AGRICULTURAL POLICY OF THE EUROPEAN UNION

This paper sets out the results of a research project carried out by the University of Palermo and financed by the Sicilian Region, which aims to establish the impact of the Fischler Reform on Sicilian agriculture, and to project future scenarios that take into account some of the changes that the production process may undergo in the Region, following both the application of the Reform itself (now in force) and the eventual application of indications contained in the Health check. The impacts of the Fischler Reform, and especially the application of the Single Payment scheme to companies, were examined in cereal cropping companies, especially considering the significant amount of durum wheat cultivation in vast areas of the Region’s hilly and its strategic importance for many areas where there is a risk of farming being abandoned, with grave consequences for the territory and its farmland, for employment and for the encouragement of food and processing industries. The chosen means for assessing the effects of the reform was that of direct interviews at a statistically representative sample made up of 400 agricultural companies, determining possible earnings within the current situation, but also in the eventuality of some of the indications in the Health check being applied. The results indicate that Community aid plays a crucial role in the companies looked at, allowing them to remain on the market. Indeed, the elimination of the aid planned within the framework of the Common Agricultural Policy in the hypothetical scenarios showed a negative impact on earnings for the companies and could cause their exclusion from the market.CAP, Future of the CAP, Sicilian agriculture, Agricultural and Food Policy, Q10, Q18.,

Statistical regimes of random laser fluctuations

Statistical fluctuations of the light emitted from amplifying random media are studied theoretically and numerically. The characteristic scales of the diffusive motion of light lead to Gaussian or power-law (Levy) distributed fluctuations depending on external control parameters. In the Levy regime, the output pulse is highly irregular leading to huge deviations from a mean--field description. Monte Carlo simulations of a simplified model which includes the population of the medium, demonstrate the two statistical regimes and provide a comparison with dynamical rate equations. Different statistics of the fluctuations helps to explain recent experimental observations reported in the literature.Comment: Revised version, resubmitted to Physical Review