A large-N approximated field theory for multipartite entanglement

We study the characterization of multipartite entanglement for the random states of an $n$-qbit system. Unable to solve the problem exactly we generalize it, changing complex numbers into real vectors with $N_c$ components (the original problem is recovered for $N_c=2$). Studying the leading diagrams in the large-$N_c$ approximation, we unearth the presence of a phase transition and, in an explicit example, show that the so-called entanglement frustration disappears in the large-$N_c$ limit.Comment: 12 pages, 15 figure

Polarized ensembles of random pure states

A new family of polarized ensembles of random pure states is presented. These ensembles are obtained by linear superposition of two random pure states with suitable distributions, and are quite manageable. We will use the obtained results for two purposes: on the one hand we will be able to derive an efficient strategy for sampling states from isopurity manifolds. On the other, we will characterize the deviation of a pure quantum state from separability under the influence of noise.Comment: 14 pages, 1 figur

Local Hamiltonians for Maximally Multipartite Entangled States

We study the conditions for obtaining maximally multipartite entangled states (MMES) as non-degenerate eigenstates of Hamiltonians that involve only short-range interactions. We investigate small-size systems (with a number of qubits ranging from 3 to 5) and show some example Hamiltonians with MMES as eigenstates.Comment: 6 pages, 3 figures, published versio

Consumers’ Attitudes on Services of General Interest in the EU: Accessibility, Price and Quality 2000-2004

The research question addressed by this paper is a simple one: are European consumers happy with the services provided by the utilities after two decades of reforms? We focus on electricity, gas, water, telephone in the EU 15 Member States. The variables we analyse are consumers’ satisfaction with accessibility, price and quality, as reported in three waves of Eurobarometer survey, 2000-2002-2004, comprising around 47,000 observations. We use ordered logit models to analyze the impact of privatization and regulatory reforms, as represented by an OECD dataset, controlling for individual and country characteristics. Our results do not support a clear association between consumers’ satisfaction and a standard reform package of privatization, vertical disintegration, liberalization.Consumers’ Satisfaction, Gas, Electricity, Telephone, Water, Eurobarometer

Multipartite entanglement characterization of a quantum phase transition

A probability density characterization of multipartite entanglement is tested on the one-dimensional quantum Ising model in a transverse field. The average and second moment of the probability distribution are numerically shown to be good indicators of the quantum phase transition. We comment on multipartite entanglement generation at a quantum phase transition.Comment: 10 pages, 6 figures, final versio

Invariant measures on multimode quantum Gaussian states

We derive the invariant measure on the manifold of multimode quantum Gaussian states, induced by the Haar measure on the group of Gaussian unitary transformations. To this end, by introducing a bipartition of the system in two disjoint subsystems, we use a parameterization highlighting the role of nonlocal degrees of freedom -- the symplectic eigenvalues -- which characterize quantum entanglement across the given bipartition. A finite measure is then obtained by imposing a physically motivated energy constraint. By averaging over the local degrees of freedom we finally derive the invariant distribution of the symplectic eigenvalues in some cases of particular interest for applications in quantum optics and quantum information.Comment: 17 pages, comments are welcome. v2: presentation improved and typos corrected. Close to the published versio

Probability density function characterization of multipartite entanglement

We propose a method to characterize and quantify multipartite entanglement for pure states. The method hinges upon the study of the probability density function of bipartite entanglement and is tested on an ensemble of qubits in a variety of situations. This characterization is also compared to several measures of multipartite entanglement.Comment: 7 pages, 2 figures; published version; title changed; further explanations and comparison with several measures of multipartite entanglement adde

Market organization and propagation of shocks: the furniture industry in Germany and Italy

In this paper we study the furniture industry in two European countries, Germany and Italy. Although the two industries are characterized by very similar output and technology, they differ widely in terms of market organization, most notably the distribution of firms by size, and the organization of retail. We find some evidences that these differences have an influence on the dynamic behavior of industry output, prices and exports in the two countries

Binary mixtures of condensates in generic confining potentials

We study a binary mixture of Bose-Einstein condensates, confined in a generic potential, in the Thomas-Fermi approximation. We search for the zero-temperature ground state of the system, both in the case of fixed numbers of particles and fixed chemical potentials.Comment: 20 pages, 2 figure