Entanglement in continuous variable systems: Recent advances and current perspectives

We review the theory of continuous-variable entanglement with special emphasis on foundational aspects, conceptual structures, and mathematical methods. Much attention is devoted to the discussion of separability criteria and entanglement properties of Gaussian states, for their great practical relevance in applications to quantum optics and quantum information, as well as for the very clean framework that they allow for the study of the structure of nonlocal correlations. We give a self-contained introduction to phase-space and symplectic methods in the study of Gaussian states of infinite-dimensional bosonic systems. We review the most important results on the separability and distillability of Gaussian states and discuss the main properties of bipartite entanglement. These include the extremal entanglement, minimal and maximal, of two-mode mixed Gaussian states, the ordering of two-mode Gaussian states according to different measures of entanglement, the unitary (reversible) localization, and the scaling of bipartite entanglement in multimode Gaussian states. We then discuss recent advances in the understanding of entanglement sharing in multimode Gaussian states, including the proof of the monogamy inequality of distributed entanglement for all Gaussian states, and its consequences for the characterization of multipartite entanglement. We finally review recent advances and discuss possible perspectives on the qualification and quantification of entanglement in non Gaussian states, a field of research that is to a large extent yet to be explored.Comment: 61 pages, 7 figures, 3 tables; Published as Topical Review in J. Phys. A, Special Issue on Quantum Information, Communication, Computation and Cryptography (v3: few typos corrected

An implementation of the look-ahead Lanczos algorithm for non-Hermitian matrices, part 2

It is shown how the look-ahead Lanczos process (combined with a quasi-minimal residual QMR) approach) can be used to develop a robust black box solver for large sparse non-Hermitian linear systems. Details of an implementation of the resulting QMR algorithm are presented. It is demonstrated that the QMR method is closely related to the biconjugate gradient (BCG) algorithm; however, unlike BCG, the QMR algorithm has smooth convergence curves and good numerical properties. We report numerical experiments with our implementation of the look-ahead Lanczos algorithm, both for eigenvalue problem and linear systems. Also, program listings of FORTRAN implementations of the look-ahead algorithm and the QMR method are included

BARGAINING IN COMMITTEES OF REPRESENTATIVES: THE OPTIMAL VOTING RULE

Committees are often made up of representatives of different-sized groups of individuals, and make decisions by means of a voting rule which specifies what vote configurations can pass a decision. This raises the question of the choice of the optimal voting rule, given the different sizes of the groups that members represent. In this paper we take a new departure to address this problem, assuming that the committee is a bargaining scenario in which negotiations take place 'in the shadow of the voting rule' in search of unanimous consensus. That is, a general agreement is looked for, but any winning coalition can enforce an agreement.Voting rule, Bargaining, Nash solution.

FERM3D: A finite element R-matrix electron molecule scattering code

FERM3D is a three-dimensional finite element program, for the elastic scattering of a low energy electron from a general polyatomic molecule, which is converted to a potential scattering problem. The code is based on tricubic polynomials in spherical coordinates. The electron-molecule interaction is treated as a sum of three terms: electrostatic, exchange. and polarisation. The electrostatic term can be extracted directly from ab initio codes ({\sc{GAUSSIAN 98}} in the work described here), while the exchange term is approximated using a local density functional. A local polarisation potential based on density functional theory [C. Lee, W. Yang and R. G. Parr, {Phys. Rev. B} {37}, (1988) 785] describes the long range attraction to the molecular target induced by the scattering electron. Photoionisation calculations are also possible and illustrated in the present work. The generality and simplicity of the approach is important in extending electron-scattering calculations to more complex targets than it is possible with other methods.Comment: 30 pages, 4 figures, preprint, Computer Physics Communications (in press

How can the Power of Leviathans be Measured?

In certain respects, it seems expedient to describe a government as a homogeneous and self-interested entity, called ’Leviathan’. To optimize fiscal constraints, we need to know how powerful a Leviathan really is. This paper presents a new approach to measure the power of Leviathans. This new approach defines fiscal fiscal power in terms of income deviation. It supposes that there exists a positive connection between fiscal power and intergovernmental grants. To examine the approach empirically, we use data on U.S. counties in the period 1999-2002. Equations of fiscal power are estimated on the full and on stratified samples. Overall, the results support the new approach. Nonetheless, further research on the highly significant control variables would be needed to derive recommendations for more efficient fiscal constraints.Leviathan; measurement; income deviation; grants