Entanglement monotones and maximally entangled states in multipartite qubit systems

We present a method to construct entanglement measures for pure states of multipartite qubit systems. The key element of our approach is an antilinear operator that we call {\em comb} in reference to the {\em hairy-ball theorem}. For qubits (or spin 1/2) the combs are automatically invariant under SL(2,\CC). This implies that the {\em filters} obtained from the combs are entanglement monotones by construction. We give alternative formulae for the concurrence and the 3-tangle as expectation values of certain antilinear operators. As an application we discuss inequivalent types of genuine four-, five- and six-qubit entanglement.Comment: 7 pages, revtex4. Talk presented at the Workshop on "Quantum entanglement in physical and information sciences", SNS Pisa, December 14-18, 200

Fractional Quantum Hall States in Ultracold Rapidly Rotating Dipolar Fermi Gases

We demonstrate the experimental feasibility of incompressible fractional quantum Hall-like states in ultra-cold two dimensional rapidly rotating dipolar Fermi gases. In particular, we argue that the state of the system at filling fraction $\nu =1/3$ is well-described by the Laughlin wave function and find a substantial energy gap in the quasiparticle excitation spectrum. Dipolar gases, therefore, appear as natural candidates of systems that allow to realize these very interesting highly correlated states in future experiments.Comment: 4 pages, 2 figure

Enhancement of pairwise entanglement from \mathbbm{Z}_2 symmetry breaking

We study the effect of symmetry breaking in a quantum phase transition on pairwise entanglement in spin-1/2 models. We give a set of conditions on correlation functions a model has to meet in order to keep the pairwise entanglement unchanged by a parity symmetry breaking. It turns out that all mean-field solvable models do meet this requirement, whereas the presence of strong correlations leads to a violation of this condition. This results in an order-induced enhancement of entanglement, and we report on two examples where this takes place.Comment: 4 pages, 3 figures, revtex4. Slight modifications, few additional remark

Entanglement and quantum phase transitions in matrix product spin one chains

We consider a one-parameter family of matrix product states of spin one particles on a periodic chain and study in detail the entanglement properties of such a state. In particular we calculate exactly the entanglement of one site with the rest of the chain, and the entanglement of two distant sites with each other and show that the derivative of both these properties diverge when the parameter $g$ of the states passes through a critical point. Such a point can be called a point of quantum phase transition, since at this point, the character of the matrix product state which is the ground state of a Hamiltonian, changes discontinuously. We also study the finite size effects and show how the entanglement depends on the size of the chain. This later part is relevant to the field of quantum computation where the problem of initial state preparation in finite arrays of qubits or qutrits is important. It is also shown that entanglement of two sites have scaling behavior near the critical point

Out of equilibrium correlation functions of quantum anisotropic XY models: one-particle excitations

We calculate exactly matrix elements between states that are not eigenstates of the quantum XY model for general anisotropy. Such quantities therefore describe non equilibrium properties of the system; the Hamiltonian does not contain any time dependence. These matrix elements are expressed as a sum of Pfaffians. For single particle excitations on the ground state the Pfaffians in the sum simplify to determinants.Comment: 11 pages, no figures; revtex. Minor changes in the text; list of refs. modifie

Lack of Diversity in Leadership: Could Selective Randomness Break the Deadlock?

The proportion of women and ethnic minorities in senior management remains indefensibly low. Radical ideas are therefore needed. This paper proposes one. It is to use a form of selective randomness -- random selection from among a pool of pre-chosen and qualified candidates -- as a new HRM tool. We argue this in two parts – an equity case and an efficiency case. First, selective randomness would ensure greater equity between the sexes and races over time; offer ‘rejection insurance’ to candidates wary of discrimination, and thereby mitigate the fear of failure; and encourage women and non-whites to enter tournaments. Second, we consider also the criterion of efficiency. The standard of candidates going into management would be raised; homophily would be reduced, thus improving diversity of people and ideas, and reducing the ‘chosen one’ factor. By using Jensen’s inequality from applied mathematics, we provide the first demonstration that random selection could act to improve organizational efficiency by raising the chance of an extraordinary manager being hired