Scaling laws for the decay of multiqubit entanglement

We investigate the decay of entanglement of generalized N-particle Greenberger-Horne-Zeilinger (GHZ) states interacting with independent reservoirs. Scaling laws for the decay of entanglement and for its finite-time extinction (sudden death) are derived for different types of reservoirs. The latter is found to increase with the number of particles. However, entanglement becomes arbitrarily small, and therefore useless as a resource, much before it completely disappears, around a time which is inversely proportional to the number of particles. We also show that the decay of multi-particle GHZ states can generate bound entangled states.Comment: Minor mistakes correcte

Diffusion Limited Aggregation with Power-Law Pinning

Using stochastic conformal mapping techniques we study the patterns emerging from Laplacian growth with a power-law decaying threshold for growth $R_N^{-\gamma}$ (where $R_N$ is the radius of the $N-$ particle cluster). For $\gamma > 1$ the growth pattern is in the same universality class as diffusion limited aggregation (DLA) growth, while for $\gamma < 1$ the resulting patterns have a lower fractal dimension $D(\gamma)$ than a DLA cluster due to the enhancement of growth at the hot tips of the developing pattern. Our results indicate that a pinning transition occurs at $\gamma = 1/2$, significantly smaller than might be expected from the lower bound $\alpha_{min} \simeq 0.67$ of multifractal spectrum of DLA. This limiting case shows that the most singular tips in the pruned cluster now correspond to those expected for a purely one-dimensional line. Using multifractal analysis, analytic expressions are established for $D(\gamma)$ both close to the breakdown of DLA universality class, i.e., $\gamma \lesssim 1$, and close to the pinning transition, i.e., $\gamma \gtrsim 1/2$.Comment: 5 pages, e figures, submitted to Phys. Rev.

Robustness of Entanglement as a Resource

The robustness of multipartite entanglement of systems undergoing decoherence is of central importance to the area of quantum information. Its characterization depends however on the measure used to quantify entanglement and on how one partitions the system. Here we show that the unambiguous assessment of the robustness of multipartite entanglement is obtained by considering the loss of functionality in terms of two communication tasks, namely the splitting of information between many parties and the teleportation of states.Comment: 11 pages, 5 figure

A Novel Approach to Study Highly Correlated Nanostructures: The Logarithmic Discretization Embedded Cluster Approximation

This work proposes a new approach to study transport properties of highly correlated local structures. The method, dubbed the Logarithmic Discretization Embedded Cluster Approximation (LDECA), consists of diagonalizing a finite cluster containing the many-body terms of the Hamiltonian and embedding it into the rest of the system, combined with Wilson's idea of a logarithmic discretization of the representation of the Hamiltonian. The physics associated with both one embedded dot and a double-dot side-coupled to leads is discussed in detail. In the former case, the results perfectly agree with Bethe ansatz data, while in the latter, the physics obtained is framed in the conceptual background of a two-stage Kondo problem. A many-body formalism provides a solid theoretical foundation to the method. We argue that LDECA is well suited to study complicated problems such as transport through molecules or quantum dot structures with complex ground states.Comment: 17 pages, 13 figure

Effect of topology on the transport properties of two interacting dots

The transport properties of a system of two interacting dots, one of them directly connected to the leads constituting a side-coupled configuration (SCD), are studied in the weak and strong tunnel-coupling limits. The conductance behavior of the SCD structure has new and richer physics than the better studied system of two dots aligned with the leads (ACD). In the weak coupling regime and in the case of one electron per dot, the ACD configuration gives rise to two mostly independent Kondo states. In the SCD topology, the inserted dot is in a Kondo state while the side-connected one presents Coulomb blockade properties. Moreover, the dot spins change their behavior, from an antiferromagnetic coupling to a ferromagnetic correlation, as a consequence of the interaction with the conduction electrons. The system is governed by the Kondo effect related to the dot that is embedded into the leads. The role of the side-connected dot is to introduce, when at resonance, a new path for the electrons to go through giving rise to the interferences responsible for the suppression of the conductance. These results depend on the values of the intra-dot Coulomb interactions. In the case where the many-body interaction is restricted to the side-connected dot, its Kondo correlation is responsible for the scattering of the conduction electrons giving rise to the conductance suppression

Kondo resonance effect on persistent currents through a quantum dot in a mesoscopic ring

The persistent current through a quantum dot inserted in a mesoscopic ring of length L is studied. A cluster representing the dot and its vicinity is exactly diagonalized and embedded into the rest of the ring. The Kondo resonance provides a new channel for the current to flow. It is shown that due to scaling properties, the persistent current at the Kondo regime is enhanced relative to the current flowing either when the dot is at resonance or along a perfect ring of same length. In the Kondo regime the current scales as $L^{-1/2}$, unlike the $L^{-1}$ scaling of a perfect ring. We discuss the possibility of detection of the Kondo effect by means of a persistent current measurement.Comment: 11 pages, 3 Postscript figure

Laplacian growth with separately controlled noise and anisotropy

Conformal mapping models are used to study competition of noise and anisotropy in Laplacian growth. For that, a new family of models is introduced with the noise level and directional anisotropy controlled independently. Fractalization is observed in both anisotropic growth and the growth with varying noise. Fractal dimension is determined from cluster size scaling with its area. For isotropic growth we find d = 1.7, both at high and low noise. For anisotropic growth with reduced noise the dimension can be as low as d = 1.5 and apparently is not universal. Also, we study fluctuations of particle areas and observe, in agreement with previous studies, that exceptionally large particles may appear during the growth, leading to pathologically irregular clusters. This difficulty is circumvented by using an acceptance window for particle areas.Comment: 13 pages, 15 figure

Conditional large Fock state preparation and field state reconstruction in Cavity QED

We propose a scheme for producing large Fock states in Cavity QED via the implementation of a highly selective atom-field interaction. It is based on Raman excitation of a three-level atom by a classical field and a quantized field mode. Selectivity appears when one tunes to resonance a specific transition inside a chosen atom-field subspace, while other transitions remain dispersive, as a consequence of the field dependent electronic energy shifts. We show that this scheme can be also employed for reconstructing, in a new and efficient way, the Wigner function of the cavity field state.Comment: 4 Revtex pages with 3 postscript figures. Submitted for publicatio