Entanglement Detection in the Stabilizer Formalism

We investigate how stabilizer theory can be used for constructing sufficient conditions for entanglement. First, we show how entanglement witnesses can be derived for a given state, provided some stabilizing operators of the state are known. These witnesses require only a small effort for an experimental implementation and are robust against noise. Second, we demonstrate that also nonlinear criteria based on uncertainty relations can be derived from stabilizing operators. These criteria can sometimes improve the witnesses by adding nonlinear correction terms. All our criteria detect states close to Greenberger-Horne-Zeilinger states, cluster and graph states. We show that similar ideas can be used to derive entanglement conditions for states which do not fit the stabilizer formalism, such as the three-qubit W state. We also discuss connections between the witnesses and some Bell inequalities.Comment: 15 pages including 2 figures, revtex4; typos corrected, presentation improved; to appear in PR

Entanglement Witnesses in Spin Models

We construct entanglement witnesses using fundamental quantum operators of spin models which contain two-particle interactions and posses a certain symmetry. By choosing the Hamiltonian as such an operator, our method can be used for detecting entanglement by energy measurement. We apply this method to the cubic Heisenberg lattice model in a magnetic field, the XY model and other familiar spin systems. Our method is used to obtain a temperature bound for separable states for systems in thermal equilibrium. We also study the Bose-Hubbard model and relate its energy minimum for separable states to the minimum obtained from the Gutzwiller ansatz.Comment: 5 pages including 3 figures, revtex4; some typos correcte

Growth of ZnO nanostructures on Si by means of plasma immersion ion implantation and deposition

Crystalline zinc oxide (ZnO) nanostructures have been grown on Si substrates by means of Plasma Based Ion Implantation and Deposition (PIII&D) at temperature of about 300 0C and in the presence of an argon glow discharge. In the process a crucible filled with small pieces of metallic zinc plays the role of the anode of the discharge itself, being polarized by positive DC voltage of about 400V. Electrons produced by thermionic emission by an oxide cathode (Ba, Sr, Ca)O impact this crucible, causing its heating and vaporization of Zn. Partial ionization of Zn atoms takes place due to collisions with plasma particles. High negative voltage pulses (7 kv/40μs/250Hz) applied to the sample holder cause the implantation of metallic zinc into Si surface, while Zn deposition happens between pulses. After annealing at 700 0C, strong UV and various visible photoluminescence bands are observed at room temperature, as well as the presence of ZnO nanoparticles. The coated surface was characterized in detail using X-ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS), energy dispersive spectroscopy (EDS), scanning electron microscopy (SEM), atomic force microscopy (AFM) and photoluminescence (PL) spectroscopy. XRD indicated the presence of only ZnO peaks after annealing. The composition analysis by EDS revealed distinct Zn/O stoichiometry relation depending on the conditions of the process. AFM images showed the formation of columns in the nanoscale range. Topography viewed by SEM showed the formation of structures similar to cactus with nanothorns. Depth analysis performed by XPS indicated an increase of concentration of metallic Zn with increasing depth and the exclusive presence of ZnO for outer regions. PIII&D allowed to growing nanostructures of ZnO on Si without the need of a buffer layer

Statistical mechanical systems on complete graphs, infinite exchangeability, finite extensions and a discrete finite moment problem

We show that a large collection of statistical mechanical systems with quadratically represented Hamiltonians on the complete graph can be extended to infinite exchangeable processes. This extends a known result for the ferromagnetic Curie--Weiss Ising model and includes as well all ferromagnetic Curie--Weiss Potts and Curie--Weiss Heisenberg models. By de Finetti's theorem, this is equivalent to showing that these probability measures can be expressed as averages of product measures. We provide examples showing that ``ferromagnetism'' is not however in itself sufficient and also study in some detail the Curie--Weiss Ising model with an additional 3-body interaction. Finally, we study the question of how much the antiferromagnetic Curie--Weiss Ising model can be extended. In this direction, we obtain sharp asymptotic results via a solution to a new moment problem. We also obtain a ``formula'' for the extension which is valid in many cases.Comment: Published at http://dx.doi.org/10.1214/009117906000001033 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

On an almost-universal hash function family with applications to authentication and secrecy codes

Universal hashing, discovered by Carter and Wegman in 1979, has many important applications in computer science. MMH$^*$, which was shown to be $\Delta$-universal by Halevi and Krawczyk in 1997, is a well-known universal hash function family. We introduce a variant of MMH$^*$, that we call GRDH, where we use an arbitrary integer $n>1$ instead of prime $p$ and let the keys $\mathbf{x}=\langle x_1, \ldots, x_k \rangle \in \mathbb{Z}_n^k$ satisfy the conditions $\gcd(x_i,n)=t_i$ ($1\leq i\leq k$), where $t_1,\ldots,t_k$ are given positive divisors of $n$. Then via connecting the universal hashing problem to the number of solutions of restricted linear congruences, we prove that the family GRDH is an $\varepsilon$-almost-$\Delta$-universal family of hash functions for some $\varepsilon<1$ if and only if $n$ is odd and $\gcd(x_i,n)=t_i=1$ $(1\leq i\leq k)$. Furthermore, if these conditions are satisfied then GRDH is $\frac{1}{p-1}$-almost-$\Delta$-universal, where $p$ is the smallest prime divisor of $n$. Finally, as an application of our results, we propose an authentication code with secrecy scheme which strongly generalizes the scheme studied by Alomair et al. [{\it J. Math. Cryptol.} {\bf 4} (2010), 121--148], and [{\it J.UCS} {\bf 15} (2009), 2937--2956].Comment: International Journal of Foundations of Computer Science, to appea

Safe Concurrency Introduction through Slicing

Traditional refactoring is about modifying the structure of existing code without changing its behaviour, but with the aim of making code easier to understand, modify, or reuse. In this paper, we introduce three novel refactorings for retrofitting concurrency to Erlang applications, and demonstrate how the use of program slicing makes the automation of these refactorings possible

Financial correlations at ultra-high frequency: theoretical models and empirical estimation

A detailed analysis of correlation between stock returns at high frequency is compared with simple models of random walks. We focus in particular on the dependence of correlations on time scales - the so-called Epps effect. This provides a characterization of stochastic models of stock price returns which is appropriate at very high frequency.Comment: 22 pages, 8 figures, 1 table, version to appear in EPJ

Using geophysical log data to predict the fracture density in a claystone host rock for storing high-level nuclear waste

Previously drilled boreholes of a host rock for a potential nuclear waste repository in Hungary revealed a highly fractured claystone rock body. A crucial step for characterizing the hydrodynamic behavior of such a fractured reservoir is fracture identification and accurate calculation of the fracture density. Although acoustic borehole televiewers provide a reliable base for determining the fracture density, older boreholes usually lack such data. However, conventional borehole geophysical measurements are often accessible in such cases. The aim of this study was to identify any correlations between well log data and fracture density. Multiple linear regression analysis was performed on data from two boreholes penetrating the Boda Claystone Formation in southwest Hungary. The upper section of the BAF-4 borehole was used for training, where the fracture density was estimated with a fit of R 2 = 0.767. The computed regression function predicted the fracture density with high accuracy in both boreholes for all intervals with typical lithological features. However, in some sections where anomalous well log data indicated changes in the lithology, the prediction accuracy decreased. For example, the function underestimated the fracture density in sandy intervals