Quantum Correlation Bounds for Quantum Information Experiments Optimization: the Wigner Inequality Case

Violation of modified Wigner inequality by means binary bipartite quantum system allows the discrimination between the quantum world and the classical local-realistic one, and also ensures the security of Ekert-like quantum key distribution protocol. In this paper we study both theoretically and experimentally the bounds of quantum correlation associated to the modified Wigner's inequality finding the optimal experimental configuration for its maximal violation. We also extend this analysis to the implementation of Ekert's protocol

The orbital poles of Milky Way satellite galaxies: a rotationally supported disc-of-satellites

Available proper motion measurements of Milky Way (MW) satellite galaxies are used to calculate their orbital poles and projected uncertainties. These are compared to a set of recent cold dark-matter (CDM) simulations, tailored specifically to solve the MW satellite problem. We show that the CDM satellite orbital poles are fully consistent with being drawn from a random distribution, while the MW satellite orbital poles indicate that the disc-of-satellites of the Milky Way is rotationally supported. Furthermore, the bootstrapping analysis of the spatial distribution of theoretical CDM satellites also shows that they are consistent with being randomly drawn. The theoretical CDM satellite population thus shows a significantly different orbital and spatial distribution than the MW satellites, most probably indicating that the majority of the latter are of tidal origin rather than being DM dominated sub-structures. A statistic is presented that can be used to test a possible correlation of satellite galaxy orbits with their spatial distribution.Comment: Accepted for publication in Ap

Strong violations of Bell-type inequalities for Werner-like states

We investigate the violation of Bell-type inequalities for two-qubit Werner-like states parametrized by the positive parameter 0<p<1. We use an unbalanced homodyne detection scheme to obtain the quantum mechanical probabilities. A violation of the Bell-Wigner and Janssens inequalities is obtained for a large range of the parameter p. The range given by these inequalities is greater than the one given by the Clauser-Horne inequality. The range in which a violation is attained actually coincides with the range where the Werner-like states are known to be nonseparabel, i.e., for p>1/3. However, the improvement over the Clauser-Horne inequality is achieved at the price of restricting the class of possible local hidden variable theories.Comment: Revised manuscript, accepted for publication in PR

J.S. Bell's Concept of Local Causality

John Stewart Bell's famous 1964 theorem is widely regarded as one of the most important developments in the foundations of physics. It has even been described as "the most profound discovery of science." Yet even as we approach the 50th anniversary of Bell's discovery, its meaning and implications remain controversial. Many textbooks and commentators report that Bell's theorem refutes the possibility (suggested especially by Einstein, Podolsky, and Rosen in 1935) of supplementing ordinary quantum theory with additional ("hidden") variables that might restore determinism and/or some notion of an observer-independent reality. On this view, Bell's theorem supports the orthodox Copenhagen interpretation. Bell's own view of his theorem, however, was quite different. He instead took the theorem as establishing an "essential conflict" between the now well-tested empirical predictions of quantum theory and relativistic \emph{local causality}. The goal of the present paper is, in general, to make Bell's own views more widely known and, in particular, to explain in detail Bell's little-known mathematical formulation of the concept of relativistic local causality on which his theorem rests. We thus collect and organize many of Bell's crucial statements on these topics, which are scattered throughout his writings, into a self-contained, pedagogical discussion including elaborations of the concepts "beable", "completeness", and "causality" which figure in the formulation. We also show how local causality (as formulated by Bell) can be used to derive an empirically testable Bell-type inequality, and how it can be used to recapitulate the EPR argument.Comment: 19 pages, 4 figure

The Identity Problem for Matrix Semigroups in SL2(Z) is NP-complete

In this paper, we show that the problem of determining if the identity matrix belongs to a finitely generated semigroup of $2\times 2$ matrices from the modular group $\text{PSL}_2(\mathbb Z)$ and thus the Special Linear group $\text{SL}_2(\mathbb Z)$ is solvable in $\mathbf{NP}$. From this fact, we can immediately derive that the fundamental problem of whether a given finite set of matrices from $\text{SL}_2(\mathbb Z)$ or $\text{PSL}_2(\mathbb Z)$ generates a group or free semigroup is also decidable in $\mathbf{NP}$. The previous algorithm for these problems, shown in 2005 by Choffrut and Karhum\"aki, was in \EXPSPACE mainly due to the translation of matrices into exponentially long words over a binary alphabet $\{s,r\}$ and further constructions with a large nondeterministic finite state automaton that is built on these words. Our algorithm is based on various new techniques that allow us to operate with compressed word representations of matrices without explicit expansions. When combined with the known $\mathbf{NP}$-hard lower bound, this proves that the membership problem for the identity problem, the group problem and the freeness problem in $\text{SL}_2(\mathbb Z)$ are $\mathbf{NP}$-complete

The Anisotropic Distribution of M 31 Satellite Galaxies: A Polar Great Plane of Early-Type Companions

The highly anisotropic distribution and apparent alignment of the Galactic satellites in polar great planes begs the question how common such distributions are. The satellite system of M31 is the only nearby system for which we currently have sufficiently accurate distances to study the three-dimensional satellite distribution. We present the spatial distribution of the 15 presently known M31 companions in a coordinate system centered on M31 and aligned with its disk. Through a detailed statistical analysis we show that the full satellite sample describes a plane that is inclined by -56 deg with respect to the poles of M31 and that has an r.m.s. height of 100 kpc. With 88% the statistical significance of this plane is low and it is unlikely to have a physical meaning. The great stellar stream found near Andromeda is inclined to this plane by 7 deg. There is little evidence for a Holmberg effect. If we confine our analysis to early-type dwarfs, we find a best-fit polar plane within 5 deg to 7 deg from the pole of M31. This polar great plane has a statistical significance of 99.3% and includes all dSphs (except for And II), M32, NGC 147, and PegDIG. The r.m.s. distance of these galaxies from the polar plane is 16 kpc. The nearby spiral M33 has a distance of only about 3 kpc from this plane, which points toward the M81 group. We discuss the anisotropic distribution of M31's early-type companions in the framework of three scenarios, namely as remnants of the break-up of a larger progenitor, as tracer of a prolate dark matter halo, and as tracer of collapse along large-scale filaments. (Abridged)Comment: 14 pages, 5 figures, accepted for publication in the Astronomical Journa

Crystalline silicates as a probe of disk formation history

We present a new perspective on the crystallinity of dust in protoplanetary disks. The dominant crystallization by thermal annealing happens in the very early phases of disk formation and evolution. Both the disk properties and the level of crystallinity are thereby directly linked to the properties of the molecular cloud core from which the star+disk system was formed. We show that, under the assumption of single star formation, rapidly rotating clouds produce disks which, after the main infall phase (i.e. in the optically revealed class II phase), are rather massive and have a high accretion rate but low crystallinity. Slowly rotating clouds, on the other hand, produce less massive disks with lower accretion rate, but high levels of crystallinity. Cloud fragmentation and the formation of multiple stars complicates the problem and necessitates further study. The underlying physics of the model is insufficiently understood to provide the precise relationship between crystallinity, disk mass and accretion rate. But the fact that with `standard' input physics the model produces disks which, in comparison to observations, appear to have either too high levels of crystallinity or too high disk masses, demonstrates that the comparison of these models to observations can place strong contraints on the disk physics. The question to ask is not why some sources are so crystalline, but why some other sources have such a low level of crystallinity.Comment: Accepted for publication in ApJ

Full characterization of a three-photon GHZ state using quantum state tomography

We have performed the first experimental tomographic reconstruction of a three-photon polarization state. Quantum state tomography is a powerful tool for fully describing the density matrix of a quantum system. We measured 64 three-photon polarization correlations and used a "maximum-likelihood" reconstruction method to reconstruct the GHZ state. The entanglement class has been characterized using an entanglement witness operator and the maximum predicted values for the Mermin inequality was extracted.Comment: 3 pages, 3 figure

Entanglement properties of quantum spin chains

We investigate the entanglement properties of a finite size 1+1 dimensional Ising spin chain, and show how these properties scale and can be utilized to reconstruct the ground state wave function. Even at the critical point, few terms in a Schmidt decomposition contribute to the exact ground state, and to physical properties such as the entropy. Nevertheless the entanglement here is prominent due to the lower-lying states in the Schmidt decomposition.Comment: 5 pages, 6 figure

Angular momentum dependent friction slows down rotational relaxation under non-equilibrium conditions

It has recently been shown that relaxation of the rotational energy of hot non-equlibrium photofragments (i) slows down significantly with the increase of their initial rotational temperature and (ii) differs dramatically from the relaxation of the equilibrium rotational energy correlation function, manifesting thereby breakdown of the linear response description [Science 311, 1907 (2006)]. We demonstrate that this phenomenon may be caused by the angular momentum dependence of rotational friction. We have developed the generalized Fokker-Planck equation whose rotational friction depends upon angular momentum algebraically. The calculated rotational correlation functions correspond well to their counterparts obtained via molecular dynamics simulations in a broad range of initial non-equilibrium conditions. It is suggested that the angular momentum dependence of friction should be taken into account while describing rotational relaxation far from equilibrium