Witnessed entanglement and the geometric measure of quantum discord

We establish relations between geometric quantum discord and entanglement quantifiers obtained by means of optimal witness operators. In particular, we prove a relation between negativity and geometric discord in the Hilbert-Schmidt norm, which is slightly different from a previous conjectured one [Phys. Rev. A 84, 052110 (2011)].We also show that, redefining the geometric discord with the trace norm, better bounds can be obtained. We illustrate our results numerically.Comment: 8 pages + 3 figures. Revised version with erratum for PRA 86, 024302 (2012). Simplified proof that discord is bounded by entanglement in any nor

Structure of the Natural Transgene PgiC2 in the Common Grass Festuca ovina

BACKGROUND: A horizontal gene transfer has brought an active nuclear gene, PgiC2, from a polyploid Poa species (P. palustris or a close relative) into the common grass sheep's fescue (Festuca ovina). The donor and the receptor species are strictly reproductively separated, and PgiC2 occurs in a polymorphic state within F. ovina. The active gene copy is normally closely linked to a very similar pseudogene. METHODOLOGY/PRINCIPAL FINDINGS: By genome walking we have obtained the up- and downstream sequences of PgiC2 and of corresponding genes in the donor and recipient species. Comparisons of these sequences show that the complete upstream region necessary for the gene's expression is included in the transferred segment. About 1 kb upstream of PgiC2 a fragment with transposition associated properties has been found (TAF). It is present in P. palustris and its polyploid relatives, though not at the homologous position, and is absent from many other grasses, including non-transgenic F. ovina plants. It is possible that it is a part of a transposing element involved in getting the gene into a transferring agent and/or into the recipient chromosome. CONCLUSIONS/SIGNIFICANCE: The close similarity of the up- and downstream regions with the corresponding regions in P. palustris excludes all suggestions that PgiC2 is not a HGT but the result of a duplication within the F. ovina lineage. The small size of the genetic material transferred, the complex nature of the PgiC2 locus, and the associated fragment with transposition associated properties suggest that the horizontal transfer occurred via a vector and not via illegitimate pollination

Statistical bounds on the dynamical production of entanglement

We present a random-matrix analysis of the entangling power of a unitary operator as a function of the number of times it is iterated. We consider unitaries belonging to the circular ensembles of random matrices (CUE or COE) applied to random (real or complex) non-entangled states. We verify numerically that the average entangling power is a monotonic decreasing function of time. The same behavior is observed for the "operator entanglement" --an alternative measure of the entangling strength of a unitary. On the analytical side we calculate the CUE operator entanglement and asymptotic values for the entangling power. We also provide a theoretical explanation of the time dependence in the CUE cases.Comment: preprint format, 14 pages, 2 figure

Geometrically induced singular behavior of entanglement

We show that the geometry of the set of quantum states plays a crucial role in the behavior of entanglement in different physical systems. More specifically it is shown that singular points at the border of the set of unentangled states appear as singularities in the dynamics of entanglement of smoothly varying quantum states. We illustrate this result by implementing a photonic parametric down conversion experiment. Moreover, this effect is connected to recently discovered singularities in condensed matter models.Comment: v2: 4 pags, 4 figs. A discussion before the proof of Proposition 1 and tomographic results were included, Propostion 2 was removed and the references were fixe

Higher Spin Scattering in Superstring Theory

We compute scattering amplitudes of leading Regge trajectory states in open superstring theories. Highest spin states at mass level n with spin s=n+1 for bosons and s=n+1/2 for fermions are generated by particularly simple vertex operators. Hence, the cubic couplings of bosons and fermions on the leading Regge trajectory are given for arbitrary n. The same can be achieved for higher point amplitudes, and this article focuses on four point level with one heavy maximum spin state and three massless states in any bose-fermi combination, putting particular emphasis on manifest cyclic symmetry. Except for the four fermion coupling, all our results remain valid in any D<10 dimensional compactification scenario, so they might become relevant at LHC in case of an experimentally accessible low string scale. But even if not directly observable, superstring amplitudes provide important clues on higher spin dynamics and their consistent interactions in field theory.Comment: 31 pages; v3: final version published in Nuclear Physics

Particle Induced X-Ray Emission Microanalysis of Root Samples from Beech (Fagus sylvatica)

Beech seedlings (Fagus Sylvatica) were grown in a nutrient solution to which AlCl3 had been added. The experiments were designed to evaluate the effect of aluminum on the localization of elements in plant root tissue. Cross-sections of roots were analyzed with micro-PIXE (particle induced X-ray emission) and Rutherford backscattering (RBS) simultaneously. A proton beam of either 30x30 μm2 or 5x5 μm2 was scanned over the samples, and quantitative elemental maps were created. Aluminum was found to accumulate in high concentrations (percent levels) in the epidermis and the outer layer of the cortex, when the nutrient solution held 1.0 mM AlCl3. It was also obvious that calcium was depleted where aluminum accumulated. The distribution of aluminum was inhomogeneous, and therefore, it was necessary to analyze the total area of the cross-section and not only look at a small part of it, for example along a diametrical line

Microscopic Origin of Quantum Chaos in Rotational Damping

The rotational spectrum of $^{168}$Yb is calculated diagonalizing different effective interactions within the basis of unperturbed rotational bands provided by the cranked shell model. A transition between order and chaos taking place in the energy region between 1 and 2 MeV above the yrast line is observed, associated with the onset of rotational damping. It can be related to the higher multipole components of the force acting among the unperturbed rotational bands.Comment: 7 pages, plain TEX, YITP/K-99

Partial separability revisited: Necessary and sufficient criteria

We extend the classification of mixed states of quantum systems composed of arbitrary number of subsystems of arbitrary dimensions. This extended classification is complete in the sense of partial separability and gives 1+18+1 partial separability classes in the tripartite case contrary to a former 1+8+1. Then we give necessary and sufficient criteria for these classes, which make it possible to determine to which class a mixed state belongs. These criteria are given by convex roof extensions of functions defined on pure states. In the special case of three-qubit systems, we define a different set of such functions with the help of the Freudenthal triple system approach of three-qubit entanglement.Comment: v3: 22 pages, 5 tables, 1 figure, minor corrections (typos), clarification in the Introduction. Accepted in Phys. Rev. A. Comments are welcom