Entangled symmetric states of N qubits with all positive partial transpositions

From both theoretical and experimental points of view symmetric states constitute an important class of multipartite states. Still, entanglement properties of these states, in particular those with positive partial transposition (PPT), lack a systematic study. Aiming at filling in this gap, we have recently affirmatively answered the open question of existence of four-qubit entangled symmetric states with positive partial transposition and thoroughly characterized entanglement properties of such states [J. Tura et al., Phys. Rev. A 85, 060302(R) (2012)] With the present contribution we continue on characterizing PPT entangled symmetric states. On the one hand, we present all the results of our previous work in a detailed way. On the other hand, we generalize them to systems consisting of arbitrary number of qubits. In particular, we provide criteria for separability of such states formulated in terms of their ranks. Interestingly, for most of the cases, the symmetric states are either separable or typically separable. Then, edge states in these systems are studied, showing in particular that to characterize generic PPT entangled states with four and five qubits, it is enough to study only those that assume few (respectively, two and three) specific configurations of ranks. Finally, we numerically search for extremal PPT entangled states in such systems consisting of up to 23 qubits. One can clearly notice regularity behind the ranks of such extremal states, and, in particular, for systems composed of odd number of qubits we find a single configuration of ranks for which there are extremal states.Comment: 16 pages, typos corrected, some other improvements, extension of arXiv:1203.371

Four-qubit entangled symmetric states with positive partial transpositions

We solve the open question of the existence of four-qubit entangled symmetric states with positive partial transpositions (PPT states). We reach this goal with two different approaches. First, we propose a half-analytical-half-numerical method that allows to construct multipartite PPT entangled symmetric states (PPTESS) from the qubit-qudit PPT entangled states. Second, we adapt the algorithm allowing to search for extremal elements in the convex set of bipartite PPT states [J. M. Leinaas, J. Myrheim, and E. Ovrum, Phys. Rev. A 76, 034304 (2007)] to the multipartite scenario. With its aid we search for extremal four-qubit PPTESS and show that generically they have ranks (5,7,8). Finally, we provide an exhaustive characterization of these states with respect to their separability properties.Comment: 5+4 pages, improved version, title slightly modifie

The pgip family in soybean and three other legume species: evidence for a birth-and-death model of evolution

Polygalacturonase-inhibiting proteins (PGIPs) are leucine-rich repeat (LRR) plant cell wall glycoproteins involved in plant immunity. They are typically encoded by gene families with a small number of gene copies whose evolutionary origin has been poorly investigated. Here we report the complete characterization of the full complement of the pgip family in soybean (Glycine max [L.] Merr.) and the characterization of the genomic region surrounding the pgip family in four legume species. Results: BAC clone and genome sequence analyses showed that the soybean genome contains two pgip loci. Each locus is composed of three clustered genes that are induced following infection with the fungal pathogen Sclerotinia sclerotiorum (Lib.) de Bary, and remnant sequences of pgip genes. The analyzed homeologous soybean genomic regions (about 126 Kb) that include the pgip loci are strongly conserved and this conservation extends also to the genomes of the legume species Phaseolus vulgaris L., Medicago truncatula Gaertn. and Cicer arietinum L., each containing a single pgip locus. Maximum likelihood-based gene trees suggest that the genes within the pgip clusters have independently undergone tandem duplication in each species. Conclusions: The paleopolyploid soybean genome contains two pgip loci comprised in large and highly conserved duplicated regions, which are also conserved in bean, M. truncatula and C. arietinum. The genomic features of these legume pgip families suggest that the forces driving the evolution of pgip genes follow the birth-and-death model, similar to that proposed for the evolution of resistance (R) genes of NBS-LRR-type

Holistic Approach to Biodiversity and Bioindication in Soil

To study and investigate soil biodiversity is a difficult task because of the complex interactions that exist in soil and the need for considerable expertise to undertake the necessary investigations. The factors that influence biodiversity are diverse: some are natural, for example soil acidity, water retention, temperature and organic matter content, others are anthropogenic, for example human population pressure. This report summarises the results of the multidisciplinary BIO-BIO study of biodiversity and bioindication, conducted within the Pavia Project, which had as its principal objective the evaluation of the quality and health of soil in Pavia Province, Lombardy, in northern Italy. The area under investigation covered 3000 km2 and the project took into account of the different uses of soil. International standard methods were adopted for the identification of sampling points, the collection, treatment and analysis of the samples for heavy metals, macro-elements, dioxins, furans, soil acidity, physical properties (water retention, pore size, geochemical profile, etc.) and biological data (bacteria and terrestrial mosses). The differences in soil biodiversity that have resulted from different management practices, namely: organic or ¿biological¿ farming; conventional ¿manure¿ farming using animal excreta and mineral fertilizers; and sewage sludge ¿amended¿ applications to soil, have been studied on a seasonal basis (4 sampling per year) and analysis of soil samples taken at 0--5 cm; 0-15 cm and 15-30 cm depth. Some general ideas of what needs to be done in this field are outlined, whilst, at the same time, suggesting the basis for further studies. Bacteria, collembola and earthworms, which cover the three nutritional nets, are the most useful bio-indicators for appraising the evolution of biodiversity and assessing soil quality. To evaluate the biodiversity ¿in soil¿ means to appraise the quality of the soil. Only integrated studies, that take into consideration the chemical, physical and biological nature of soil, will lead to a full understanding of soil biodiversity.JRC.DDG.H.7-Land management and natural hazard

Uso de atmosfera controlada para conservação pós-colheita do mamão "Golden".

Frutos de mamoeiro 'Golden' colhidos no estádio 3 de maturação foram armazenados sob controle de atmosfera (3%O2 e 3%CO2 , 3%O2 e 6%CO2 ou 8%CO2 , 5%O2 e 8%CO2) e sob atmosfera ambiente (70% ou 90% U.R.), por 20 ou 25 dias, seguidos de mais 5 dias em atmosfera ambiente, a 10º C. Após 4 dias a 22º C não se verificaram muitas diferenças entre tratamentos, porém o maior teor de sólidos solúveis em frutos armazenados sob 3%O2/3%CO2, e os maiores índices de maturidade nos frutos armazenados sob 3%O2/6%CO2, por 20 dias, sugerem que novos estudos possam ser realizados adotando-se tais concentrações

Linear to Circular Polarisation Conversion using Birefringent Properties of Aligned Crystals for Multi-GeV Photons

We present the first experimental results on the use of a thick aligned Si crystal acting as a quarter wave plate to induce a degree of circular polarisation in a high energy linearly polarised photon beam. The linearly polarised photon beam is produced from coherent bremsstrahlung radiation by 178 GeV unpolarised electrons incident on an aligned Si crystal, acting as a radiator. The linear polarisation of the photon beam is characterised by measuring the asymmetry in electron-positron pair production in a Ge crystal, for different crystal orientations. The Ge crystal therefore acts as an analyser. The birefringence phenomenon, which converts the linear polarisation to circular polarisation, is observed by letting the linearly polarised photons beam pass through a thick Si quarter wave plate crystal, and then measuring the asymmetry in electron-positron pair production again for a selection of relative angles between the crystallographic planes of the radiator, analyser and quarter wave plate. The systematics of the difference between the measured asymmetries with and without the quarter wave plate are predicted by theory to reveal an evolution in the Stokes parameters from which the appearance of a circularly polarised component in the photon beam can be demonstrated. The measured magnitude of the circularly polarised component was consistent with the theoretical predictions, and therefore is in indication of the existence of the birefringence effect.Comment: 12 pages, 12 figures, 1 table, REVTeX4 two column, Version for publicatio

Coherent bremsstrahlung, boherent pair production, birefringence and polarimetry in the 20-170 GeV energy range using aligned crystals

The processes of coherent bremsstrahlung (CB) and coherent pair production (CPP) based on aligned crystal targets have been studied in the energy range 20-170 GeV. The experimental arrangement allowed for measurements of single photon properties of these phenomena including their polarization dependences. This is significant as the theoretical description of CB and CPP is an area of active theoretical debate and development. With the theoretical approach used in this paper both the measured cross sections and polarization observables are predicted very well. This indicates a proper understanding of CB and CPP up to energies of 170 GeV. Birefringence in CPP on aligned crystals is applied to determine the polarization parameters in our measurements. New technologies for high energy photon beam optics including phase plates and polarimeters for linear and circular polarization are demonstrated in this experiment. Coherent bremsstrahlung for the strings-on-strings (SOS) orientation yields a larger enhancement for hard photons than CB for the channeling orientations of the crystal. Our measurements and our calculations indicate low photon polarizations for the high energy SOS photons.Comment: 23 pages, 27 figures, 2 tables, REVTeX4 two column

Coherent Pair Production by Photons in the 20-170 GeV Energy Range Incident on Crystals and Birefringence

The cross section for coherent pair production by linearly polarised photons in the 20-170 GeV energy range was measured for photon aligned incidence on ultra-high quality diamond and germanium crystals. The theoretical description of coherent bremsstrahlung and coherent pair production phenomena is an area of active theoretical debate and development. However, under our experimental conditions, the theory predicted the combined cross section and polarisation experimental observables very well indeed. In macroscopic terms, our experiment measured a birefringence effect in pair production in a crystal. This study of this effect also constituted a measurement of the energy dependent linear polarisation of photons produced by coherent bremsstrahlung in aligned crystals. New technologies for manipulating high energy photon beams can be realised based on an improved understanding of QED phenomena at these energies. In particular, this experiment demonstrates an efficient new polarimetry technique. The pair production measurements were done using two independent methods simultaneously. The more complex method using a magnet spectrometer showed that the simpler method using a multiplicity detector was also viable.Comment: 10 pages, 13 figures, 1 table, REVTeX4 two column, Version for publicatio