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

Symmetric mixed states of nn qubits: local unitary stabilizers and entanglement classes

We classify, up to local unitary equivalence, local unitary stabilizer Lie algebras for symmetric mixed states into six classes. These include the stabilizer types of the Werner states, the GHZ state and its generalizations, and Dicke states. For all but the zero algebra, we classify entanglement types (local unitary equivalence classes) of symmetric mixed states that have those stabilizers. We make use of the identification of symmetric density matrices with polynomials in three variables with real coefficients and apply the representation theory of SO(3) on this space of polynomials.Comment: 10 pages, 1 table, title change and minor clarifications for published versio

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

Entanglement classes of symmetric Werner states

The symmetric Werner states for $n$ qubits, important in the study of quantum nonlocality and useful for applications in quantum information, have a surprisingly simple and elegant structure in terms of tensor products of Pauli matrices. Further, each of these states forms a unique local unitary equivalence class, that is, no two of these states are interconvertible by local unitary operations.Comment: 4 pages, 1 table, additional references in version 2, revised abstract and introduction in version 3, small clarifications for published version in version

Feeding Frequency Affects Cultured Rat Pituitary Cells in Low Gravity

In this report, we describe the results of a rat pituitary cell culture experiment done on STS-65 in which the effect of cell feeding on the release of the six anterior pituitary hormones was studied. We found complex microgravity related interactions between the frequency of cell feeding and the quantity and quality (i.e. biological activity) of some of the six hormones released in flight. Analyses of growth hormone (GH) released from cells into culture media on different mission days using gel filtration and ion exchange chromatography yielded qualitatively similar results between ground and flight samples. Lack of cell feeding resulted in extensive cell clumping in flight (but not ground) cultures. Vigorous fibroblast growth occurred in both ground and flight cultures fed 4 times. These results are interpreted within the context of autocrine and or paracrine feedback interactions. Finally the payload specialist successfully prepared a fresh trypsin solution in microgravity, detached the cells from their surface and reinserted them back into the culture chamber. These cells reattached and continued to release hormone in microgravity. In summary, this experiment shows that pituitary cells are microgravity sensitive and that coupled operations routinely associated with laboratory cel1 culture can also be accomplished in low gravity

Detection of tet(M) gene from raw milk by rapid DNA extraction followed by a two-step PCR with nested primers.

The likelihood that milk and milk products may act as a vehicle for antibiotic-resistant bacterial genes has become a concern to the food industry and a public health issue, and the demand for rapid tests has increased. The purity of DNA extracted from food samples is a key issue in the sensitivity and usefulness of biological analyses, such as PCR for pathogens and nonpathogens. A rapid, phenol-chloroform free method based on a modification of a sodium iodide DNA extraction, followed by a two-step PCR was developed for direct detection of the tet(M) gene in milk samples within a single working day. This study compares the proposed method with a traditional phenol solvent extraction method and with a commercial kit (QIAamp DNA blood mini kit, Qiagen). The three DNA extraction methods were used to ensure access to the tet(M) gene from 1 ml of raw milk, inoculated with a strain of Enterococcus faecalis, which carries the tet(M) gene. The proposed method, followed by a two-step PCR with nested primers specific for the tet(M) gene, was able to reach a detection limit below 10 CFU/ml in less than 4 h, including the two amplification cycles, thus outperforming in sensitivity and rapidity both the traditional and the commercial method

Power supply ramping for quasi-static testing of PLLs

An innovative approach for testing PLLs in open loop-mode is presented. The operational method consists of ramping the PLL's power supply by means of a periodic sawtooth signal. The reference and feedback inputs of the PLL in open-loop mode are connected to the clock reference signal or to ground. Then, the corresponding quiescent current, clock output, and oscillator control voltage signatures are monitored and sampled at specific times. When the power supply is swept, all transistors are forced into various regions of operation causing the sensitivity of the faults to the specific stimulus to be magnified. The developed method of structural testing for PLLs yields high fault coverage results making it a potential and attractive technique for production wafer testing

How do roots respond to osmotic stress? A transcriptomic approach to address this question in a non-model crop

Drought is a complex phenomenon that is relevant for many crops. Performing high-throughput transcriptomics in non-model crops is challenging. The non-model crop where our workflow has been tested on is banana (Musa spp.), which ranks among the top ten staple foods (total production over 145 million tons in 2013 (FAOstat)[1]). Bananas need vast amounts of water and even mild-drought conditions are responsible for considerable yield losses[2]. To characterize drought in the roots of different banana genotypes, we designed a lab model based on osmotic stress (5% PEG treatment for 3 days) and performed mRNA-seq analysis[3]. Using Illumina technology, 18 cDNA libraries were sequenced producing around 568 million high quality reads, of which 70-84% were mapped to the diploid reference genome[4]. We show that the applied stress leads to a drop in energy levels inducing a metabolic shift towards (i) higher oxidative respiration, (ii) alternative respiration and (iii) fermentation. We also analyzed the expression patterns of paralogous genes belonging to the same gene families and detected possible cases of sub-functionalization