Additivity and non-additivity of multipartite entanglement measures

We study the additivity property of three multipartite entanglement measures, i.e. the geometric measure of entanglement (GM), the relative entropy of entanglement and the logarithmic global robustness. First, we show the additivity of GM of multipartite states with real and non-negative entries in the computational basis. Many states of experimental and theoretical interests have this property, e.g. Bell diagonal states, maximally correlated generalized Bell diagonal states, generalized Dicke states, the Smolin state, and the generalization of D\"{u}r's multipartite bound entangled states. We also prove the additivity of other two measures for some of these examples. Second, we show the non-additivity of GM of all antisymmetric states of three or more parties, and provide a unified explanation of the non-additivity of the three measures of the antisymmetric projector states. In particular, we derive analytical formulae of the three measures of one copy and two copies of the antisymmetric projector states respectively. Third, we show, with a statistical approach, that almost all multipartite pure states with sufficiently large number of parties are nearly maximally entangled with respect to GM and relative entropy of entanglement. However, their GM is not strong additive; what's more surprising, for generic pure states with real entries in the computational basis, GM of one copy and two copies, respectively, are almost equal. Hence, more states may be suitable for universal quantum computation, if measurements can be performed on two copies of the resource states. We also show that almost all multipartite pure states cannot be produced reversibly with the combination multipartite GHZ states under asymptotic LOCC, unless relative entropy of entanglement is non-additive for generic multipartite pure states.Comment: 45 pages, 4 figures. Proposition 23 and Theorem 24 are revised by correcting a minor error from Eq. (A.2), (A.3) and (A.4) in the published version. The abstract, introduction, and summary are also revised. All other conclusions are unchange

Minimum Degree up to Local Complementation: Bounds, Parameterized Complexity, and Exact Algorithms

The local minimum degree of a graph is the minimum degree that can be reached by means of local complementation. For any n, there exist graphs of order n which have a local minimum degree at least 0.189n, or at least 0.110n when restricted to bipartite graphs. Regarding the upper bound, we show that for any graph of order n, its local minimum degree is at most 3n/8+o(n) and n/4+o(n) for bipartite graphs, improving the known n/2 upper bound. We also prove that the local minimum degree is smaller than half of the vertex cover number (up to a logarithmic term). The local minimum degree problem is NP-Complete and hard to approximate. We show that this problem, even when restricted to bipartite graphs, is in W[2] and FPT-equivalent to the EvenSet problem, which W[1]-hardness is a long standing open question. Finally, we show that the local minimum degree is computed by a O*(1.938^n)-algorithm, and a O*(1.466^n)-algorithm for the bipartite graphs

The maximally entangled symmetric state in terms of the geometric measure

The geometric measure of entanglement is investigated for permutation symmetric pure states of multipartite qubit systems, in particular the question of maximum entanglement. This is done with the help of the Majorana representation, which maps an n qubit symmetric state to n points on the unit sphere. It is shown how symmetries of the point distribution can be exploited to simplify the calculation of entanglement and also help find the maximally entangled symmetric state. Using a combination of analytical and numerical results, the most entangled symmetric states for up to 12 qubits are explored and discussed. The optimization problem on the sphere presented here is then compared with two classical optimization problems on the S^2 sphere, namely Toth's problem and Thomson's problem, and it is observed that, in general, they are different problems.Comment: 18 pages, 15 figures, small corrections and additions to contents and reference

The Association Between Social Networks and Self-rated risk of HIV Infection among Secondary School Students in Moshi Municipality, Tanzania.

Abstract This study describes the social networks of secondary school students in Moshi Municipality, and their association with self-rated risk of human immunodeficiency virus (HIV) infection. A cross-sectional analytical study was conducted among 300 students aged 15-24 years in 5 secondary schools in Moshi, Tanzania. Bonding networks were defined as social groupings of students participating in activities within the school, while bridging networks were groups that included students participating in social groupings from outside of the school environs. A structured questionnaire was used to ask about participation in bonding and bridging social networks and self-rated HIV risk behavior. More participants participated in bonding networks (72%) than in bridging networks (29%). Participation in bridging networks was greater among females (25%) than males (12%, p < .005). Of 300 participants, 88 (29%) were sexually experienced, and of these 62 (70%) considered themselves to be at low risk of HIV infection. Factors associated with self-rated risk of HIV included: type of school (p < .003), family structure (p < .008), being sexually experienced (p < .004), having had sex in the past three months (p < .009), having an extra sexual partner (p < .054) and non-condom use in last sexual intercourse (p < .001), but not the presence or type of social capital. The study found no association between bonding and bridging social networks on self-rated risk of HIV among study participants. However, sexually experienced participants rated themselves at low risk of HIV infection despite practicing unsafe sex. Efforts to raise adolescents' self-awareness of risk of HIV infection through life skills education and HIV/acquired immunodeficiency syndrome risk reduction strategies may be beneficial to students in this at-risk group

Work-Unit Absenteeism: Effects of Satisfaction, Commitment, Labor Market Conditions, and Time

Prior research is limited in explaining absenteeism at the unit level and over time. We developed and tested a model of unit-level absenteeism using five waves of data collected over six years from 115 work units in a large state agency. Unit-level job satisfaction, organizational commitment, and local unemployment were modeled as time-varying predictors of absenteeism. Shared satisfaction and commitment interacted in predicting absenteeism but were not related to the rate of change in absenteeism over time. Unit-level satisfaction and commitment were more strongly related to absenteeism when units were located in areas with plentiful job alternatives

3D virtual worlds as environments for literacy learning

Background: Although much has been written about the ways in which new technology might transform educational practice, particularly in the area of literacy learning, there is relatively little empirical work that explores the possibilities and problems - or even what such a transformation might look like in the classroom. 3D virtual worlds offer a range of opportunities for children to use digital literacies in school, and suggest one way in which we might explore changing literacy practices in a playful, yet meaningful context. Purpose: This paper identifies some of the key issues that emerged in designing and implementing virtual world work in a small number of primary schools in the UK. It examines the tensions between different discourses about literacy and literacy learning and shows how these were played out by teachers and pupils in classroom settings.Sources of evidence: Case study data are used as a basis for exploring and illustrating key aspects of design and implementation. The case study material includes views from a number of perspectives including classroom observations, chatlogs, in-world avatar interviews with teachers and also pupils, as well as the author’s field notes of the planning process with accompanying minutes and meeting documents.Main argument: From a Foucauldian perspective, the article suggests that social control of pedagogical practice through the regulation of curriculum time, the normalisation of teaching routines and the regimes of individual assessment restricts teachers’ and pupils’ conceptions of what constitutes literacy. The counternarrative, found in recent work in new litearcies (Lankshear & Knobel, 2006) provides an attractive alternative, but a movement in this direction requires a fundamental shift of emphasis and a re-conceptualisation of what counts as learning.Conclusions: This work on 3D virtual worlds questions the notion of how transformative practice can be achieved with the use of new technologies. It suggests that changes in teacher preparation, continuing professional development as well as wider educational reform may be needed

Measurement Based Quantum Computation on Fractal Lattices

In this article we extend on work which establishes an analology between one-way quantum computation and thermodynamics to see how the former can be performed on fractal lattices. We find fractals lattices of arbitrary dimension greater than one which do all act as good resources for one-way quantum computation, and sets of fractal lattices with dimension greater than one all of which do not. The difference is put down to other topological factors such as ramification and connectivity. This work adds confidence to the analogy and highlights new features to what we require for universal resources for one-way quantum computation

Demonstration of entanglement-by-measurement of solid state qubits

Projective measurements are a powerful tool for manipulating quantum states. In particular, a set of qubits can be entangled by measurement of a joint property such as qubit parity. These joint measurements do not require a direct interaction between qubits and therefore provide a unique resource for quantum information processing with well-isolated qubits. Numerous schemes for entanglement-by-measurement of solid-state qubits have been proposed, but the demanding experimental requirements have so far hindered implementations. Here we realize a two-qubit parity measurement on nuclear spins in diamond by exploiting the electron spin of a nitrogen-vacancy center as readout ancilla. The measurement enables us to project the initially uncorrelated nuclear spins into maximally entangled states. By combining this entanglement with high-fidelity single-shot readout we demonstrate the first violation of Bells inequality with solid-state spins. These results open the door to a new class of experiments in which projective measurements are used to create, protect and manipulate entanglement between solid-state qubits.Comment: 6 pages, 4 figure

T helper cell subsets specific for pseudomonas aeruginosa in healthy individuals and patients with cystic fibrosis

Background: We set out to determine the magnitude of antigen-specific memory T helper cell responses to Pseudomonas aeruginosa in healthy humans and patients with cystic fibrosis. Methods: Peripheral blood human memory CD4+ T cells were co-cultured with dendritic cells that had been infected with different strains of Pseudomonas aeruginosa. The T helper response was determined by measuring proliferation, immunoassay of cytokine output, and immunostaining of intracellular cytokines. Results: Healthy individuals and patients with cystic fibrosis had robust antigen-specific memory CD4+ T cell responses to Pseudomonas aeruginosa that not only contained a Th1 and Th17 component but also Th22 cells. In contrast to previous descriptions of human Th22 cells, these Pseudomonal-specific Th22 cells lacked the skin homing markers CCR4 or CCR10, although were CCR6+. Healthy individuals and patients with cystic fibrosis had similar levels of Th22 cells, but the patient group had significantly fewer Th17 cells in peripheral blood. Conclusions: Th22 cells specific to Pseudomonas aeruginosa are induced in both healthy individuals and patients with cystic fibrosis. Along with Th17 cells, they may play an important role in the pulmonary response to this microbe in patients with cystic fibrosis and other conditions