Weak approximate unitary designs and applications to quantum encryption

Unitary t-designs are the bread and butter of quantum information theory and beyond. An important issue in practice is that of efficiently constructing good approximations of such unitary t-designs. Building on results by Aubrun (Comm. Math. Phys. 2009), we prove that sampling dtpoly(t,logd,1/ϵ) unitaries from an exact t-design provides with positive probability an ϵ-approximate t-design, if the error is measured in one-to-one norm distance of the corresponding t-twirling channels. As an application, we give a partially derandomized construction of a quantum encryption scheme that has roughly the same key size and security as the quantum one-time pad, but possesses the additional property of being non-malleable against adversaries without quantum side information

Tsetse and human trypanosomiasis challenge in south eastern Uganda

Pièges pyramidaux (8000) ont été mis en place contre #Glossina fuscipes fuscipes afin de lutter contre la maladie du sommeil à #Trypanosoma rhodésiense dans le Busoga. Dans le but de comprendre les modalités du contact homme/mouche, la récolte des données sur la densité, la distribution spatiale et la mobilité des mouches, ont été mis en relation avec la dynamique de la transmission de la trypanosomiase humaine dans le Bugosa. Comme pour #T. gambiense$, peu de corrélations entre la densité globale de mouche et l'incidence de la maladie ont été trouvées. Cependant, des observations de terrain avec un enregistrement daté des mouvements saisonniers des hommes et des animaux dans des habitats favorables aux mouches demeure la clé de la compréhension de la transmission de la maladie. (Résumé d'auteur

ON THE COARSE GEOMETRY OF JAMES SPACES

International audienceIn this note we prove that the Kalton interlaced graphs do not equi-coarsely embed into the James space J nor into its dual J *. It is a particular case of a more general result on the non equi-coarse embeddability of the Kalton graphs into quasi-reflexive spaces with a special asymptotic stucture. This allows us to exhibit a coarse invariant for Banach spaces, namely the non equi-coarse embeddability of this family of graphs, which is very close to but different from the celebrated property Q of Kalton. We conclude with a remark on the coarse geometry of the James tree space J T and of its predual

Weighted maximal regularity estimates and solvability of non-smooth elliptic systems II

We continue the development, by reduction to a first order system for the conormal gradient, of $L^2$ \textit{a priori} estimates and solvability for boundary value problems of Dirichlet, regularity, Neumann type for divergence form second order, complex, elliptic systems. We work here on the unit ball and more generally its bi-Lipschitz images, assuming a Carleson condition as introduced by Dahlberg which measures the discrepancy of the coefficients to their boundary trace near the boundary. We sharpen our estimates by proving a general result concerning \textit{a priori} almost everywhere non-tangential convergence at the boundary. Also, compactness of the boundary yields more solvability results using Fredholm theory. Comparison between classes of solutions and uniqueness issues are discussed. As a consequence, we are able to solve a long standing regularity problem for real equations, which may not be true on the upper half-space, justifying \textit{a posteriori} a separate work on bounded domains.Comment: 76 pages, new abstract and few typos corrected. The second author has changed nam

Quantum Correlations in Multipartite Quantum Systems

We review some concepts and properties of quantum correlations, in particular multipartite measures, geometric measures and monogamy relations. We also discuss the relation between classical and total correlationsComment: to be published as a chapter of the book "Lectures on general quantum correlations and their applications" edited by F. Fanchini, D. Soares-Pinto, and G. Adesso (Springer, 2017

Should entanglement measures be monogamous or faithful?

“Is entanglement monogamous?” asks the title of a popular article [B. Terhal, IBM J. Res. Dev. 48, 71 (2004)], celebrating C. H. Bennett’s legacy on quantum information theory. While the answer is affirmative in the qualitative sense, the situation is less clear if monogamy is intended as a quantitative limitation on the distribution of bipartite entanglement in a multipartite system, given some particular measure of entanglement. Here, we formalize what it takes for a bipartite measure of entanglement to obey a general quantitative monogamy relation on all quantum states. We then prove that an important class of entanglement measures fail to be monogamous in this general sense of the term, with monogamy violations becoming generic with increasing dimension. In particular, we show that every additive and suitably normalized entanglement measure cannot satisfy any nontrivial general monogamy relation while at the same time faithfully capturing the geometric entanglement structure of the fully antisymmetric state in arbitrary dimension. Nevertheless, monogamy of such entanglement measures can be recovered if one allows for dimension-dependent relations, as we show explicitly with relevant examples

Shift invariant preduals of ℓ₁(ℤ)

The Banach space ℓ<sub>1</sub>(ℤ) admits many non-isomorphic preduals, for example, C(K) for any compact countable space K, along with many more exotic Banach spaces. In this paper, we impose an extra condition: the predual must make the bilateral shift on ℓ<sub>1</sub>(ℤ) weak<sup>*</sup>-continuous. This is equivalent to making the natural convolution multiplication on ℓ<sub>1</sub>(ℤ) separately weak*-continuous and so turning ℓ<sub>1</sub>(ℤ) into a dual Banach algebra. We call such preduals <i>shift-invariant</i>. It is known that the only shift-invariant predual arising from the standard duality between C<sub>0</sub>(K) (for countable locally compact K) and ℓ<sub>1</sub>(ℤ) is c<sub>0</sub>(ℤ). We provide an explicit construction of an uncountable family of distinct preduals which do make the bilateral shift weak<sup>*</sup>-continuous. Using Szlenk index arguments, we show that merely as Banach spaces, these are all isomorphic to c<sub>0</sub>. We then build some theory to study such preduals, showing that they arise from certain semigroup compactifications of ℤ. This allows us to produce a large number of other examples, including non-isometric preduals, and preduals which are not Banach space isomorphic to c<sub>0</sub>

Improving the Cost-Effectiveness of Artificial Visual Baits for Controlling the Tsetse Fly Glossina fuscipes fuscipes

Tsetse flies, which transmit sleeping sickness to humans and nagana to cattle, are commonly controlled by stationary artificial baits consisting of traps or insecticide-treated screens known as targets. In Kenya the use of electrocuting sampling devices showed that the numbers of Glossina fuscipes fuscipes (Newstead) visiting a biconical trap were nearly double those visiting a black target of 100 cm×100 cm. However, only 40% of the males and 21% of the females entered the trap, whereas 71% and 34%, respectively, alighted on the target. The greater number visiting the trap appeared to be due to its being largely blue, rather than being three-dimensional or raised above the ground. Through a series of variations of target design we show that a blue-and-black panel of cloth (0.06 m2) flanked by a panel (0.06 m2) of fine black netting, placed at ground level, would be about ten times more cost-effective than traps or large targets in control campaigns. This finding has important implications for controlling all subspecies of G. fuscipes, which are currently responsible for more than 90% of sleeping sickness cases

Genetic Diversity and Population Structure of the Secondary Symbiont of Tsetse Flies, Sodalis glossinidius, in Sleeping Sickness Foci in Cameroon

Human African trypanosomiasis remains a threat to the poorest people in Africa. The trypanosomes causing the disease are transmitted by tsetse flies. The drugs currently used are unsatisfactory: some are toxic and all are difficult to administer. Furthermore, drug resistance is increasing. Therefore, investigations for novel disease control strategies are urgently needed. Previous analyses showed the association between the presence of Glossina symbiont, Sodalis glossinidius, and the fly infection by trypanosomes in a south-western region in Cameroon: flies harbouring symbionts had a threefold higher probability of being infected by trypanosomes than flies devoid of symbionts. But the study also showed substantial differences in S. glossinidius and trypanosome infection rates between Glossina populations from two Cameroonian foci of sleeping sickness. We hypothesized that the geographical isolation of the two foci may have induced the independent evolution of each one, leading to the diversification of symbiont genotypes. Microsatellite markers were used and showed that genetic diversity structuring of S. glossinidius varies at different geographical scales with a low but significant differentiation between the Campo and Bipindi HAT foci. This encourages further work on interactions between S. glossinidius subpopulations and Glossina species that could favor tsetse fly infections by a given trypanosome species

Mild reductions in cytosolic NADP-dependent isocitrate dehydrogenase activity result in lower amino acid contents and pigmentation without impacting growth

Transgenic tomato (Solanum lycopersicum) plants were generated targeting the cytosolic NADP-dependent isocitrate dehydrogenase gene (SlICDH1) via the RNA interference approach. The resultant transformants displayed a relatively mild reduction in the expression and activity of the target enzyme in the leaves. However, biochemical analyses revealed that the transgenic lines displayed a considerable shift in metabolism, being characterized by decreases in the levels of the TCA cycle intermediates, total amino acids, photosynthetic pigments, starch and NAD(P)H. The plants showed little change in photosynthesis with the exception of a minor decrease in maximum photosynthetic efficiency (Fv/Fm), and a small decrease in growth compared to the wild type. These results reveal that even small changes in cytosolic NADP-dependent isocitrate dehydrogenase activity lead to noticeable alterations in the activities of enzymes involved in primary nitrate assimilation and in the synthesis of 2-oxoglutarate derived amino acids. These data are discussed within the context of current models for the role of the various isoforms of isocitrate dehydrogenase within plant amino acid metabolism