Structure de la distribution de probabilités de l'état GHZ sous l'action locale de transformations du groupe U(2)

Dans ce mémoire, je démontre que la distribution de probabilités de l'état quantique Greenberger-Horne-Zeilinger (GHZ) sous l'action locale de mesures de von Neumann indépendantes sur chaque qubit suit une distribution qui est une combinaison convexe de deux distributions. Les coefficients de la combinaison sont reliés aux parties équatoriales des mesures et les distributions associées à ces coefficients sont reliées aux parties réelles des mesures. Une application possible du résultat est qu'il permet de scinder en deux la simulation de l'état GHZ. Simuler, en pire cas ou en moyenne, un état quantique comme GHZ avec des ressources aléatoires, partagées ou privées, et des ressources classiques de communication, ou même des ressources fantaisistes comme les boîtes non locales, est un problème important en complexité de la communication quantique. On peut penser à ce problème de simulation comme un problème où plusieurs personnes obtiennent chacune une mesure de von Neumann à appliquer sur le sous-système de l'état GHZ qu'il partage avec les autres personnes. Chaque personne ne connaît que les données décrivant sa mesure et d'aucune façon une personne ne connaît les données décrivant la mesure d'une autre personne. Chaque personne obtient un résultat aléatoire classique. La distribution conjointe de ces résultats aléatoires classiques suit la distribution de probabilités trouvée dans ce mémoire. Le but est de simuler classiquement la distribution de probabilités de l'état GHZ. Mon résultat indique une marche à suivre qui consiste d'abord à simuler les parties équatoriales des mesures pour pouvoir ensuite savoir laquelle des distributions associées aux parties réelles des mesures il faut simuler. D'autres chercheurs ont trouvé comment simuler les parties équatoriales des mesures de von Neumann avec de la communication classique dans le cas de 3 personnes, mais la simulation des parties réelles résiste encore et toujours.

Quantum nonlocality, cryptography and complexity

Thèse numérisée par la Division de la gestion de documents et des archives de l'Université de Montréal

Interplay Of Weak Interactions In The Atom-by-atom Condensation Of Xenon Within Quantum Boxes.

Condensation processes are of key importance in nature and play a fundamental role in chemistry and physics. Owing to size effects at the nanoscale, it is conceptually desired to experimentally probe the dependence of condensate structure on the number of constituents one by one. Here we present an approach to study a condensation process atom-by-atom with the scanning tunnelling microscope, which provides a direct real-space access with atomic precision to the aggregates formed in atomically defined 'quantum boxes'. Our analysis reveals the subtle interplay of competing directional and nondirectional interactions in the emergence of structure and provides unprecedented input for the structural comparison with quantum mechanical models. This approach focuses on-but is not limited to-the model case of xenon condensation and goes significantly beyond the well-established statistical size analysis of clusters in atomic or molecular beams by mass spectrometry.

GLOBAL SOLUTIONS FOR ABSTRACT FUNCTIONAL DIFFERENTIAL EQUATIONS WITH NONLOCAL CONDITIONS

In this paper we study the existence of global solutions for a class of abstract functional differential equation with nonlocal conditions. An application is considered.

Nonlocal magnetorotational instability

An analytical theory of the nonlocal magnetorotational instability (MRI) is developed for the simplest astrophysical plasma model. It is assumed that the rotation frequency profile has a steplike character, so that there are two regions in which it has constant different values, separated by a narrow transition layer. The surface wave approach is employed to investigate the MRI in this configuration. It is shown that the main regularities of the nonlocal MRI are similar to those of the local instability and that driving the nonaxisymmetric MRI is less effective than the axisymmetric one, also for the case of the nonlocal instability. The existence of nonlocal instabilities in nonmagnetized plasma is predicted. (c) 2008 American Institute of Physics.

DAVID HOMEOMORPHISMS VIA CARLESON BOXES

We construct a family of examples of increasing homeomorphisms of the real line whose local quasi-symmetric distortion blows up almost everywhere, which nevertheless can be realized as the boundary values of David homeomorphisms of the upper half-plane. The construction of such David extensions uses Carleson boxes.

Existence Results for Second Order Differential Equations with Nonlocal Conditions in Banach Spaces

This work is concerned with implicit second order abstract differential equations with nonlocal conditions. Assuming that the involved operators satisfy sonic compactness properties, we establish the existence of local mild solutions, the existence of global mild solutions and the existence of asymptotically almost periodic solutions.

Existence of solutions for a class of abstract differential equations with nonlocal conditions

We discuss the existence of mild, classical and strict solutions for a class of abstract differential equations with nonlocal conditions. Our technical approach allows the study of partial differential equations with nonlocal conditions involving partial derivatives or nonlinear expressions of the solution. Some concrete applications to partial differential equations are considered. (C) 2010 Elsevier Ltd. All rights reserved.

Tilted boxes on inclined planes

We propose the study of a box placed on an inclined plane, with an initial tilt with respect to the plane. This is a paradigmatic example of the role played by friction as a link between translational and rotational motion. This example has two advantages over the usual example of a sphere (or cylinder) rolling down an inclined plane. First, it provides a good model for a much greater variety of "real-life" situations. Second, it exhibits a much richer structure in parameter space, even when the box starts from rest. (C) 2000 American Association of Physics Teachers.

Controllability results for impulsive mixed type functional integro-differential evolution equations with nonlocal conditions

In this paper, we establish the controllability for a class of abstract impulsive mixed-type functional integro-differential equations with finite delay in a Banach space. Some sufficient conditions for controllability are obtained by using the Mönch fixed point theorem via measures of noncompactness and semigroup theory. Particularly, we do not assume the compactness of the evolution system. An example is given to illustrate the effectiveness of our results.

Sensitivity of Gomez-Nuñez boxes for the detection of household infestation with Panstrongylus megistus

Four methods for detecting household infestations with Panstrongylus megistus were compared: 1) manual collection; 2) collection after pyrethrum application; 3) search viable eggs; and 4) Gomez-Nuñez boxes. Manual collection was the most sensitive method (23% infested), followed by pyrethrum (21%), Gomez-Nuñez boxes (15%) and viable eggs (12%). About 10% of infested houses were positive exclusively on the Gomez-Nuñez box test. More over, 6 out of the 7 houses positive exclusively on the Gomez-Nuñez method were located in a recently sprayed area, where P. megistus density was low. Inspection of Gomez-Nuñez boxes at 12 weekspost-application was twice as effective as inspection at 6 weekspost-application. Triatomine feces was the most common evidencefor thepresence of P. megistus found within Gomez-Nuñez boxes. Gomez-Nuñez boxes area a useful adjunct to manual collection in detecting domestic infestations with P. megistus, especially in areas where bug densities are low. However, the utility of Gomez-Nuhez boxes must be weighed against the time and labor they require.

CLOCK-controlled polyphonic regulation of circadian rhythms through canonical and noncanonical E-boxes.

In mammalian circadian clockwork, the CLOCK-BMAL1 complex binds to DNA enhancers of target genes and drives circadian oscillation of transcription. Here we identified 7,978 CLOCK-binding sites in mouse liver by chromatin immunoprecipitation-sequencing (ChIP-Seq), and a newly developed bioinformatics method, motif centrality analysis of ChIP-Seq (MOCCS), revealed a genome-wide distribution of previously unappreciated noncanonical E-boxes targeted by CLOCK. In vitro promoter assays showed that CACGNG, CACGTT, and CATG(T/C)G are functional CLOCK-binding motifs. Furthermore, we extensively revealed rhythmically expressed genes by poly(A)-tailed RNA-Seq and identified 1,629 CLOCK target genes within 11,926 genes expressed in the liver. Our analysis also revealed rhythmically expressed genes that have no apparent CLOCK-binding site, indicating the importance of indirect transcriptional and posttranscriptional regulations. Indirect transcriptional regulation is represented by rhythmic expression of CLOCK-regulated transcription factors, such as Krüppel-like factors (KLFs). Indirect posttranscriptional regulation involves rhythmic microRNAs that were identified by small-RNA-Seq. Collectively, CLOCK-dependent direct transactivation through multiple E-boxes and indirect regulations polyphonically orchestrate dynamic circadian outputs.

Cis-acting elements, CArG-, E-, CCAAT- and TATA-boxes may be involved in sexually regulated gene transcription in Schistosoma mansoni

Schistosomes undergo various morphological and metabolic changes during their development, reflected in a finely tuned regulation of protein and/or gene expression. The mechanisms involved in the control of gene expression during the development of the parasite are not understood. Two actin genes had been previously cloned and observed to be differentially expressed during the maturation of the parasite. The SmAct gene contains four putative cis-regulatory elements (TATA-, CCAAT-, E- and CArG-boxes). Our objective was to investigate in greater detail the expression pattern of two actin genes and verify if the binding of nuclear proteins to the promoter elements of SmAct correlated with the expression profile observed. We detected little variation in the expression of actin genes during the first seven days of schistosomula culture in vitro. However, we observed significantly higher levels of expression in males compared to female adults. CArG and CCAAT elements bound to a greater extent and formed distinct complexes with male in comparison to female nuclear extracts. In contrast, female extracts bound weakly to the E-box probe while no binding was observed with male extracts. Taken together these results describe cis-acting elements that appear to be involved in sexually regulated gene expression in Schistosoma mansoni.

Hamiltonian formalism for nonlocal Lagrangians

A Hamiltonian formalism is set up for nonlocal Lagrangian systems. The method is based on obtaining an equivalent singular first order Lagrangian, which is processed according to the standard Legendre transformation and then, the resulting Hamiltonian formalism is pulled back onto the phase space defined by the corresponding constraints. Finally, the standard results for local Lagrangians of any order are obtained as a particular case.