A posteriori analysis of discontinuous galerkin schemes for systems of hyperbolic conservation laws

In this work we construct reliable a posteriori estimates for some semi- (spatially) discrete discontinuous Galerkin schemes applied to nonlinear systems of hyperbolic conservation laws. We make use of appropriate reconstructions of the discrete solution together with the relative entropy stability framework, which leads to error control in the case of smooth solutions. The methodology we use is quite general and allows for a posteriori control of discontinuous Galerkin schemes with standard flux choices which appear in the approximation of conservation laws. In addition to the analysis, we conduct some numerical benchmarking to test the robustness of the resultant estimator

Robust Quantum Communication Using A Polarization-Entangled Photon Pair

Noise and imperfection of realistic devices are major obstacles for implementing quantum cryptography. In particular birefringence in optical fibers leads to decoherence of qubits encoded in polarization of photon. We show how to overcome this problem by doing single qubit quantum communication without a shared spatial reference frame and precise timing. Quantum information will be encoded in pair of photons using ``tag'' operations which corresponds to the time delay of one of the polarization modes. This method is robust against the phase instability of the interferometers despite the use of time-bins. Moreover synchronized clocks are not required in the ideal situation no photon loss case as they are only necessary to label the different encoded qubits.Comment: 4 pages, 2 figure

Meilleures techniques disponibles de lavage de sols contaminés par les HAP : Etude d'un procédé basé sur les cyclodextrines

http://www.ait.org.tn/gdsdd/International audienceLa pollution des sols par les Hydrocarbures Aromatiques Polycycliques (HAP) a été reconnue comme un problème majeur depuis de nombreuses années. L'impact environnemental de ces molécules hydrophobes, persistantes, aux effets toxiques (mutagènes et cancérigènes) rend nécessaire la décontamination des sites concernés. L'efficacité des techniques de bioremédiation ou d'extraction à l'eau pure est limitée par la faible solubilité aqueuse et donc la faible biodisponibilité des HAP. Les méthodes actuelles de lavage de sols augmentent cette solubilité par l'emploi de surfactants ou de solvants organiques, mais ont pour la plupart un impact écologique et/ou humain non négligeable

Experimental Implementation of Discrete Time Quantum Random Walk on an NMR Quantum Information Processor

We present an experimental implementation of the coined discrete time quantum walk on a square using a three qubit liquid state nuclear magnetic resonance (NMR) quantum information processor (QIP). Contrary to its classical counterpart, we observe complete interference after certain steps and a periodicity in the evolution. Complete state tomography has been performed for each of the eight steps making a full period. The results have extremely high fidelity with the expected states and show clearly the effects of quantum interference in the walk. We also show and discuss the importance of choosing a molecule with a natural Hamiltonian well suited to NMR QIP by implementing the same algorithm on a second molecule. Finally, we show experimentally that decoherence after each step makes the statistics of the quantum walk tend to that of the classical random walk.Comment: revtex4, 8 pages, 6 figures, submitted to PR