A qutrit Quantum Key Distribution protocol with better noise resistance

The Ekert quantum key distribution protocol uses pairs of entangled qubits and performs checks based on a Bell inequality to detect eavesdropping. The 3DEB protocol uses instead pairs of entangled qutrits to achieve better noise resistance than the Ekert protocol. It performs checks based on a Bell inequality for qutrits named CHSH-3. In this paper, we present a new protocol, which also uses pairs of entangled qutrits, but achieves even better noise resistance than 3DEB. This gain of performance is obtained by using another inequality called here hCHSH-3. As the hCHSH3 inequality involve products of observables which become incompatible when using quantum states, we show how the parties running the protocol can measure the violation of hCHSH3 in the presence of noise, to ensure the secrecy of the key.Comment: 11 page

Wavelet analysis of the multivariate fractional Brownian motion

The work developed in the paper concerns the multivariate fractional Brownian motion (mfBm) viewed through the lens of the wavelet transform. After recalling some basic properties on the mfBm, we calculate the correlation structure of its wavelet transform. We particularly study the asymptotic behavior of the correlation, showing that if the analyzing wavelet has a sufficient number of null first order moments, the decomposition eliminates any possible long-range (inter)dependence. The cross-spectral density is also considered in a second part. Its existence is proved and its evaluation is performed using a von Bahr-Essen like representation of the function \sign(t) |t|^\alpha. The behavior of the cross-spectral density of the wavelet field at the zero frequency is also developed and confirms the results provided by the asymptotic analysis of the correlation

Projections of determinantal point processes

Let $\mathbf x=\{x^{(1)},\dots,x^{(n)}\}$ be a space filling-design of $n$ points defined in $[0{,}1]^d$. In computer experiments, an important property seeked for $\mathbf x$ is a nice coverage of $[0{,}1]^d$. This property could be desirable as well as for any projection of $\mathbf x$ onto $[0{,}1]^\iota$ for $\iota<d$ . Thus we expect that $\mathbf x_I=\{x_I^{(1)},\dots,x_I^{(n)}\}$, which represents the design $\mathbf x$ with coordinates associated to any index set $I\subseteq\{1,\dots,d\}$, remains regular in $[0{,}1]^\iota$ where $\iota$ is the cardinality of $I$. This paper examines the conservation of nice coverage by projection using spatial point processes, and more specifically using the class of determinantal point processes. We provide necessary conditions on the kernel defining these processes, ensuring that the projected point process $\mathbf{X}_I$ is repulsive, in the sense that its pair correlation function is uniformly bounded by 1, for all $I\subseteq\{1,\dots,d\}$. We present a few examples, compare them using a new normalized version of Ripley's function. Finally, we illustrate the interest of this research for Monte-Carlo integration

Identification of the Multivariate Fractional Brownian Motion

This paper deals with the identification of the multivariate fractional Brownian motion, a recently developed extension of the fractional Brownian motion to the multivariate case. This process is a $p$-multivariate self-similar Gaussian process parameterized by $p$ different Hurst exponents $H_i$, $p$ scaling coefficients $\sigma_i$ (of each component) and also by $p(p-1)$ coefficients $\rho_{ij},\eta_{ij}$ (for $i,j=1,...,p$ with $j>i$) allowing two components to be more or less strongly correlated and allowing the process to be time reversible or not. We investigate the use of discrete filtering techniques to estimate jointly or separately the different parameters and prove the efficiency of the methodology with a simulation study and the derivation of asymptotic results

Projections of determinantal point processes

In computer experiments setting, space-filling designs are used to produce inputs, viewed as point patterns. A first important property of the design is that the point pattern covers regularly the input space. A second property is the conservation of this regular covering if the point pattern is projected onto a lower dimensional space. According to the first requirement, it seems then natural to consider classes of spatial point process which generate repulsive patterns. The class of determinantal point processes (DPPs) is considered in this paper. In particular, we address the question: Can we construct a DPP such that any projection on a lower-dimensional space remains a DPP, or at least remains repulsive? By assuming a particular form for the kernel defining the DPP, we prove rigorously that the answer is positive. We propose several examples of models, and in particular stationary models, achieving this property. These models defined on a compact set of $\mathbb{R}^d$ are shown to be efficient for Monte-Carlo integration problems; we show that the same initial spatial design, defined in $\mathbb{R}^d$, can be used to efficiently estimate integrals of $\mathbb{R}^\omega$-valued for any $\omega=1,\dots,d$

Fusion of Distance Measurements between Agents with Unknown Correlations

Cooperative localization is a promising solution to improve the accuracy and overcome the shortcomings of GNSS. Cooperation is often achieved by measuring the distance between users. To optimally integrate a distance measurement between two users into a navigation filter, the correlation between the errors of their estimates must be known. Unfortunately, in large scale networks the agents cannot compute these correlations and must use consistent filters. A consistent filter provides an upper bound on the covariance of the error of the estimator taking into account all the possible correlations. In this paper, a consistent linear filter for integrating a distance measurement is derived using Split Covariance Intersection. Its analysis shows that a distance measurement between two agents can only benefit one of them, i.e., only one of the two can use the distance measurement to improve its estimator. Furthermore, in some cases, none can. A necessary condition for an agent to benefit from the measurement is given for a general class of objective functions. When the objective function is the trace or the determinant, necessary and sufficient conditions are given

Mardis de Tempo : ouvrir les médiathèques le dimanche (Les)

Tempo territorial est une association à but non lucratif crée en 2004. Il s\u27agit du premier réseau national des acteurs des démarches temporelles, réunit des collectivités, des organisations scientifiques, des associations, des consultants et des entreprises, des individus soucieux de faciliter la conciliation des temps personnels et professionnels. Tempo Territorial, a pour objet de favoriser l’échange, le partage, l’apprentissage, la mutualisation, la coopération, entre acteurs des démarches temporelles. Ce document rend compte des travaux menés par l\u27association, et propose un examen des conditions favorables à l’ouverture de certaines bibliothèques le dimanche