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We consider two quantum cryptographic schemes relying on encoding the key into qudits, i.e., quantum states in a d-dimensional Hilbert space. The first cryptosystem uses two mutually unbiased bases (thereby extending the BB84 scheme), while the second exploits all d+1 available such bases (extending the six-state protocol for qubits). We derive the(More)
It is shown that the Hilbert geometry (D, h D) associated to a bounded convex domain D ⊂ E n is isometric to a normed vector space (V, || · ||) if and only if D is an open n-simplex. One further result on the asymptotic geometry of Hilbert's metric is obtained with corollaries for the behavior of geodesics. Finally we prove that every geodesic ray in a(More)
Presently surgery is the most effective way to obtain a controlled weight reduction in morbidly obese patients. Roux-en-Y gastric bypass (RYGBP) surgery is effective and used worldwide, but the exact mechanism of action is unknown. The effect of RYGBP on ghrelin, insulin, adiponectin, and leptin levels was investigated in 66 obese subjects; mean weight 127(More)
Petri nets have been widely used to model dynamic systems, namely manufacturing systems. In this paper we introduce the use of Petri nets to model robotic tasks. Diierent views of the robotic task model can be modeled by distinct Petri net types: interpreted Petri nets for task design and execution, generalized stochastic Petri nets for task quantitative(More)
We prove a general noncommutative law of large numbers. This applies in particular to random walks on any locally finite homogeneous graph, as well as to Brownian motion on Riemannian manifolds which admit a compact quotient. It also generalizes Oseledec's mul-tiplicative ergodic theorem. In addition, we show that ε-shadows of any ballistic random walk with(More)
—One of the essential building-blocks of miniature pho-tonic crystal (PC)-based photonic integrated circuits (PICs) is the sharp bend. Our group has focused on the 2-D photonic crystal based on a triangular lattice of holes perforating a standard het-erostructure. The latter, GaAlAs-based or InP-based, is vertically a monomode waveguide. We consider(More)
We obtain precise descriptions of all horoballs for Hilbert's geometry on simplices and for normed finite-dimensional vector spaces with norm given by some polyhedron. Certain geometrical consequences are deduced and several other applications are pointed out, which concern the dynamics of important classes of nonlinear self-maps of convex cones.