Decoherence in the quantum walk on the line

We investigate the quantum walk on the line when decoherences are introduced either through simultaneous measurements of the chirality and particle position, or as a result of broken links. Both mechanisms drive the system to a classical diffusive behavior. In the case of measurements, we show that the diffusion coefficient is proportional to the variance of the initially localized quantum random walker just before the first measurement. When links between neighboring sites are randomly broken with probability $p$ per unit time, the evolution becomes decoherent after a characteristic time that scales as $1/p$. The fact that the quadratic increase of the variance is eventually lost even for very small frequencies of disrupting events, suggests that the implementation of a quantum walk on a real physical system may be severely limited by thermal noise and lattice imperfections.Comment: Elsevier style, 18 pages. New enhanced version with more material: new title, a new section was added and the discussion was updated; references added; submitted to Physica

NEW UPPER BOUND ON THE LARGEST LAPLACIAN EIGENVALUE OF GRAPHS

Let G = (V;E) be a simple, undirected graph with maximum and minimum degree ∆ and respectively, and let A be the adjacency matrix and Q be the Laplacianmatrix of G. In the past decades, the Laplacian spectrum has received much more and more attention, since it has been applied to several elds, such as randomized algorithms, combinatorial optimization problems and machine learning. In this paper, we compute lower and upper bounds for the largest Laplacian eigenvalue which is related with a given maximum and minimum degree and a given number of vertices and edges. We also compare our results in this paper with some known results

Probabilistic analysis of Online Bin Coloring algorithms via Stochastic Comparison

This paper proposes a new method for probabilistic analysis of online algorithms that is based on the notion of stochastic dominance. We develop the method for the Online Bin Coloring problem introduced by Krumke et al. Using methods for the stochastic comparison of Markov chains we establish the strong result that the performance of the online algorithm GreedyFit is stochastically dominated by the performance of the algorithm OneBin for any number of items processed. This result gives a more realistic picture than competitive analysis and explains the behavior observed in simulations.mathematical applications;