3,693 research outputs found
Compressed Sensing Based on Random Symmetric Bernoulli Matrix
The task of compressed sensing is to recover a sparse vector from a small
number of linear and non-adaptive measurements, and the problem of finding a
suitable measurement matrix is very important in this field. While most recent
works focused on random matrices with entries drawn independently from certain
probability distributions, in this paper we show that a partial random
symmetric Bernoulli matrix whose entries are not independent, can be used to
recover signal from observations successfully with high probability. The
experimental results also show that the proposed matrix is a suitable
measurement matrix.Comment: arXiv admin note: text overlap with arXiv:0902.4394 by other author
Continuous-variable controlled-Z gate using an atomic ensemble
The continuous-variable controlled-Z gate is a canonical two-mode gate for
universal continuous-variable quantum computation. It is considered as one of
the most fundamental continuous-variable quantum gates. Here we present a
scheme for realizing continuous-variable controlled-Z gate between two optical
beams using an atomic ensemble. The gate is performed by simply sending the two
beams propagating in two orthogonal directions twice through a spin-squeezed
atomic medium. Its fidelity can run up to one if the input atomic state is
infinitely squeezed. Considering the noise effects due to atomic decoherence
and light losses, we show that the observed fidelities of the scheme are still
quite high within presently available techniques.Comment: 7 pages, 3 figures, to appear in Physical Review
Linear spectral Turan problems for expansions of graphs with given chromatic number
An -uniform hypergraph is linear if every two edges intersect in at most
one vertex. The -expansion of a graph is the -uniform
hypergraph obtained from by enlarging each edge of with a vertex subset
of size disjoint from the vertex set of such that distinct edges are
enlarged by disjoint subsets. Let and
be the maximum number of edges and the maximum
spectral radius of all -free linear -uniform hypergraphs with
vertices, respectively. In this paper, we present the sharp (or asymptotic)
bounds of and by
establishing the connection between the spectral radii of linear hypergraphs
and those of their shadow graphs, where is a -color critical graph
or a graph with chromatic number
- β¦