58,121 research outputs found
Some Boas-Bellman Type Inequalities in 2-Inner Product Spaces
Some inequalities in 2-inner product spaces generalizing Bessel's result that
are similar to the Boas-Bellman inequality from inner product spaces, are
given. Applications for determinantal integral inequalities are also provided
Refinements of Some Reverses of Schwarz's Inequality in 2-Inner Product Spaces and Applications for Integrals
Refinements of some recent reverse inequalities for the celebrated
Cauchy-Bunyakovsky-Schwarz inequality in 2-inner product spaces are given.
Using this framework, applications for determinantal integral inequalities are
also provided
Norm Estimates for the Difference Between Bochner's Integral and the Convex Combination of Function's Values
Norm estimates are developed between the Bochner integral of a vector-valued
function in Banach spaces having the Radon-Nikodym property and the convex
combination of function values taken on a division of the interval [a,b]
Percolation Transitions in Scale-Free Networks under Achlioptas Process
It has been recently shown that the percolation transition is discontinuous
in Erd\H{o}s-R\'enyi networks and square lattices in two dimensions under the
Achlioptas Process (AP). Here, we show that when the structure is highly
heterogeneous as in scale-free networks, a discontinuous transition does not
always occur: a continuous transition is also possible depending on the degree
distribution of the scale-free network. This originates from the competition
between the AP that discourages the formation of a giant component and the
existence of hubs that encourages it. We also estimate the value of the
characteristic degree exponent that separates the two transition types.Comment: 4 pages, 6 figure
Generation of graph-state streams
We propose a protocol to generate a stream of mobile qubits in a graph state
through a single stationary parent qubit and discuss two types of its physical
implementation, namely, the generation of photonic graph states through an
atom-like qubit and those of flying atoms through a cavity-mode photonic qubit.
The generated graph states fall into an important class that can hugely reduce
the resource requirement of fault-tolerant linear optics quantum computation,
which was previously known to be far from realistic. In regard to the flying
atoms, we also propose a heralded generation scheme, which allows for
high-fidelity graph states even under the photon loss.Comment: Accepted for publication at PRA Rapid Communication
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