8,766 research outputs found
Maximal violation of Clauser-Horne-Shimony-Holt inequality for four-level systems
Clauser-Horne-Shimony-Holt inequality for bipartite systems of 4-dimension is
studied in detail by employing the unbiased eight-port beam splitters
measurements. The uniform formulae for the maximum and minimum values of this
inequality for such measurements are obtained. Based on these formulae, we show
that an optimal non-maximally entangled state is about 6% more resistant to
noise than the maximally entangled one. We also give the optimal state and the
optimal angles which are important for experimental realization.Comment: 7 pages, three table
Sharp modulus of continuity for parabolic equations on manifolds and lower bounds for the first eigenvalue
We derive sharp estimates on modulus of continuity for solutions of the heat
equation on a compact Riemannian manifold with a Ricci curvature bound, in
terms of initial oscillation and elapsed time. As an application, we give an
easy proof of the optimal lower bound on the first eigenvalue of the Laplacian
on such a manifold as a function of diameter
A Privacy-Preserving Finite-Time Push-Sum based Gradient Method for Distributed Optimization over Digraphs
This paper addresses the problem of distributed optimization, where a network
of agents represented as a directed graph (digraph) aims to collaboratively
minimize the sum of their individual cost functions. Existing approaches for
distributed optimization over digraphs, such as Push-Pull, require agents to
exchange explicit state values with their neighbors in order to reach an
optimal solution. However, this can result in the disclosure of sensitive and
private information. To overcome this issue, we propose a
state-decomposition-based privacy-preserving finite-time push-sum (PrFTPS)
algorithm without any global information such as network size or graph
diameter. Then, based on PrFTPS, we design a gradient descent algorithm
(PrFTPS-GD) to solve the distributed optimization problem. It is proved that
under PrFTPS-GD, the privacy of each agent is preserved and the linear
convergence rate related to the optimization iteration number is achieved.
Finally, numerical simulations are provided to illustrate the effectiveness of
the proposed approach
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