Robust quantum repeater with atomic ensembles and single-photon sources

We present a quantum repeater protocol using atomic ensembles, linear optics and single-photon sources. Two local 'polarization' entangled states of atomic ensembles $u$ and $d$ are generated by absorbing a single photon emitted by an on-demand single-photon sources, based on which high-fidelity local entanglement between four ensembles can be established efficiently through Bell-state measurement. Entanglement in basic links and entanglement connection between links are carried out by the use of two-photon interference. In addition to being robust against phase fluctuations in the quantum channels, this scheme may speed up quantum communication with higher fidelity by about 2 orders of magnitude for 1280 km compared with the partial read (PR) protocol (Sangouard {\it et al.}, Phys. Rev. A {\bf77}, 062301 (2008)) which may generate entanglement most quickly among the previous schemes with the same ingredients.Comment: 5 pages 4 figure

Existence of translating solutions to the flow by powers of mean curvature on unbounded domains

In this paper, we prove the existence of classical solutions of the Dirichlet problem for a class of quasi-linear elliptic equations on unbounded domains like a cone or a U-type domain. This problem comes from the study of mean curvature flow and its generalization, the flow by powers of mean curvature. Our approach is a modified version of the classical Perron method, where the solutions to the minimal surface equation are used as sub-solutions and a family auxiliary functions are constructed as super-solutions.Comment: 30 page