Entanglement renormalization and integral geometry

We revisit the applications of integral geometry in AdS$_3$ and argue that the metric of the kinematic space can be realized as the entanglement contour, which is defined as the additive entanglement density. From the renormalization of the entanglement contour, we can holographically understand the operations of disentangler and isometry in multi-scale entanglement renormalization ansatz. Furthermore, a renormalization group equation of the long-distance entanglement contour is then derived. We then generalize this integral geometric construction to higher dimensions and in particular demonstrate how it works in bulk space of homogeneity and isotropy.Comment: 40 pages, 7 figures. v2: discussions on the general measure added, typos fixed; v3: sections reorganized, various points clarified, to appear in JHE

OPE of the stress tensors and surface operators

We demonstrate that the divergent terms in the OPE of a stress tensor and a surface operator of general shape cannot be constructed only from local geometric data depending only on the shape of the surface. We verify this holographically at d=3 for Wilson line operators or equivalently the twist operator corresponding to computing the entanglement entropy using the Ryu-Takayanagi formula. We discuss possible implications of this result.Comment: 20 pages, no figur

Demonstration of Deutsch's Algorithm on a Stable Linear-Optical Quantum Computer

We report an experimental demonstration of quantum Deutsch's algorithm by using linear-optical system. By employing photon's polarization and spatial modes, we implement all balanced and constant functions for quantum computer. The experimental system is very stable and the experimental data are excellent in accordance with the theoretical results.Comment: 7 pages, 4 figure

The GRB-Supernova Connection

Long-duration gamma-ray bursts (GRBs) are believed to be produced by the core collapse of massive stars and hence to be connected with supernovae (SNe). Indeed, for four pairs of GRBs and SNe, spectroscopically confirmed connection has been firmly established. For more than a dozen of GRBs the SN signature (the `red bump') has been detected in the afterglow lightcurves. Based on the four pairs of GRBs and SNe with spectroscopically confirmed connection a tight correlation was found between the peak spectral energy of GRBs and the peak bolometric luminosity of the underlying SNe. The recent discovery of X-ray flash 080109 associated with a normal core-collapse SN 2008D confirmed this relation and extended the GRB-SN connection. Progress on the GRB-SN connection is briefly reviewed.Comment: 6 pages, 5 figures. To appear in the proceedings of "2008 Nanjing GRB conference", Nanjing, 23-27 June 200

How to Train Your Dragon: Tamed Warping Network for Semantic Video Segmentation

Real-time semantic segmentation on high-resolution videos is challenging due to the strict requirements of speed. Recent approaches have utilized the inter-frame continuity to reduce redundant computation by warping the feature maps across adjacent frames, greatly speeding up the inference phase. However, their accuracy drops significantly owing to the imprecise motion estimation and error accumulation. In this paper, we propose to introduce a simple and effective correction stage right after the warping stage to form a framework named Tamed Warping Network (TWNet), aiming to improve the accuracy and robustness of warping-based models. The experimental results on the Cityscapes dataset show that with the correction, the accuracy (mIoU) significantly increases from 67.3% to 71.6%, and the speed edges down from 65.5 FPS to 61.8 FPS. For non-rigid categories such as "human" and "object", the improvements of IoU are even higher than 18 percentage points