Diffusion and entanglement of a kicked particle in an infinite square well under frequent measurements

We investigate the dynamics of a kicked particle in an infinite square well undergoing frequent measurements of energy. For a large class of periodic kicking force, constant diffusion is found in such a non-KAM system. The influence of phase shift of the kicking potential on the short-time dynamical behavior is discussed. The general asymptotical measurement-assisted diffusion rate is obtained. The entanglement between the particle and the measuring apparatus is investigated. There exist two distinct dynamical behaviors of entanglement. The bipartite entanglement grows with the kicking steps and it gains larger value for the more chaotic system. However, the pairwise entanglement between the system of interest and the partial spins of the measuring apparatus decreases with the kicking steps. The relation between the entanglement and quantum diffusion is also analyzed. PACS numbers: 05.45.Mt, 03.65.TaComment: 7 pages, 5 figures, RevTex4, Accepted by Phys. Rev.

Efficient Approximations for the Online Dispersion Problem

The dispersion problem has been widely studied in computational geometry and facility location, and is closely related to the packing problem. The goal is to locate n points (e.g., facilities or persons) in a k-dimensional polytope, so that they are far away from each other and from the boundary of the polytope. In many real-world scenarios however, the points arrive and depart at different times, and decisions must be made without knowing future events. Therefore we study, for the first time in the literature, the online dispersion problem in Euclidean space. There are two natural objectives when time is involved: the all-time worst-case (ATWC) problem tries to maximize the minimum distance that ever appears at any time; and the cumulative distance (CD) problem tries to maximize the integral of the minimum distance throughout the whole time interval. Interestingly, the online problems are highly non-trivial even on a segment. For cumulative distance, this remains the case even when the problem is time-dependent but offline, with all the arriving and departure times given in advance. For the online ATWC problem on a segment, we construct a deterministic polynomial-time algorithm which is (2ln2+epsilon)-competitive, where epsilon>0 can be arbitrarily small and the algorithm\u27s running time is polynomial in 1/epsilon. We show this algorithm is actually optimal. For the same problem in a square, we provide a 1.591-competitive algorithm and a 1.183 lower-bound. Furthermore, for arbitrary k-dimensional polytopes with k>=2, we provide a 2/(1-epsilon)-competitive algorithm and a 7/6 lower-bound. All our lower-bounds come from the structure of the online problems and hold even when computational complexity is not a concern. Interestingly, for the offline CD problem in arbitrary k-dimensional polytopes, we provide a polynomial-time black-box reduction to the online ATWC problem, and the resulting competitive ratio increases by a factor of at most 2. Our techniques also apply to online dispersion problems with different boundary conditions

Integrated Deep and Shallow Networks for Salient Object Detection

Deep convolutional neural network (CNN) based salient object detection methods have achieved state-of-the-art performance and outperform those unsupervised methods with a wide margin. In this paper, we propose to integrate deep and unsupervised saliency for salient object detection under a unified framework. Specifically, our method takes results of unsupervised saliency (Robust Background Detection, RBD) and normalized color images as inputs, and directly learns an end-to-end mapping between inputs and the corresponding saliency maps. The color images are fed into a Fully Convolutional Neural Networks (FCNN) adapted from semantic segmentation to exploit high-level semantic cues for salient object detection. Then the results from deep FCNN and RBD are concatenated to feed into a shallow network to map the concatenated feature maps to saliency maps. Finally, to obtain a spatially consistent saliency map with sharp object boundaries, we fuse superpixel level saliency map at multi-scale. Extensive experimental results on 8 benchmark datasets demonstrate that the proposed method outperforms the state-of-the-art approaches with a margin.Comment: Accepted by IEEE International Conference on Image Processing (ICIP) 201

Stationary state entanglement and total correlation of two qubits or qutrits

We investigate the mutual information and entanglement of stationary state of two locally driven qubits under the influence of collective dephasing. It is shown that both the mutual information and the entanglement of two qubits in the stationary state exhibit damped oscillation with the scaled action time $\gamma{T}$ of the local external driving field. It means that we can control both the entanglement and total correlation of the stationary state of two qubits by adjusting the action time of the driving field. We also consider the influence of collective dephasing on entanglement of two qutrits and obtain the sufficient condition that the stationary state is entangled.Comment: 5 pages, 2 figures, RevTex