Distinguishability and indistinguishability by LOCC

We show that a set of linearly independent quantum states $\{(U_{m,n}\otimes I)\rho ^{AB}(U_{m,n}^{\dagger}\otimes I)\}_{m,n=0}^{d-1}$, where $U_{m,n}$ are generalized Pauli matrices, cannot be discriminated deterministically or probabilistically by local operations and classical communications (LOCC). On the other hand, any $l$ maximally entangled states from this set are locally distinguishable if $l(l-1)\le 2d$. The explicit projecting measurements are obtained to locally discriminate these states. As an example, we show that four Werner states are locally indistinguishable.Comment: 5 page

Nonconcave penalized likelihood with a diverging number of parameters

A class of variable selection procedures for parametric models via nonconcave penalized likelihood was proposed by Fan and Li to simultaneously estimate parameters and select important variables. They demonstrated that this class of procedures has an oracle property when the number of parameters is finite. However, in most model selection problems the number of parameters should be large and grow with the sample size. In this paper some asymptotic properties of the nonconcave penalized likelihood are established for situations in which the number of parameters tends to \infty as the sample size increases. Under regularity conditions we have established an oracle property and the asymptotic normality of the penalized likelihood estimators. Furthermore, the consistency of the sandwich formula of the covariance matrix is demonstrated. Nonconcave penalized likelihood ratio statistics are discussed, and their asymptotic distributions under the null hypothesis are obtained by imposing some mild conditions on the penalty functions

Erratum: Dynamics of the Bounds of Squared Concurrence [Phys. Rev. A 79, 032306 (2009)]

This is an erratum to our paper.Comment: a little different from the published versio

SANet: Structure-Aware Network for Visual Tracking

Convolutional neural network (CNN) has drawn increasing interest in visual tracking owing to its powerfulness in feature extraction. Most existing CNN-based trackers treat tracking as a classification problem. However, these trackers are sensitive to similar distractors because their CNN models mainly focus on inter-class classification. To address this problem, we use self-structure information of object to distinguish it from distractors. Specifically, we utilize recurrent neural network (RNN) to model object structure, and incorporate it into CNN to improve its robustness to similar distractors. Considering that convolutional layers in different levels characterize the object from different perspectives, we use multiple RNNs to model object structure in different levels respectively. Extensive experiments on three benchmarks, OTB100, TC-128 and VOT2015, show that the proposed algorithm outperforms other methods. Code is released at http://www.dabi.temple.edu/~hbling/code/SANet/SANet.html.Comment: In CVPR Deep Vision Workshop, 201