Unifying Treatment of Discord via Relative Entropy

A new form of zero-discord state via Petz's monotonicity condition on relative entropy with equality has been derived systematically. A generalization of symmetric zero-discord states is presented and the related physical implications are discussed.Comment: 12 pages, LaTeX. Some parts are deleted. Any comments are welcome

Lower bound on concurrence for arbitrary-dimensional tripartite quantum systems

In this paper, we study the concurrence of arbitrary dimensional tripartite quantum systems. An explicit operational lower bound of concurrence is obtained in terms of the concurrence of sub-states. A given example show that our lower bound may improve the well known existing lower bounds of concurrence. The significance of our result is to get a lower bound when we study the concurrence of arbitrary dimensional multipartite quantum systems.Comment: 1 figures, Quantum Information Processing 201

Lower bound of multipartite concurrence based on sub-multipartite quantum systems

We study the concurrence of arbitrary dimensional multipartite quantum systems. An explicit analytical lower bound of concurrence for four-partite mixed states is obtained in terms of the concurrences of tripartite mixed states. Detailed examples are given to show that our lower bounds improve the existing lower bounds of concurrence. The approach is generalized to five-partite quantum systems.Comment: 9 pages,2 figures, correct some error

On small set of one-way LOCC indistinguishability of maximally entangled states

In this paper, we study the one-way local operations and classical communication (LOCC) problem. In $\mathbb{C}^d\otimes\mathbb{C}^d$ with $d\geq4$, we construct a set of $3\lceil\sqrt{d}\rceil-1$ one-way LOCC indistinguishable maximally entangled states which are generalized Bell states. Moreover, we show that there are four maximally entangled states which cannot be perfectly distinguished by one-way LOCC measurements for any dimension $d\geq 4$.Comment: 10 pages.Very recently, we became aware of related work \cite{Zhang2} in which the same $\lceil\frac{d}{2}\rceil+2$ states in $\mathbb{C}^d\otimes\mathbb{C}^d$ is proved to be one-way LOCC indistinguishable. arXiv admin note: text overlap with arXiv:1310.4220 by other autho

2-Modules and the Representation of 2-Rings

In this paper, we develop 2-dimensional algebraic theory which closely follows the classical theory of modules. The main results are giving definitions of 2-module and the representation of 2-ring. Moreover, for a 2-ring \cR, we prove that its modules form a 2-Abelian category.Comment: 78 pages, 99 figure

Higher Dimensional Homology Algebra III:Projective Resolutions and Derived 2-Functors in (2-SGp)

In this paper, we will define the derived 2-functor by projective resolution of any symmetric 2-group, and give some related properties of the derived 2-functor.Comment: 30 pages, 50 figures. This is the third paper of the series of our works on higher dimensional homological algebra. In the coming papers, we define the right derived 2-functor in the 2-categories (2-SGp) and (\cR-2-Mod). In this version, we correct some errors in last version, add more results, such as 2-chain homotopy, its related results, et

Higher Dimensional Homology Algebra II:Projectivity

In this paper, we will prove that the 2-category (2-SGp) of symmetric 2-groups and 2-category (\cR-2-Mod) of \cR-2-modules(\cite{5}) have enough projective objects, respectively.Comment: 10 pages, 4 figures. This is the second paper of the series works on higher dimensional homology algebra. The first paper is "2-Modules and the Representation of 2-Rings\cite{4}". In the coming papers, we shall give the definition of injective object in the 2-category (\cR-2-Mod), prove that this 2-category has enough injective objects and develop the (co)homology theory of i

Higher Dimensional Homology Algebra IV:Projective Resolutions and Derived 2-Functors in (\cR-2-Mod)

In this paper, we will construct the projective resolution of any \cR-2-module, define the derived 2-functor and give some related properties of the derived 2-functor.Comment: 17pages, 32 figures, This is the fourth paper of the series of our works on higher dimensional homological algebra. In the coming papers, we shall define the right derived 2-functor in the 2-categories (2-SGp) and (\cR-2-Mod), and give some relations of left derived 2-functors and right derived 2-functor

RANet: Ranking Attention Network for Fast Video Object Segmentation

Despite online learning (OL) techniques have boosted the performance of semi-supervised video object segmentation (VOS) methods, the huge time costs of OL greatly restrict their practicality. Matching based and propagation based methods run at a faster speed by avoiding OL techniques. However, they are limited by sub-optimal accuracy, due to mismatching and drifting problems. In this paper, we develop a real-time yet very accurate Ranking Attention Network (RANet) for VOS. Specifically, to integrate the insights of matching based and propagation based methods, we employ an encoder-decoder framework to learn pixel-level similarity and segmentation in an end-to-end manner. To better utilize the similarity maps, we propose a novel ranking attention module, which automatically ranks and selects these maps for fine-grained VOS performance. Experiments on DAVIS-16 and DAVIS-17 datasets show that our RANet achieves the best speed-accuracy trade-off, e.g., with 33 milliseconds per frame and J&F=85.5% on DAVIS-16. With OL, our RANet reaches J&F=87.1% on DAVIS-16, exceeding state-of-the-art VOS methods. The code can be found at https://github.com/Storife/RANet.Comment: Accepted by ICCV 2019. 10 pages, 7 figures, 6 tables. The supplementary file can be found at https://csjunxu.github.io/paper/2019ICCV/RANet_supp.pdf ; Code is available at https://github.com/Storife/RANe

Higher Dimensional Homology Algebra V:Injective Resolutions and Derived 2-Functors in (\cR-2-Mod)

In this paper, we will construct the injective resolution of any \cR-2-module, define the right derived 2-functor, and give some related properties of the derived 2-functor in (\cR-2-Mod).Comment: 29 pages, 57 figures. This paper is the fifth paper of the series of our works on higher dimensional homology algebra. In our coming papers, we shall define \cExt 2-functor and spectral sequence in an abelian 2-category, try to give the relation between \cExt 2-functor and the extension of 2-module