Deterministic versus probabilistic quantum information masking

We investigate quantum information masking for arbitrary dimensional quantum states. We show that mutually orthogonal quantum states can always be served for deterministic masking of quantum information. We further construct a probabilistic masking machine for linearly independent states. It is shown that a set of d dimensional states, $\{ |a_1 \rangle_A, |t a_2 \rangle_A, \dots, |a_n \rangle_A \}$, $n \leq d$, can be probabilistically masked by a general unitary-reduction operation if they are linearly independent. The maximal successful probability of probabilistic masking is analyzed and derived for the case of two initial states.Comment: 5 pages, 1 figure

Monolayer Molybdenum Disulfide Nanoribbons with High Optical Anisotropy

Two-dimensional Molybdenum Disulfide (MoS2) has shown promising prospects for the next generation electronics and optoelectronics devices. The monolayer MoS2 can be patterned into quasi-one-dimensional anisotropic MoS2 nanoribbons (MNRs), in which theoretical calculations have predicted novel properties. However, little work has been carried out in the experimental exploration of MNRs with a width of less than 20 nm where the geometrical confinement can lead to interesting phenomenon. Here, we prepared MNRs with width between 5 nm to 15 nm by direct helium ion beam milling. High optical anisotropy of these MNRs is revealed by the systematic study of optical contrast and Raman spectroscopy. The Raman modes in MNRs show strong polarization dependence. Besides that the E' and A'1 peaks are broadened by the phonon-confinement effect, the modes corresponding to singularities of vibrational density of states are activated by edges. The peculiar polarization behavior of Raman modes can be explained by the anisotropy of light absorption in MNRs, which is evidenced by the polarized optical contrast. The study opens the possibility to explore quasione-dimensional materials with high optical anisotropy from isotropic 2D family of transition metal dichalcogenides

The ultra-low-frequency shear modes of 2-4 layer graphenes observed in their scroll structures at edges

The in-plane shear modes between neighbor-layers of 2-4 layer graphenes (LGs) and the corresponding graphene scrolls rolled up by 2-4LGs were investigated by Raman scattering. In contrast to that just one shear mode was observed in 3-4LGs, all the shear modes of 3-4LGs were observed in 3-4 layer scrolls (LSs), whose frequencies agree well with the theoretical predication by both a force-constant model and a linear chain model. In comparison to the broad width (about 12cm$^{-1}$) for the G band in graphite, all the shear modes exhibit an intrinsic line width of about 1.0 cm$^{-1}$. The local electronic structures dependent on the local staking configurations enhance the intensity of the shear modes in corresponding 2-4LSs zones, which makes it possible to observe all the shear modes. It provides a direct evidence that how the band structures of FLGs can be sensitive to local staking configurations. This result can be extended to n layer graphene (n > 4) for the understanding of the basic phonon properties of multi-layer graphenes. This observation of all-scale shear modes can be foreseen in other 2D materials with similar scroll structures.Comment: 14 pages, 5 figure

Non-Autoregressive Math Word Problem Solver with Unified Tree Structure

Existing MWP solvers employ sequence or binary tree to present the solution expression and decode it from given problem description. However, such structures fail to handle the variants that can be derived via mathematical manipulation, e.g., $(a_1+a_2) * a_3$ and $a_1 * a_3+a_2 * a_3$ can both be possible valid solutions for a same problem but formulated as different expression sequences or trees. The multiple solution variants depicting different possible solving procedures for the same input problem would raise two issues: 1) making it hard for the model to learn the mapping function between the input and output spaces effectively, and 2) wrongly indicating \textit{wrong} when evaluating a valid expression variant. To address these issues, we introduce a unified tree structure to present a solution expression, where the elements are permutable and identical for all the expression variants. We propose a novel non-autoregressive solver, named \textit{MWP-NAS}, to parse the problem and deduce the solution expression based on the unified tree. For evaluating the possible expression variants, we design a path-based metric to evaluate the partial accuracy of expressions of a unified tree. The results from extensive experiments conducted on Math23K and MAWPS demonstrate the effectiveness of our proposed MWP-NAS. The codes and checkpoints are available at: \url{https://github.com/mengqunhan/MWP-NAS}.Comment: Accepted at EMNLP202

Probing the edge-related properties of atomically thin MoS2 at nanoscale

层状二维材料具有独特的物理化学性质，使其在光电器件、传感、能源和催化等领域得到了高度关注和广泛应用。二维材料在制备过程中不可避免引入结构缺陷，虽然这些缺陷尺度仅为数纳米甚至单原子，但是会极大地改变材料的结构和电子性质，从而影响其应用。化学化工学院任斌教授课题组在层状二维材料缺陷表征方面取得进展。该工作表明了TERS在原位、高空间分辨表征缺陷位的结构和电子性质方面具有独特的优势，可以进一步推广到其他二维材料，从而有效地指导缺陷设计和材料应用。 该工作通过校内外课题组紧密合作，在任斌教授、谭平恒研究员（中科院半导体研究所）和王翔博士共同指导下完成。实验部分主要由黄腾翔博士（第一作者，已毕业化学系博士生）完成，电子能带结构与光谱理论计算由谭平恒研究员课题组从鑫博士生（共同第一作者）完成，吴思思、林楷强、姚旭、何玉韩、吴江滨、包一凡、黄声超等参与了实验与讨论。【Abstract】Defects can induce drastic changes of the electronic properties of two-dimensional transition metal dichalcogenides and influence their applications. It is still a great challenge to characterize small defects and correlate their structures with properties. Here, we show that tipenhanced Raman spectroscopy (TERS) can obtain distinctly different Raman features of edge defects in atomically thin MoS2, which allows us to probe their unique electronic properties and identify defect types (e.g., armchair and zigzag edges) in ambient. We observed an edgeinduced Raman peak (396 cm−1) activated by the double resonance Raman scattering (DRRS) process and revealed electron–phonon interaction in edges. We further visualize the edge-induced band bending region by using this DRRS peak and electronic transition region using the electron density-sensitive Raman peak at 406 cm−1. The power of TERS demonstrated in MoS2 can also be extended to other 2D materials, which may guide the defect engineering for desired properties.The authors acknowledge the final supports from MOST of China (2016YFA0200601 and 2016YFA0301204), NSFC (21633005, 21790354, 21503181, 21711530704, 21621091, 11874350, 11474277, and 11434010), Natural Science Foundation of Fujian Province (2016J05046), and China Postdoctoral Science Foundation (2017M622062). 研究工作得到科技部、国家自然科学基金委员会、福建省自然科学基金和中国博士后基金资助

The Genomes of Oryza sativa: A History of Duplications

We report improved whole-genome shotgun sequences for the genomes of indica and japonica rice, both with multimegabase contiguity, or almost 1,000-fold improvement over the drafts of 2002. Tested against a nonredundant collection of 19,079 full-length cDNAs, 97.7% of the genes are aligned, without fragmentation, to the mapped super-scaffolds of one or the other genome. We introduce a gene identification procedure for plants that does not rely on similarity to known genes to remove erroneous predictions resulting from transposable elements. Using the available EST data to adjust for residual errors in the predictions, the estimated gene count is at least 38,000–40,000. Only 2%–3% of the genes are unique to any one subspecies, comparable to the amount of sequence that might still be missing. Despite this lack of variation in gene content, there is enormous variation in the intergenic regions. At least a quarter of the two sequences could not be aligned, and where they could be aligned, single nucleotide polymorphism (SNP) rates varied from as little as 3.0 SNP/kb in the coding regions to 27.6 SNP/kb in the transposable elements. A more inclusive new approach for analyzing duplication history is introduced here. It reveals an ancient whole-genome duplication, a recent segmental duplication on Chromosomes 11 and 12, and massive ongoing individual gene duplications. We find 18 distinct pairs of duplicated segments that cover 65.7% of the genome; 17 of these pairs date back to a common time before the divergence of the grasses. More important, ongoing individual gene duplications provide a never-ending source of raw material for gene genesis and are major contributors to the differences between members of the grass family