Multi-mode entangled states represented as Grassmannian polynomials

Quantum Information Processing - We introduce generalized Grassmannian representatives of multi-mode state vectors. By implementing the fundamental properties of Grassmann coherent states, we map...     

Coordination in multiagent systems and Laplacian spectra of digraphs

Constructing and studying distributed control systems requires the analysis of the Laplacian spectra and the forest structure of directed graphs. In this paper, we present some basic results of this analysis. We also discuss the application of these results published earlier to decentralized control and touch upon some problems of spectral graph theory.     

Fast local Laplacian filtering based enhanced medical image fusion using parameter-adaptive PCNN and local features-based fuzzy weighted matrices

Generally, the anatomical CT/MRI modalities exhibit the brain tissue anatomy with a high spatial resolution, where PET/SPECT modalities show the metabolic features with low spatial resolution. Therefore, the integration of these two classes significantly improves several clinical applications and computer-aided diagnoses. In the proposed scheme, a fast local Laplacian filter (FLLF) is first applied to the source images to enhance the edge information and suppress the noise artifacts. Second, the RGB images are converted to YUV color space to separate the Y-component. Then to capture the spatial and spectral features of the source images, the NSST is applied to decompose the input (grayscale and/or Y-component) images into one low (LFS) and several high-frequency subbands (HFS). Third, an improved salience measure and matching factor (SMF) method by the local features-based fuzzy-weighted matrix (FW-SMF) is introduced to fuse the LFS coefficient. Due to the fast convergence with fewer iterations and robust pixels selection procedure, the PA-PCNN model is adopted to fuse the HFS coefficients. Fourth, the final fused image is obtained by applying inverse NSST and YUV format. Visual and statistical analysis performed on various experiments prove that the proposed scheme not only integrates the spatial and texture features details of the source images but also enhances the visual quality and contrast of the fused image compared to the existing state-of-arts.

     

Series expansion of weighted pseudoinverse matrices and iterative methods for calculating weighted pseudoinverse matrices and weighted normal pseudosolutions

Weighted pseudoinverse matrices are expanded into matrix power series with negative exponents and arbitrary positive parameters. Based on this expansion, iterative methods for evaluating weighted pseudoinverse matrices and weighted normal pseudosolutions are designed and analyzed. The iterative methods for weighted normal pseudosolutions are extended to solving constrained least-squares problems. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 32–62, January–February 2006.     

Multipartite entangled magnon states as quantum communication channels

We investigate the entanglement properties of the two magnon states and explicate conditions under which, the two magnon state becomes useful for several quantum communication protocols. We systematically study the temporal behaviour of concurrence to find out the effect of exchange interaction on entanglement. The two magnon state, which is potentially realizable in quantum dots using Heisenberg exchange interaction, is found to be suitable for carrying out deterministic teleportation of an arbitrary two qubit composite system. Further, conditions for which the channel capacity reaches “Holevo bound”, allowing four classical bits to be transmitted through two qubits are derived. Later, an unconventional protocol is given to demonstrate that this state can be used for sharing of a two qubit entangled state among two parties.     

A distributed algorithm for average consensus on strongly connected weighted digraphs

In this work we propose a distributed algorithm to solve the discrete-time average consensus problem on strongly connected weighted digraphs (SCWDs). The key idea is to couple the computation of the average with the estimation of the left eigenvector associated with the zero eigenvalue of the Laplacian matrix according to the protocol described in Qu et al. (2012). The major contribution is the removal of the requirement of the knowledge of the out-neighborhood of an agent, thus paving the way for a simple implementation based on a pure broadcast-based communication scheme.     

Laplacian versus adjacency matrix in quantum walk search

A quantum particle evolving by Schrödinger’s equation contains, from the kinetic energy of the particle, a term in its Hamiltonian proportional to Laplace’s operator. In discrete space, this is replaced by the discrete or graph Laplacian, which gives rise to a continuous-time quantum walk. Besides this natural definition, some quantum walk algorithms instead use the adjacency matrix to effect the walk. While this is equivalent to the Laplacian for regular graphs, it is different for non-regular graphs and is thus an inequivalent quantum walk. We algorithmically explore this distinction by analyzing search on the complete bipartite graph with multiple marked vertices, using both the Laplacian and adjacency matrix. The two walks differ qualitatively and quantitatively in their required jumping rate, runtime, sampling of marked vertices, and in what constitutes a natural initial state. Thus the choice of the Laplacian or adjacency matrix to effect the walk has important algorithmic consequences.     

Constructive quantum scaling of unitary matrices

In this work, we present a method of decomposition of arbitrary unitary matrix \(U\in \mathbf {U}(2^k)\) into a product of single-qubit negator and controlled-\(\sqrt{\text{ NOT }}\) gates. Since the product results with negator matrix, which can be treated as complex analogue of bistochastic matrix, our method can be seen as complex analogue of Sinkhorn–Knopp algorithm, where diagonal matrices are replaced by adding and removing an one-qubit ancilla. The decomposition can be found constructively, and resulting circuit consists of \(O(4^k)\) entangling gates, which is proved to be optimal. An example of such transformation is presented.     

Entropies of general quantum states

The entropy and the mutual entropy for states and channels are totally studied in general quantum systems described byC*-algebras. In particular, we discuss the relations among theS-entropy and the mutual entropy introduced by Ohya and the Connes-Narnhofer-Thirring entropy.     

Methods of computing weighted pseudoinverse matrices with singular weights

Three iterative processes are constructed and investigated for computing weighted pseudoinverse matrices with singular weights and ML-weighted pseudoinverse matrices. Two of them are based on the decompositions of the weighted pseudoinverse matrix with singular weights into matrix power series, and the third is a generalization of the Schulz method to nonsingular square matrices. Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 150–169, September–October, 1999.     

Generalized Choi states and 2-distillability of quantum states

We investigate the distillability of bipartite quantum states in terms of positive and completely positive maps. We construct the so-called generalized Choi states and show that it is distillable when it has negative partial transpose. We convert the distillability problem of 2-copy \(n\times n\) Werner states into the determination of the positivity of an Hermitian matrix. We obtain several sufficient conditions by which the positivity holds. Further, we investigate the case \(n=3\) by the classification of \(2\times 3\times 3\) pure states.     

按对角阵加权信息融合Kalman滤波器

为了克服按矩阵加权信息融合非稳态Kalman滤波器的在线计算负担大的缺点,和按标量加权融合Kalman滤波器精度较低的缺点,应用现代时间序列分析方法,提出了按对角阵加权的线性最小方差多传感器信息融合稳态Kalman滤波器.它等价于状态分量按标量加权信息融合Kalman滤波器,实现了解耦信息融合Kalman滤波器.它的精度和计算负担介于按矩阵和按标量加权融合器两者之间,且便于实时应用.为了计算最优加权,提出了计算稳态滤波误差方差阵和协方差阵的Lyapunov方程.一个三传感器的雷达跟踪系统的仿真例子说明了其有效性.     

Existence of states on quantum structures

Orthomodular lattices occurred as generalized event structures in the models of probability for quantum mechanics. Here we contribute to the question of existence of states (=probability measures) on orthomodular lattices. We prove that known techniques do not allow to find examples with less than 19 blocks (=maximal Boolean subalgebras). This bound is achieved by the example by Mayet [R. Mayet, Personal communication, 1993]. Although we do not finally exclude the existence of other techniques breaking this bound, existence of smaller examples is highly unexpected.     

Data mining of social networks represented as graphs

In this survey we review the literature and concepts of the data mining of social networks, with special emphasis on their representation as a graph structure. The survey is divided into two principal parts: first we conduct a survey of the literature which forms the ‘basis’ and background for the field; second we define a set of ‘hot topics’ which are currently in vogue in congresses and the literature. The ‘basis’ or background part is divided into four major themes: graph theory, social networks, online social networks and graph mining. The graph mining theme is organized into ten subthemes. The second, ‘hot topic’ part, is divided into five major themes: communities, influence and recommendation, models metrics and dynamics, behaviour and relationships, and information diffusion.     

基于纠缠的量子密钥分配协议仿真

由于受物理资源和实验条件的限制,在经典计算机上对量子密钥分配（QKD）仿真,为研究者提供一种手段以便更好地掌握这类抽象协议。对以纠缠态为基础的E91协议的量子密钥分配过程进行仿真,重点对比分析了理想环境、有噪环境以及窃听环境下的仿真结果,并验证该量子密钥分配协议的安全性。     

Coherence analysis and Laplacian energy of recursive trees with controlled initial states

Frontiers of Information Technology & Electronic Engineering - We study the consensus of a family of recursive trees with novel features that include the initial states controlled by a...     

Quantum discord of ensemble of quantum states

We highlight an information-theoretic meaning of quantum discord as the gap between the accessible information and the Holevo bound in the framework of ensemble of quantum states. This complementary relationship implies that a large amount of preexisting arguments about the evaluation of quantum discord can be directly applied to the accessible information and vice versa. For an ensemble of two pure qubit states, we show that one can avoid the optimization problem with the help of the Koashi–Winter relation. Further, for the general case (two mixed qubit states), we recover the main results presented by Fuchs and Caves (Phys Rev Lett 73:3047, 1994), but totally from the perspective of quantum discord. Following this line of thought, we also investigate the geometric discord as an indicator of quantumness of ensembles in detail. Finally, we give an example to elucidate the difference between quantum discord and geometric discord with respect to optimal measurement strategies.