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Nonlocality is one of the distinctive features of quantum mechanics and has different forms in practice, e.g., non-separability, quantum steering, and Bell nonlocality. Here, by exploiting the high-dimensional probability tensor, we propose a quantum magic square model to characterize the diverse forms of nonlocal phenomena in a single protocol. In this model, the nonlocalities are manifested in the partial-sums of the probability tensor, where the uncertainty relation serves as an “indicator” of different nonlocal phenomena. We derive a conditional majorization uncertainty relation criterion to witness the quantum steering. The new criterion is applicable to infinite number of observables and is found superior to the formerly thought optimal steering criterion.

The uncertainty principle lies at the heart of quantum physics, and is widely thought of as a fundamental limit on the measurement precisions of incompatible observables. Here we show that the traditional uncertainty relation in fact belongs to the leading order approximation of a generalized uncertainty relation. That is, the leading order linear dependence of observables gives the Heisenberg type of uncertainty relations, while higher order nonlinear dependence may reveal more different and interesting correlation properties. Applications of the generalized uncertainty relation and the high order nonlinear dependence between observables in quantum information science are also discussed., Comment: 26 pages, 3 figures; published in Ann. Phys. (Berlin)

The uncertainty relation, as one of the fundamental principles of quantum physics, captures the incompatibility of noncommuting observables in the preparation of quantum states. In this work, we derive two strong and universal uncertainty relations for $N(N\ge2)$ observables with discrete and bounded spectra, one in multiplicative form and the other in additive form. To verify their validity, for illustration, we implement in the spin-1/2 system an experiment with single-photon measurement. The experimental results exhibit the validity and robustness of these uncertainty relations, and indicate the existence of stringent lower bounds., Comment: 9 pages, 5 figures. Slightly extended

Taking advantage of coherent light beams, we experimentally investigate the variancebased uncertainty relations and the optimal majorization uncertainty relation for the two-dimensional quantum mechanical system.Different from most of the experiments which devoted to record each individual quantum, we examine the uncertainty relations by measuring an ensemble of photons with two polarization degree of freedom characterized by the Stokes parameters which allow us to determine the polarization density matrix with high precision. The optimality of the recently proposed direct-sum majorization uncertainty relation is verified by measuring the Lorenz curves. Results show that the Lorenz curve method represents a faithful verification of the majorization uncertainty relation and the uncertainty relation is indeed an ensemble property of quantum system., Comment: 7 pages, 7 figures

Employing the lattice theory on majorization, we investigate the universal quantum uncertainty relation for any number observables and general measurement. We find: 1. The least bounds of the universal uncertainty relations can only be properly defined in the lattice theory; 2. Contrary to variance and entropy, the metric induced by the majorization lattice implies an intrinsic structure of the quantum uncertainty; 3. The lattice theory correlates the optimization of uncertainty relation with the entanglement transformation under local quantum operation and classical communication. Interestingly, the optimality of the universal uncertainty relation is found can be mimicked by the Lorenz curve, initially introduced in economics to measure the wealth concentration degree of a society., Comment: 25 pages, 2 figures; published in Ann. Phys. (Berlin)

The uncertainty relation is one of the key ingredients of quantum theory. Despite the great efforts devoted to this subject, most of the variance-based uncertainty relations are state-dependent and suffering from the triviality problem of zero lower bounds. Here we develop a method to get uncertainty relations with state-independent lower bounds. The method works by exploring the eigenvalues of a Hermitian matrix composed by Bloch vectors of incompatible observables and is applicable for both pure and mixed states and for arbitrary number of N- dimensional observables. The uncertainty relation for incompatible observables can be explained by geometric relations related to the parallel postulate and the inequalities in Horn's conjecture on Hermitian matrix sum. Practical entanglement criteria are also presented based on the derived uncertainty relations., 15 pages, no figures

We present a practical scheme for the decomposition of a bipartite mixed state into a sum of direct products of local density matrices, using the technique developed in Li and Qiao (Sci. Rep. 8: 1442, 2018). In the scheme, the correlation matrix which characterizes the bipartite entanglement is first decomposed into two matrices composed of the Bloch vectors of local states. Then we show that the symmetries of Bloch vectors are consistent with that of the correlation matrix, and the magnitudes of the local Bloch vectors are lower bounded by the correlation matrix. Concrete examples for the separable decompositions of bipartite mixed states are presented for illustration., Comment: 22 pages; published in Quantum Inf. Process

As a pivotal tool to build interpretive models, variable selection plays an increasingly important role in high-dimensional data analysis. In recent years, variable selection ensembles (VSEs) have gained much interest due to their many advantages. Stability selection (Meinshausen and Bühlmann, 2010), a VSE technique based on subsampling in combination with a base algorithm like lasso, is an effective method to control false discovery rate (FDR) and to improve selection accuracy in linear regression models. By adopting lasso as a base learner, we attempt to extend stability selection to handle variable selection problems in a Cox model. According to our experience, it is crucial to set the regularization region Λ in lasso and the parameter λmin properly so that stability selection can work well. To the best of our knowledge, however, there is no literature addressing this problem in an explicit way. Therefore, we first provide a detailed procedure to specify Λ and λmin. Then, some simulated and real-world data with various censoring rates are used to examine how well stability selection performs. It is also compared with several other variable selection approaches. Experimental results demonstrate that it achieves better or competitive performance in comparison with several other popular techniques.

We present a practical entanglement classification scheme for pure state in form of $$2\times L\times M\times N$$2×L×M×N under the stochastic local operation and classical communication (SLOCC), where every inequivalent class of the entangled quantum states may be sorted out according to its standard form and the corresponding transformation matrix. This provides a practical method for determining the interconverting matrix between two SLOCC equivalent entangled states, and classification examples for some $$2\times 4\times M\times N$$2×4×M×N systems are also presented.

A new comprehensive evaluation method of tobacco mixing uniformity was presented in this paper. In this method, projection pursuit model was used to select evaluation index and determine the index weights. Seven chemical compositions which had a major impact on the overall evaluation, such as total volatile acid, total volatile bases, PH, polyphenol, protein, total nitrogen and chlorine were sampled repetitiously and calculated the average and coefficient of variance. Tobacco mixing uniformity was evaluated by the score according to coefficient of variance. Comprehensive evaluation of five batches of tobacco was carried out and the results were consistent with the traditional. This method was easy to get basic data and evaluation results fitted the actual. It was a simple and practical evaluation method of mixing uniformity.

Quantum entanglement has been regarded as one of the key physical resources in quantum information sciences. However, the determination of whether a mixed state is entangled or not is generally a hard issue, even for the bipartite system. In this work we propose an operational necessary and sufficient criterion for the separability of an arbitrary bipartite mixed state, by virtue of the multiplicative Horn's problem. The work follows the work initiated by Horodecki {\it et. al.} and uses the Bloch vector representation introduced to the separability problem by J. De Vicente. In our criterion, a complete and finite set of inequalities to determine the separability of compound system is obtained, which may be viewed as trade-off relations between the quantumness of subsystems. We apply the obtained result to explicit examples, e.g. the separable decomposition of arbitrary dimension Werner state and isotropic state., 33 pages; published in Scientific Reports

The traditional wavelet-based image fusion method has some problems, in order to further satisfy the requirements of image fusion on the right direction, this paper studies the principle and performance contourlet transformation based on the proposed sensitivity analysis. In this method, contourlet multi-resolution, locality and direction effectively capture the source image in detail, texture, direction of information, enhance the visibility of the fused image and obtain the higher quality medical images.

In this paper, the multi-input linear and nonlinear mathematical differential equations of inverted pendulum system were established based on the traditional single-input linear inverted pendulum. Aiming at multi-input nonlinear model, nonlinear state transformation are carried through on the basis of the test of distribution involution and the calculation of integral manifold, then, the multi-input nonlinear inverted pendulum system was transformed into two single-input nonlinear inverted pendulum system to study. In the end, make use of related nonlinear system control theory of the sliding mode variable structure, designed the controller structure.

Extracting axis of 3D blood vessel images is very important and useful to quantify blood vessel in medical diagnosis. According to blood vessel features, we constructed the energy constraint equation of blood vessel. The initial skeleton curve of blood vessel images obtained by thinning algorithm dynastically converges to the position of the axis under energy constraint equation and along gradient direction of the distance field of blood vessel images. When the equation energy reaches a minimum value, the initial skeleton curve also fixes in the axis position at this time. Experimental results show that the position of the blood vessels axis extracted by this method is accurate, and the axis preserves topology and connectivity.

This paper proposed the concept of centroid in particle swarm optimization which is similar to physical centroid properties of objects. Similarly, we may think of a particle swarm as a discrete system of particles and find the centroid representing the entire population. Usually, it has a more promising position than worse particles among the population. In order to verify the role of centroid which can speed up the convergence rate of the algorithm, and prevent the algorithm from being trapped into a local solution early as far as possible at the same time, A Novel Centroid Particle Swarm Optimization Algorithm Based on Two Subpopulations(CPSO) is proposed. Numerical simulation experiments show that CPSO by testing some benchmark functions is better than Linear Decreasing Weight PSO (LDWPSO) in convergence speed in the same accuracy of solution case.

We present an equivalence theorem to unify the two classes of uncertainty relations, i.e. the variance-based ones and the entropic forms, showing that the entropy of an operator in a quantum system can be built from the variances of a set of commutative operators. This means that an uncertainty relation in the language of entropy may be mapped onto a variance-based one, and vice versa. Employing the equivalence theorem, alternative formulations of entropic uncertainty relations are obtained for the qubit system that are stronger than the existing ones in the literature, and variance-based uncertainty relations for spin systems are reached from the corresponding entropic uncertainty relations.

We propose a new scheme to express the uncertainty principle in form of inequality of the bipartite correlation functions for a given multipartite state, which provides an experimentally feasible and model-independent way to verify various uncertainty and measurement disturbance relations. By virtue of this scheme the implementation of experimental measurement on the measurement disturbance relation to a variety of physical systems becomes practical. The inequality in turn also imposes a constraint on the strength of correlation, i.e. it determines the maximum value of the correlation function for two-body system and a monogamy relation of the bipartite correlation functions for multipartite system., 18 pages, 2 figures; published in J. Phys. A: Math. Theor

In this paper, we proposed a new video quality metric model, which describe the video quality feature using quaternion matrix. The four parts of the quaternion are brightness, chrominance, contour, and inter frame residual, respectively. The feature value of each block is computed from quaternion model by singular value decomposition. In addition we extract gray-level co-occurrence matrix (GLCM) of each block, then calculate differential entropy of GLCM as the weight of the block. The algorithm is tested on the video quality expert group (VQEG) Phase I FR-TV test data set. Experiments show that it has good correlation with perceived video quality.

In this paper, we propose a full-reference video quality assessment model, which describe the video structure information based on quaternion singular value decomposition (QSVD). In addition, we fully consider the characteristics of HVS, combined the luminance characteristics, texture detail and spatial location information as a weight. Finally, we enhance the importance of chrominance and consider the blocking effect. The algorithm is tested on the video quality expert group (VQEG) Phase I FR-TV test data set. Experiment results show that new model has good correlation with perceived video quality.

We propose a practical method for finding the canonical forms of arbitrary dimensional multipartite entangled states, either pure or mixed. By extending the technique developed in one of our recent works, the canonical forms for the mixed $N$-partite entangled states are constructed where they have inherited local unitary symmetries from their corresponding $N+1$ pure state counterparts. A systematic scheme to express the local symmetries of the canonical form is also presented, which provides a feasible way of verifying the local unitary equivalence for two multipartite entangled states., 22 pages; published in J. Phys. A: Math. Theor

We propose a practical entanglement classification scheme for general multipartite pure states in arbitrary dimensions under local unitary equivalence by exploiting the high order singular value decomposition technique and local symmetries of the states. By virtue of this scheme, the method of determining the local unitary equivalence of $n$-qubit states proposed by Kraus is extended to the case for arbitrary dimensional multipartite states., 10 pages; published in Phys. Rev. Lett

We develop a novel method in classifying the multipartite entanglement state of 2 × N × N under stochastic local operation and classical communication. In this method, all inequivalent classes of true entangled state can be sorted directly without knowing the classification information of lower dimension ones for any given dimension N.