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<jats:p>Teleportation is a quantum information process without classical counterparts, in which the sender can disembodiedly transfer unknown quantum states to the receiver. In probabilistic teleportation through a partial entangled quantum channel, the transmission is exact (with fidelity 1), but may fail in a probability and the initial state is destroyed simultaneously. We propose a scheme for nondestructive probabilistic teleportation of high-dimensional quantum states. With the aid of an ancilla in the hands of the sender, the initial quantum information can be recovered when teleportation fails. The ancilla acts as a quantum apparatus to measure the sender’s subsystem. Erasing the information recorded in it can resume the initial state.</jats:p>

<jats:p>Using a single-mode approximation, we carry out the entanglement measures, e.g., the negativity and von Neumann entropy when a tetrapartite generalized GHZ state is treated in a noninertial frame, but only uniform acceleration is considered for simplicity. In terms of explicit negativity calculated, we notice that the difference between the algebraic average <jats:italic>π</jats:italic> <jats:sub>4</jats:sub> and geometric average <jats:italic>Π</jats:italic> <jats:sub>4</jats:sub> is very small with the increasing accelerated observers and they are totally equal when all four qubits are accelerated simultaneously. The entanglement properties are discussed from one accelerated observer to all four accelerated observers. It is shown that the entanglement still exists even if the acceleration parameter <jats:italic>r</jats:italic> goes to infinity. It is interesting to discover that all 1-1 tangles are equal to zero, but 1-3 and 2-2 tangles always decrease when the acceleration parameter <jats:italic>r</jats:italic> increases. We also study the von Neumann entropy and find that it increases with the number of the accelerated observers. In addition, we find that the von Neumann entropy <jats:italic>S</jats:italic> <jats:sub>ABCDI</jats:sub>, <jats:italic>S</jats:italic> <jats:sub>ABCIDI</jats:sub>, <jats:italic>S</jats:italic> <jats:sub>ABICIDI</jats:sub> and <jats:italic>S</jats:italic> <jats:sub>AIBICIDI</jats:sub> always decrease with the controllable angle <jats:italic>θ</jats:italic>, while the entropies <jats:italic>S</jats:italic> <jats:sub>3 – 3 non</jats:sub>, <jats:italic>S</jats:italic> <jats:sub>3 – 2 non</jats:sub>, <jats:italic>S</jats:italic> <jats:sub>3 – 1 non</jats:sub> and <jats:italic>S</jats:italic> <jats:sub>3 – 0 non</jats:sub> first increase with the angle <jats:italic>θ</jats:italic> and then decrease with it.</jats:p>

<jats:p>Partial least squares (PLS) regression is an important linear regression method that efficiently addresses the multiple correlation problem by combining principal component analysis and multiple regression. In this paper, we present a quantum partial least squares (QPLS) regression algorithm. To solve the high time complexity of the PLS regression, we design a quantum eigenvector search method to speed up principal components and regression parameters construction. Meanwhile, we give a density matrix product method to avoid multiple access to quantum random access memory (QRAM) during building residual matrices. The time and space complexities of the QPLS regression are logarithmic in the independent variable dimension <jats:italic>n</jats:italic>, the dependent variable dimension <jats:italic>w</jats:italic>, and the number of variables <jats:italic>m</jats:italic>. This algorithm achieves exponential speed-ups over the PLS regression on <jats:italic>n</jats:italic>, <jats:italic>m</jats:italic>, and <jats:italic>w</jats:italic>. In addition, the QPLS regression inspires us to explore more potential quantum machine learning applications in future works.</jats:p>

<jats:p>The contradiction between classical and quantum physics can be identified through quantum contextuality, which does not need composite systems or spacelike separation. Contextuality is proven either by a logical contradiction between the noncontextuality hidden variable predictions and those of quantum mechanics or by the violation of noncontextual inequality. We propose an experimental scheme of state-independent contextual inequality derived from the Mermin proof of the Kochen–Specker (KS) theorem in eight-dimensional Hilbert space, which could be observed either in an individual system or in a composite system. We also show how to resolve the compatibility problems. Our scheme can be implemented in optical systems with current experiment techniques.</jats:p>

<jats:p>We propose three alternative measures for non-Gaussianity of quantum states: sine distance, Bures angle, and Bures distance, which are based on quantum fidelity introduced by Wang [<jats:italic>Phys. Lett. A</jats:italic> <jats:bold>373</jats:bold> 58 (2008)]. Using them, we evaluate the non-Gaussianity of some relevant single-mode and two-mode non-Gaussian states and find a good consistency of the three examined measures. In addition, we show that such metrics can exactly quantify the degree of Gaussianity of even Schrödinger-cat-like states of small amplitudes that can not be measured by other known non-Gaussianity measures such as the Hilbert–Schmidt metric and the relative entropy metric. We make a comparative study between all existing non-Gaussianity measures according to the metric axioms and point out that the sine distance is the best candidate among them.</jats:p>

<jats:p>The properties of the system near the instability boundary are very sensitive to external disturbances, which is important for amplifying some physical effects or improving the sensing accuracy. In this paper, the quantum properties near the instability boundary in a simple optomechanical system have been studied by numerical simulation. Calculations show that the transitional region connecting the Gaussian states and the ring states when crossing the boundary is sometimes different from the region centered on the boundary line, but it is more essential. The change of the mechanical Wigner function in the transitional region directly reflects its bifurcation behavior in classical dynamics. Besides, quantum properties, such as mechanical second-order coherence function and optomechanical entanglement, can be used to judge the corresponding bifurcation types and estimate the parameter width and position of the transitional region. The non-Gaussian transitional states exhibit strong entanglement robustness, and the transitional region as a boundary ribbon can be expected to replace the original classical instability boundary line in future applications.</jats:p>

<jats:p>As the scale and complexity have been increased in software systems, developers place more emphases on software engineering and system designs. Software architecture is evolved with update of softwares, and it plays a fundamental role in determining quality of software systems. Multifractal characteristics of software networks can reflect software quality. In this paper, we construct a software network from the dependencies between object classes, and gain a deep understanding of software through network analysis. To be specific, multifractal analysis of the software network is performed based on a modified box-covering algorithm that yields fewer boxes. We verify that software with different functions and dependencies is multifractal. Further, different versions of the software are compared to discover the evolution of the software architecture. The results show that the singularity of class dependencies decreases as the software is updated. This trend leads to a more specific division of functions between software modules. One of the visible advantages of our work is that it allows the characterization of software structures at the code level. The methodology and results of this paper provide new insights into the evaluation and design of large-scale software systems.</jats:p>

<jats:p>Time delays exist widely in real systems, and time-delayed interactions can result in abundant dynamic behaviors and functions in dynamic networks. Inferring the time delays and interactions is challenging due to systematic nonlinearity, noises, a lack of information, and so on. Recently, Shi <jats:italic>et al.</jats:italic> proposed a random state variable resetting method to detect the interactions in a continuous-time dynamic network. By arbitrarily resetting the state variable of a driving node, the equivalent coupling functions of the driving node to any response node in the network can be reconstructed. In this paper, we introduce this method in time-delayed dynamic networks. To infer actual time delays, the nearest neighbor correlation (NNC) function for a given time delay is defined. The significant increments of NNC originate from the delayed effect. Based on the increments, the time delays can be reconstructed and the reconstruction errors depend on the sampling time interval. After time delays are accurately identified, the equivalent coupling functions can also be reconstructed. The numerical results have fully verified the validity of the theoretical analysis.</jats:p>

<jats:p>This paper studies a new class of two-dimensional rational maps exhibiting self-excited and hidden attractors. The mathematical model of these maps is firstly formulated by introducing a rational term. The analysis of existence and stability of the fixed points in these maps suggests that there are four types of fixed points, i.e., no fixed point, one single fixed point, two fixed points and a line of fixed points. To investigate the complex dynamics of these rational maps with different types of fixed points, numerical analysis tools, such as time histories, phase portraits, basins of attraction, Lyapunov exponent spectrum, Lyapunov (Kaplan–Yorke) dimension and bifurcation diagrams, are employed. Our extensive numerical simulations identify both self-excited and hidden attractors, which were rarely reported in the literature. Therefore, the multi-stability of these maps, especially the hidden one, is further explored in the present work.</jats:p>

<jats:p>An accurate and fast three-step self-calibrating generalized phase-shifting interferomertry (SGPSI) is proposed. In this approach, two new phase-shifting signals are constructed by the difference interferograms normalization and noise suppressing, then the unknown phase shift between the two difference phase-shifting signals is estimated quickly through searching the minimum coefficient of variation of the modulation amplitude, a limited number of pixels are selected to participate in the search process to further save time, and finally the phase is reconstructed through the searched phase shift. Through the reconstruction of phase map by the simulation and experiment, and the comparison with several mature algorithms, the good performance of the proposed algorithm is proved, and it eliminates the limitation of requiring more than three phase-shifting interferograms for high-precision SGPSI. We expect this method to be widely used in the future.</jats:p>