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Practical approach for detecting k-nonseparability of multipartite quantum states

science China(Physics,Mechanics & Astronomy) 2025年第1期68卷 28-44页

作者： Jie Guo Jinchuan Hou Xiaofei Qi Kan He College of Mathematics Taiyuan University of TechnologyTaiyuan 030006China School of Mathematics and Statistics Shanxi UniversityTaiyuan 030006China Key Laboratory of Complex Systems and Data Science of Ministry of Education Shanxi UniversityTaiyuan 030006China

The instantaneous detection of entanglement in quantum states poses a significant challenge in the fields of quantum computation and quantum information,and there are no practical methods or tools to complete this task satisfactorily so *** propose a sufficient and necessary criterion of k-nonseparability for any n-partite finite or infinite dimensional systems,2≤k≤*** criterion serves as the foundation for a practical scheme designed to detect entanglement and k-nonseparability across multipar-tite finite-dimensional *** exemplify the application of our scheme,we have developed a software tool that facilitates swift and precise identification of entanglement,k-nonseparability,and genuine entanglement within n-qubit systems,specifically tailored for systems with 2≤n≤4.

关键词： multipartite systems entanglement states entanglement witnesses k-nonseparability

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Quantum correlations in a chain-type quantum network

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Communications in Theoretical Physics 2024年第6期76卷 77-91页

作者： Xiaofei Qi Aihong Zhai Lihua Yang School of Mathematical Science Shanxi UniversityTaiyuan 030006China Key Laboratory of Complex Systems and Data Science of Ministry of Education Shanxi UniversityTaiyuan 030006China School of Mathematics and Information Technology Yuncheng UniversityYuncheng 044000China

A quantum network concerns several independent entangled resources and can create strong quantum correlations by performing joint measurements on some *** this paper,we discuss an n-partite chain network with each of two neighboring observers sharing an arbitrary Bell state and all intermediate observers performing some positive-operator-valued measurements with parameterλ.The expressions of all post-measurement states between any two observers are obtained,and their quantifications of Bell nonlocality,Einstein-Podolsky-Rosen steering and entanglement with different ranges ofλare respectively detected and analyzed.

关键词： quantum correlation nonlocality entanglement chain-type quantum network

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Phase entanglement negativity for bipartite fermionic systems

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Physical Review A 2024年第3期110卷 032417页

作者： Bing Xu Xiaofei Qi Jinchuan Hou School of Mathematics and Statistics Key Laboratory of Complex Systems and Data Science of Ministry of Education College of Mathematics

We discuss the behavior of positive linear maps in fermionic systems and then propose the phase partial transpose and the phase entanglement negativity. We show that every fermionic state which mixes local fermion-number parity must have nonvanishing nontrivial phase entanglement negativity, which gives an affirmative answer to a conjecture proposed by Shapourian and Ryu [Phys. Rev. A 99, 022310 (2019)]. In addition, we prove that the phase entanglement negativity is an entanglement monotone and establish some equalities and inequalities related to the phase entanglement negativity which, particularly, provide some upper bounds and lower bounds of the fermionic entanglement negativity. A more detailed discussion of the (1+M)-mode case is also presented, and our results generalize some known findings.

关键词： Quantum entanglement

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Stochastic SIRS models on networks: mean and variance of infection

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Infectious Disease Modelling 2025年第3期10卷 875-896页

作者： Chen, Tingting Liu, Guirong Jin, Zhen School of Mathematics and Statistics Shanxi University Shanxi Taiyuan 030006 China Complex Systems Research Center Shanxi University Shanxi Taiyuan 030006 China Key Laboratory of Complex Systems and Data Science of Ministry of Education Shanxi University Shanxi Taiyuan 030006 China

Due to the heterogeneity of contact structure, it is more reasonable to model on networks for epidemics. Because of the stochastic nature of events and the discrete number of individuals, the spread of epidemics is more appropriately viewed as a Markov chain. Therefore, we establish stochastic SIRS models with vaccination on networks to study the mean and variance of the number of susceptible and infected individuals for large-scale populations. Using van Kampen's system-size expansion, we derive a high-dimensional deterministic system which describes the mean behaviour and a Fokker-Planck equation which characterizes the variance around deterministic trajectories. Utilizing the qualitative analysis technique and Lyapunov function, we demonstrate that the disease-free equilibrium of the deterministic system is globally asymptotically stable if the basic reproduction number R₀ < 1;and the endemic equilibrium is globally asymptotically stable if R₀ > 1. Through the analysis of the Fokker-Planck equation, we obtain the asymptotic expression for the variance of the number of susceptible and infected individuals around the endemic equilibrium, which can be approximated by the elements of principal diagonal of the solution of the corresponding Lyapunov equation. Here, the solution of Lyapunov equation is expressed by vectorization operator of matrices and Kronecker product. Finally, numerical simulations illustrate that vaccination can reduce infections and increase fluctuations of the number of infected individuals and show that individuals with greater degree are more easily infected. © 2025 The Authors

关键词： Fokker-Planck equation Networks Stochastic SIRS models Van Kampen's system-size expansion Variance

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ViGT: proposal-free video grounding with a learnable token in the transformer

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science China(Information sciences) 2023年第10期66卷 196-212页

作者： Kun LI Dan GUO Meng WANG School of Computer Science and Information Engineering Hefei University of Technology Key Laboratory of Knowledge Engineering with Big Data Ministry of Education Intelligent Interconnected Systems Laboratory of Anhui Province Institute of Artificial Intelligence Hefei Comprehensive National Science Center

The video grounding(VG) task aims to locate the queried action or event in an untrimmed video based on rich linguistic descriptions. Existing proposal-free methods are trapped in the complex interaction between video and query, overemphasizing cross-modal feature fusion and feature correlation for VG. In this paper, we propose a novel boundary regression paradigm that performs regression token learning in a transformer. Particularly, we present a simple but effective proposal-free framework, namely video grounding transformer(ViGT), which predicts the temporal boundary using a learnable regression token rather than multi-modal or cross-modal features. In ViGT, the benefits of a learnable token are manifested as follows.(1) The token is unrelated to the video or the query and avoids data bias toward the original video and query.(2) The token simultaneously performs global context aggregation from video and query ***, we employed a sharing feature encoder to project both video and query into a joint feature space before performing cross-modal co-attention(i.e., video-to-query attention and query-to-video attention) to highlight discriminative features in each modality. Furthermore, we concatenated a learnable regression token [REG] with the video and query features as the input of a vision-language transformer. Finally, we utilized the token [REG] to predict the target moment and visual features to constrain the foreground and background probabilities at each timestamp. The proposed ViGT performed well on three public datasets:ANet-Captions, TACoS, and YouCookⅡ. Extensive ablation studies and qualitative analysis further validated the interpretability of ViGT.

关键词： video grounding temporal sentence grounding boundary regression token learning proposal-free

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Limit Theorems for Critical Galton-Watson Processes with Immigration Stopped at Zero

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Acta Mathematica Sinica,English Series 2024年第2期40卷 435-450页

作者： Dou Dou LI Mei ZHANG Xian Yu ZHANG College of Statistics and Data Science Faculty of ScienceBeijing University of TechnologyBeijing 100124P.R.China Laboratory of Mathematics and Complex Systems(Ministry of Education) School of Mathematical SciencesBeijing Normal UniversityBeijing 100875P.R.China

In this paper,we consider a critical Galton-Watson branching process with immigration stopped at zero *** precise estimation on the probability generating function of the n-th population are obtained,and the tail prob... 详细信息

关键词： Branching immigration critical life period limit theorems

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Taiji-TianQin-LISA network:Precisely measuring the Hubble constant using both bright and dark sirens

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science China(Physics,Mechanics & Astronomy) 2024年第2期67卷 59-77页

作者： Shang-Jie Jin Ye-Zhu Zhang Ji-Yu Song Jing-Fei Zhang Xin Zhang Key Laboratory of Cosmology and Astrophysics(Liaoning)&College of Sciences Northeastern UniversityShenyang 110819China Key Laboratory of Data Analytics and Optimization for Smart Industry(Ministry of Education) Northeastern UniversityShenyang 110819China National Frontiers Science Center for Industrial Intelligence and Systems Optimization Northeastern UniversityShenyang 110819China

In the coming decades,the space-based gravitational-wave(GW)detectors such as Taiji,TianQin,and LISA are expected to form a network capable of detecting millihertz GWs emitted by the mergers of massive black hole binaries(MBHBs).In this work,we investigate the potential of GW standard sirens from the Taiji-TianQin-LISA network in constraining cosmological *** the optimistic scenario in which electromagnetic(EM)counterparts can be detected,we predict the number of detectable bright sirens based on three different MBHB population models,i.e.,popⅢ,Q3d,and *** results show that the TaijiTianQin-LISA network alone could achieve a constraint precision of 0.9%for the Hubble constant,meeting the standard of precision ***,the Taiji-TianQin-LISA network could effectively break the cosmological parameter degeneracies generated by the CMB data,particularly in the dynamical dark energy *** combined with the CMB data,the joint CMB+Taiji-TianQin-LISA data offerσ(w)=0.036 in the wCDM model,which is close to the latest constraint result obtained from the CMB+SN *** also consider a conservative scenario in which EM counterparts are not *** to the precise sky localizations of MBHBs by the Taiji-TianQin-LISA network,the constraint precision of the Hubble constant is expected to reach 1.2%.In conclusion,the GW standard sirens from the Taiji-TianQin-LISA network will play a critical role in helping solve the Hubble tension and shedding light on the nature of dark energy.

关键词： space-based gravitational wave detection standard sirens the Taiji-TianQin-LISA network the Hubble constant dark energy

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Prescribed-Time Nash Equilibrium Seeking for Pursuit-Evasion Game

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IEEE/CAA Journal of Automatica Sinica 2024年第6期11卷 1518-1520页

作者： Lei Xue Jianfeng Ye Yongbao Wu Jian Liu D.C.Wunsch Key Laboratory of Measurement and Control of Complex Systems of Engineering Ministry of EducationNanjing 210096 School of Automation Southeast UniversityNanjing 210096China Department of Electrical and Computer Engineering Missouri University of Science and TechnologyRollaMO 65409 USA IEEE

Dear Editor,This letter is concerned with prescribed-time Nash equilibrium(PTNE)seeking problem in a pursuit-evasion game(PEG)involving agents with second-order *** order to achieve the prior-given and user-defined convergence time for the PEG,a PTNE seeking algorithm has been developed to facilitate collaboration among multiple pursuers for capturing the evader without the need for any global ***,it is theoretically proved that the prescribedtime convergence of the designed algorithm for achieving Nash equilibrium of ***,the effectiveness of the PTNE method was validated by numerical simulation results.A PEG consists of two groups of agents:evaders and *** pursuers aim to capture the evaders through cooperative efforts,while the evaders strive to evade *** is a classic noncooperative *** has attracted plenty of attention due to its wide application scenarios,such as smart grids[1],formation control[2],[3],and spacecraft rendezvous[4].It is noteworthy that most previous research on seeking the Nash equilibrium of the game,where no agent has an incentive to change its actions,has focused on asymptotic and exponential convergence[5]-[7].

关键词： seeking prescribed convergence

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Large Deviations for a Critical Galton-Watson Branching Process

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Acta Mathematicae Applicatae Sinica 2025年第2期41卷 456-478页

作者： Dou-dou LI Wan-lin SHI Mei ZHANG College of Statistics and Data Science Faculty of ScienceBeijing University of TechnologyBeijing 100124China Department of Mathematics and Physics North China Electric Power UniversityBeijing 102206China Laboratory of Mathematics and Complex Systems(Ministry of Education) School of Mathematical SciencesBeijing Normal UniversityBeijing 100875China

In this paper,a critical Galton-Watson branching process {Z_(n)} is *** deviation rates of SZ_(n):=Σ_(i=1)^_(Z_(n)) Xi are obtained,where {X_(i);i≥1} is a sequence of independent and identically distributed random variables and X_(1) is in the domain of attraction of an-stable law with α∈(0,2).One shall see that the convergence rate is determined by the tail index of X_(1) and the variance of Z_(1).Our results can be compared with those ones of the supercritical case.

关键词： large deviation branching process critical α-stable

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Analysis of the SEIR mean-field model in dynamic networks under intervention

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Infectious Disease Modelling 2025年第3期10卷 850-874页

作者： Li, Jiangmin Jin, Zhen Tang, Ming Complex System Research Center Shanxi University Shanxi Taiyuan 030006 China Key Laboratory of Complex Systems and Data Science of Ministry of Education Shanxi University Shanxi Taiyuan 030006 China Shanxi Key Laboratory for Mathematical Technology in Complex Systems Shanxi University Shanxi Taiyuan 030006 China School of Physics and Electronic Science East China Normal University Shanghai 200241 China Shanghai Key Laboratory of Multidimensional Information Processing East China Normal University Shanghai 200241 China

For emerging respiratory infectious diseases like COVID-19, non-pharmaceutical interventions such as isolation are crucial for controlling the spread. From the perspective of network transmission, non-pharmaceutical interventions like isolation alter the degree distribution and other topological structures of the network, thereby controlling the spread of the infectious disease. In this paper, we establish a SEIR mean-field propagation dynamics model for the synchronous evolution of dynamic networks caused by propagation and tracing isolation. We employ the reducing-dimension method to convert the mean-field model in networks into an equivalent and simpler low-dimension model, and then calculate the exact expression of the final size. In addition, we get the differential equations of the degree distribution over time in dynamic networks under tracing isolation and the relationships between the first and second moment of the dynamic network. While the degree of a node remains constant regardless of its state in many previous studies, this paper takes into account that the degree of each node changes over time whatever its state under the disease spread and intervention measures. © 2025 The Authors

关键词： Degree distribution Dynamic network The final size Tracing isolation

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