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Practical approach for detecting k-nonseparability of multipartite quantum states

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science China(Physics,Mechanics & Astronomy) 2025年第1期Mechanics & Astronomy) .卷 32-48页

作者： Jie Guo Jinchuan Hou Xiaofei Qi Kan He College of mathematics Taiyuan University of Technology school of mathematics and Statistics Shanxi University Key Laboratory of Complex systems and Data science of Ministry of Education Shanxi University

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 far. We propose a sufficient and necessary criterion of k-nonseparability for any n-partite finite or infinite dimensional systems, 2 ≤ k ≤ n. This criterion serves as the foundation for a practical scheme designed to detect entanglement and k-nonseparability across multipartite finite-dimensional systems. To 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 ${\bm~k}$-nonseparability

An autonomous dynamic recovery technology for autonomous underwater vehicles based on unmanned surface vehicles

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science China Technological sciences 2025年

作者： Yueying WANG Yiqi SHI Guanghui WEN Huaicheng YAN school of Mechatronic Engineering and Automation Shanghai University Department of systems science School of Mathematics Southeast University school of Information science and Engineering East China University of Science and Technology

Autonomous underwater vehicles (AUVs) have attracted considerable attention due to their vast potential applications, such as offshore oil exploration, underwater rescue, military reconnaissance, and marine scientific...

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Dynamical complexity of Anosov systems driven by a quasi-periodic force

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science China mathematics 2025年第1期 89-136页

作者： Wen Huang Zeng Lian Kening Lu Department of mathematics University of Science and Technology of China school of mathematics Sichuan University

Consider C2Anosov systems on a compact manifold driven by a quasi-periodic *** study their dynamical complexity on various levels from the perspectives of both path-wise dynamics and stochastic *** that these systems are non-wandering（i.e.,every point in the phase space is nonwandering）,we prove a set of results:（1） the existence of abundance of random periodic points;（2） a random Liv?ic theorem;（3） a random Ma?é-Bousch-Conze-Guivarc'h lemma;（4） the existence of strong random ***,a concrete example constructed on a 2-dimensional torus is also given to uncover some interesting phenomena of the systems.

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Weak KAM theory for two classes of almost periodic Hamiltonian systems

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science China mathematics 2025年

作者： Xun Niu Kaizhi Wang Yong Li school of mathematics and Statistics Center for Mathematics and Interdisciplinary SciencesNortheast Normal University school of Mathematical sciences Shanghai Frontier Science Center of Modern Analysis (CMA-Shanghai)Shanghai Jiao Tong University Institute of mathematics Jilin University

The purpose of this paper is to investigate the dynamics of Bohr almost periodic and Levitan almost periodic Hamiltonian systems via the weak KAM theory. We obtain minimal measures and weak KAM solutions in both cases. The weak KAM solution is a weak solution to the Hamilton-Jacobi equation, which formally transforms the original Hamiltonian systems into an integrable one. Consequently, we get the existence of an invariant torus in the aforementioned weak sense.

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THE EVENTUALLY DISTANCE MINIMIZING RAYS IN MODULI SPACES

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Acta Mathematica Scientia 2018年第3期38卷 950-964页

作者： Fei SONG Yi QI Guangming HU lmib school of mathematics and systems science Beihang University lmib School of Mathematics and Systems Science Beihang University

The eventually distance minimizing ray（EDM ray） in moduli spaces of the Riemann surfaces of analytic finite type with 3 g ＋ n-3 〉 0 is studied, which was introduced by Farb and Masur [5]. The asymptotic distance of EDM rays in a moduli space and the distance of end points of EDM rays in the boundary of the moduli space in the augmented moduli space are discussed in this article. A relation between the asymptotic distance of EDM rays and the distance of their end points is established. It is proved also that the distance of end points of two EDM rays is equal to that of end points of two Strebel rays in the Teichmu¨ller space of a covering Riemann surface which are leftings of some representatives of the EDM rays. Meanwhile, simpler proofs for some known results are given.

关键词： Augmented Teichmüller space augmented moduli space Strebel differential EDM ray

THE REAL HYPER-ELLIPTIC SUBSPACES OF TEICHMüLLER SPACE AND MODULI SPACE

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Acta Mathematica Scientia 2019年第4期39卷 1121-1135页

作者： Guangming HU Yi QI lmib School of Mathematics and Systems Science Beihang University

Although the existence and uniqueness of Strebel differentials are proved by Jenkins and Strebel, the specific constructions of Strebel differentials are difficult. Two special kinds of special Strebel differentials are constructed in [5, 6]. The Strebel rays [3] and the eventually distance minimizing rays [9] are important in Teichm¨uller spaces and moduli spaces, respectively. Motivated by the study of [3, 9], two special kinds of Strebel rays in the real hyper-elliptic subspace of Teichm¨uller space and two special kinds of EDM rays in the real hyper-elliptic subspace of moduli space are studied in this article.

关键词： Teichmüller space Strebel ray moduli space EDM ray real hyper-elliptic subspace

On the Periodic Logistic Map

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Acta Mathematica Sinica,English Series 2018年第5期34卷 891-900页

作者： Cui Ping LI Ming ZHAO lmib-school of mathematics and systems science Beihang University

In this paper, the famous logistic map is studied in a new point of view. We study the boundedness and the periodicity of non-autonomous logistic map xn＋1=rnxx（1-xn）, n=0, 1,...,where {rn} is a positive p-periodic sequence. The sufficient conditions are given to support the existence of asymptotically stable and unstable p-periodic orbits. This appears to be the first study of the map with variable parameter r.

关键词： Non-autonomous logistic map periodic orbit asymptotic stable

Dynamics of different compound bursting in two phantom bursting mechanism models

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science China(Technological sciences) 2014年第5期57卷 885-892页

作者： YANG ZhuoQin HAO LiJie school of mathematics and systems science and lmib Beihang University

The generic phantom bursting model proposed by Bertram et *** evoke complex bursting oscillations in collaboration with two generic slow variables with different time *** models with the phantom bursting mechanism are suggested,when these two generic slow variables are provided with some specific biological significances by combining slowly varying intracellular Ca2+concentration of the Chay-Keizer electrical bursting model with two different glycolytic oscillations,***,complex dynamic behaviors of different compound bursting occurring in these two models are comprehensively surveyed by two fast/slow analyses for a moderately and a slower slow variable,respectively.

关键词： phantom bursting mechanism compound bursting different time scales fast/slow dynamics analysis

THE NORMALITY OF ALGEBROID MULTIFUNCTIONS AND THEIR COEFFICIENT FUNCTIONS

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Acta Mathematica Scientia 2015年第1期35卷 121-132页

作者：柴富杰高宗升 lmib & school of mathematics and systems science Beihang University

In this paper, we investigate the normality relationship between algebroid multifunctions and their coefficient functions. We prove that the normality of a k-valued entire algebroid multifunctions family is equivalent to their coefficient functions in some conditions. Furthermore, we obtain some new normality criteria for algebroid multifunctions families based on these results. We also provide some examples to expound that some restricted conditions of our main results are necessary.

关键词： algebroid multifunctions normal families coefficient functions Hausdorff distance