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Subelliptic Harmonic Maps with Values in Metric Spaces of Nonpositive Curvature

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Communications in Mathematical Research 2022年第4期38卷 516-534页

作者： Yaoting Gui Jürgen Jost Xianqing Li-Jost School of Mathematical sciences University of Science and Technology of ChinaHefeiChina max planck institute for mathematics in the sciences LeipzigGermany

We prove the Holder continuity of a harmonic map from a domain of a sub-Riemannian manifold into a locally compact manifold with nonpositive curvature,and more generally into a non-positively curved metric space in th... 详细信息

关键词： Subelliptic harmonic maps nonpositive curvature Holder continuity

Tighter Constraints of Multiqubit Entanglement

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Communications in Theoretical Physics 2019年第5期71卷 545-554页

作者：杨龙妹陈斌费少明王志玺 School of Mathematical sciences Capital Normal University College of Mathematical Science Tianjin Normal University Max-Planck-Institute for Mathematics in the Sciences

Monogamy and polygamy relations characterize the distributions of entanglement in multipartite systems.We provide classes of monogamy and polygamy inequalities of multiqubit entanglement in terms of concurrence, entanglement of formation, negativity, Tsallis-q entanglement, and Rényi-α entanglement, respectively. We show that these inequalities are tighter than the existing ones for some classes of quantum states.

关键词： monogamy relation polygamy relation entanglement measure

Variational Characterization of Multitype Galton-Watson Branching Processes

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Acta Mathematicae Applicatae Sinica 2014年第1期30卷 27-36页

作者： Ying Wang Max-Planck-Institute for Mathematics in the Sciences Academy of mathematics and Systems Science Chinese Academy of Sciences Warwick Systems Biology Centre University of Warwick

In this paper, we give a variational characterization for the growth rate of a multitype population modelled by a multitype Galton-Watson branching process. In particular, the so-called retrospective process plays an important role in the description of the equilibrium state used in the variational characterization. We define the retrospective process associated with a multitype Galton-Watson branching process and identify it with the mutation process describing the type evolution along typical lineages of the multitype Galton-Watson branching process.

关键词： multitype branching processes retrospective processes variational analysis equilibrium states large deviations

Geometry of skew information-based quantum coherence

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Communications in Theoretical Physics 2020年第10期72卷 70-79页

作者： Zhao-Qi Wu Huai-Jing Huang Shao-Ming Fei Xian-Qing Li-Jost Department of mathematics Nanchang UniversityNanchang 330031China School of Mathematical sciences Capital Normal UniversityBeijing 100048China Max-Planck-Institute for Mathematics in the Sciences D-04103 LeipzigGermany

We study the skew information-based coherence of quantum states and derive explicit formulas for Werner states and isotropic states in a set of autotensors of mutually unbiased bases(MUBs).We also give surfaces of skew information-based coherence for Bell-diagonal states and a special class of X states in both computational basis and in MUBs.Moreover,we depict the surfaces of the skew information-based coherence for Bell-diagonal states under various types of local nondissipative quantum channels.The results show similar as well as different features compared with relative entropy of coherence and l1 norm of coherence.

关键词： coherence skew information mutually unbiased bases quantum channels

Concurrence,tangle and fully entangled fraction

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Chinese Physics B 2010年第9期19卷 161-167页

作者：李明费少明李先清 College of mathematics and Computational Science China University of Petroleum Department of mathematics Capital Normal University Max-Planck-Institute for Mathematics in the Sciences

We show that although we cannot distil a singlet frora many pairs of bound entangled states, the concurrence and the tangle of two entangled quantum states are always strictly larger than those of one of them, even both entangled quantum states are bound entangled. We present a relation between the concurrence and the fidelity of optimal teleportation. We also give new upper and lower bounds for concurrence and tangle.

关键词： concurrence entanglement teleportation

Parameterized monogamy and polygamy relations of multipartite entanglement

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Chinese Physics B 2023年第12期32卷 231-240页

作者：沈中喜王珂珂费少明 School of Mathematical sciences Capital Normal UniversityBeijing 100048China Max-Planck-Institute for Mathematics in the Sciences Leipzig 04103Germany

Monogamy and polygamy relations are important properties of entanglement,which characterize the entanglement distribution of multipartite systems.We explore monogamy and polygamy relations of entanglement in multipartite systems by using two newly derived parameterized mathematical inequalities,and establish classes of parameterized monogamy and polygamy relations of multiqubit entanglement in terms of concurrence and entanglement of formation.We show that these new parameterized monogamy and poelygamy inequalities are tighter than the existing ones by detailed examples.

关键词： monogamy polygamy concurrence entanglement of formation

Sharing quantum nonlocality in star network scenarios

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Frontiers of physics 2023年第3期18卷 193-201页

作者： Tinggui Zhang Naihuan Jing Shao-Ming Fei School of mathematics and Statistics Hainan Normal UniversityHaikou 571158China College of sciences Shanghai UniversityShanghai 200444China Department of mathematics North Carolina State UniversityRaleighNC 27695USA School of Mathematical sciences Capital Normal UniversityBeijing 100048China Max-Planck-Institute for Mathematics in the Sciences Leipzig 04103Germany

The Bell nonlocality is closely related to the foundations of quantum physics and has significant applications to security questions in quantum key distributions.In recent years,the sharing ability of the Bell nonlocality has been extensively studied.The nonlocality of quantum network states is more complex.We first discuss the sharing ability of the simplest bilocality under unilateral or bilateral POVM measurements,and show that the nonlocality sharing ability of network quantum states under unilateral measurements is similar to the Bell nonlocality sharing ability,but different under bilateral measurements.For the star network scenarios,we present for the first time comprehensive results on the nonlocality sharing properties of quantum network states,for which the quantum nonlocality of the network quantum states has a stronger sharing ability than the Bell nonlocality.

关键词： Bell nonlocality quantum network nonlocality sharing POVM measurements

Lower Bound of Concurrence Based on Generalized Positive Maps

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Communications in Theoretical Physics 2013年第12期60卷 663-666页

作者：秦慧慧费少明 Department of mathematics School of Science South China University of Technology School of Mathematical sciences Capital Normal University Max-Planck-Institute for Mathematics in the Sciences

We study the concurrence of arbitrary dimensional bipartite quantum systems. By using a positive but not completely positive map, we present an analytical lower bound of concurrence. Detailed examples are used to show... 详细信息

关键词：正映射下限广义量子系统下界纠缠

Tighter sum uncertainty relations via(α,β,γ)weighted Wigner–Yanase–Dyson skew information

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Communications in Theoretical Physics 2024年第3期76卷 91-99页

作者： Cong Xu Zhaoqi Wu Shao-Ming Fei School of Mathematical sciences Capital Normal UniversityBeijing 100048China Department of mathematics Nanchang UniversityNanchang 330031China Max-Planck-Institute for Mathematics in the Sciences 04103 LeipzigGermany

We establish tighter uncertainty relations for arbitrary finite observables via(α,β,γ)weighted Wigner–Yanase–Dyson((α,β,γ)WWYD)skew information.The results are also applicable to the(α,γ)weighted Wigner–Yanase–Dyson((α,γ)WWYD)skew information and the weighted Wigner–Yanase–Dyson(WWYD)skew information.We also present tighter lower bounds for quantum channels and unitary channels via(α,β,γ)modified weighted Wigner–Yanase–Dyson((α,β,γ)MWWYD)skew information.Detailed examples are provided to illustrate the tightness of our uncertainty relations.

关键词： quantum channels (α,β,γ)WWYD skew information (α,β,γ)MWWYD skew information uncertainty relations