Let C be a nonempty bounded subset of a p-uniformly convex Banach space X, and T = {T(t): t S} be a Lipschitzian semigroup on C with lim inf |||T(t)||| < Np, where Np is n→ t s the normal structure coefficient of ...Let C be a nonempty bounded subset of a p-uniformly convex Banach space X, and T = {T(t): t S} be a Lipschitzian semigroup on C with lim inf |||T(t)||| < Np, where Np is n→ t s the normal structure coefficient of X. Suppose also there exists a nonempty bounded closed convex subset E of C with the following properties: (P1)x: E implies ωω(χ) C E; (P2)T is asymptotically regular on E. The authors prove that there exists a z E such that T(s)z = z for all s S. Fruther, under the similar condition, the existence of fixed points of Lipschitzian semigroups in a uniformly convex Banach space is discussed.展开更多
Quantum correlations play vital roles in the quantum features in quantum information processing tasks. Among the measures of quantum correlations, quantum discord （QD） and entanglement of formation （EOF） axe two s...Quantum correlations play vital roles in the quantum features in quantum information processing tasks. Among the measures of quantum correlations, quantum discord （QD） and entanglement of formation （EOF） axe two significant ones. Recent research has shown that there exists a relation between QD and EOF, which makes QD more significant in quantum information theory. However, until now, there exists no general method of chaxaeterizing quantum discord in high-dimensional quantum systems. In this paper, we have proposed a general method for calculating quantum discord in axbitraxy-dimensionM bipaxtite quantum systems in terms of Hurwitz＇s theory. Applications including the Werner state, the spin-1 XXZ model thermal equilibrium state, the Horodecki state, and the separable-bound-free entanglement state are investigated. We present the method of obtaining the EOF of axbitraxy-dimensional bipaxtite quantum states via purification, and the relations.hip between QD and EOF.展开更多
基金the National Natural Science Foundation of China (No.19801023) and theTeaching and Research Award Fund for Outstanding Young T
文摘Let C be a nonempty bounded subset of a p-uniformly convex Banach space X, and T = {T(t): t S} be a Lipschitzian semigroup on C with lim inf |||T(t)||| < Np, where Np is n→ t s the normal structure coefficient of X. Suppose also there exists a nonempty bounded closed convex subset E of C with the following properties: (P1)x: E implies ωω(χ) C E; (P2)T is asymptotically regular on E. The authors prove that there exists a z E such that T(s)z = z for all s S. Fruther, under the similar condition, the existence of fixed points of Lipschitzian semigroups in a uniformly convex Banach space is discussed.
基金Supported by the National Natural Science Foundation of China under Grant Nos. 10874098 and 11175094 and the National Basic Research Program of China under Grant Nos. 2009CB929402 and 2011CB9216002, GLL is a Member of Center of Atomic and Molecular Nanosciences, Tsinghua University
文摘Quantum correlations play vital roles in the quantum features in quantum information processing tasks. Among the measures of quantum correlations, quantum discord （QD） and entanglement of formation （EOF） axe two significant ones. Recent research has shown that there exists a relation between QD and EOF, which makes QD more significant in quantum information theory. However, until now, there exists no general method of chaxaeterizing quantum discord in high-dimensional quantum systems. In this paper, we have proposed a general method for calculating quantum discord in axbitraxy-dimensionM bipaxtite quantum systems in terms of Hurwitz＇s theory. Applications including the Werner state, the spin-1 XXZ model thermal equilibrium state, the Horodecki state, and the separable-bound-free entanglement state are investigated. We present the method of obtaining the EOF of axbitraxy-dimensional bipaxtite quantum states via purification, and the relations.hip between QD and EOF.
