arXiv subjects

Shun Zhang

Publications and source records attributed to Shun Zhang.

132 records · Page 8Linked to original sources

arXiv2012

Gelfand and Kolmogorov numbers of Sobolev embeddings of weighted function spaces II

We consider the Gelfand and Kolmogorov numbers of compact embeddings between weighted function spaces of Besov and Triebel-Lizorkin type with polynomial weights in the non-limiting case. Our main purpose here is to complement our previous results in \cite{ZF10} in the context of the quasi-Banach setting, $0 < p, q \le \infty$. In addition, sharp estimates for their approximation numbers in several cases left open in Skrzypczak (JAT, 2005) are provided.

math.FA↗

arXiv2011

Widths of embeddings in weighted function spaces

We study the asymptotic behaviour of the approximation, Gelfand and Kolmogorov numbers of the compact embeddings of weighted function spaces of Besov and Triebel-Lizorkin type in the case where the weights belong to a large class. We obtain the exact estimates in almost all nonlimiting situations where the quasi-Banach setting is included. At the end we present complete results on related widths for polynomial weights with small perturbations, in particular the sharp estimates in the case $α=d(\frac 1{p_2}-\frac 1{p_1})>0$ therein.

math.FA↗

arXiv2011

Widths of embeddings of 2-microlocal Besov spaces

We consider the asymptotic behaviour of the approximation, Gelfand and Kolmogorov numbers of compact embeddings between 2-microlocal Besov spaces with weights defined in terms of the distance to a $d$-set $U\subset \mathbb{R}^n$. The sharp estimates are shown in most cases, where the quasi-Banach setting is included.

math.FA↗

arXiv2008

Entanglement detection beyond the cross-norm or realignment criterion

Separability problem, to decide whether a given state is entangled or not, is a fundamental problem in quantum information theory. We propose a powerful and computationally simple separability criterion, which allows us to detect the entanglement of many bound entangled states. The criterion is strictly stronger than the dV criterion, the computable cross-norm or realignment criterion and its optimal nonlinear entanglement witnesses. Furthermore, this criterion can be generalized to an analogue of permutation separability criteria in the even-partite systems.

quant-ph↗

arXiv2007

Optimal entanglement witnesses based on local orthogonal observables

We show that the entanglement witnesses based on local orthogonal observables which are introduced in [S. Yu and N.-L. Liu, Phys. Rev. Lett. 95, 150504 (2005)] and [O. Gühne, M. Mechler, G. Tóth and P. Adam, Phys. Rev. A 74, 010301 (2006)] in linear and nonlinear forms can be optimized, respectively. As applications, we calculate the optimal nonlinear witnesses of pure bipartite states and show a lower bound on the I-concurrence of bipartite higher dimensional systems with our method.

quant-ph↗

arXiv2007

Compatibility conditions from multipartite entanglement measures

We consider an arbitrary d_{1}\otimes d_{2}\otimes ... \otimes d_{N} composite quantum system and find necessary conditions for general m-party subsystem states to be the reduced states of a common N-party state. These conditions will lead to various monogamy inequalities for bipartite quantum entanglement and partial disorder in multipartite states. Our results are tightly connected with the measures of multipartite entanglement.

quant-ph↗