Monotone and convex operator functions with applications in quantum information and mathematical physics

单调和凸算子函数在量子信息和数学物理中的应用

基本信息

批准号：
23540231
负责人：
HANSEN FRANK
金额：
$ 2.58万
依托单位：
Tohoku University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2011
资助国家：
日本
起止时间：
2011 至 2013
项目状态：
已结题

项目摘要

We proved convexity of various operator or trace functionals. This line of research uses methods, including a number of operator inequalities, which we developed. We discovered and proved a convexity property for the residual entropy of a quantum system, and for the entropy gain over one or multiple quantum channels. The discovery is based on recent advances in the theory of operator monotone functions and is reported in a paper published in the Journal of Statistical Physics and at the conference "Entropy in Quantum Mechanics: Recent advances", June 25-26 2013, Paris, France.We also characterised the class of matrix entropies, which is a recent tool to establish concentration inequalities for random matrices.We obtained new results in the theory of monotone and convex operator mappings, with applications in quantum physics. We also characterised the non-commutative perspectives and initiated a study of so-called regular mappings with applications in matrix geometry.

我们证明了各种操作员或痕量功能的凸度。这一研究使用了我们开发的许多操作员不平等的方法。我们发现并证明了量子系统残留熵的凸性特性，以及在一个或多个量子通道上的熵增益。 The discovery is based on recent advances in the theory of operator monotone functions and is reported in a paper published in the Journal of Statistical Physics and at the conference "Entropy in Quantum Mechanics: Recent advances", June 25-26 2013, Paris, France.We also characterised the class of matrix entropies, which is a recent tool to establish concentration inequalities for random matrices.We obtained new results in the theory of monotone and convex operator映射，并在量子物理学中应用。我们还表征了非共同观点，并开始了对矩阵几何形状中应用的所谓常规映射研究。

项目成果

期刊论文数量（0）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

The fast track to Löwner' s theorem

勒夫纳定理的快速通道

DOI：
发表时间：
2013
期刊：
Linear Algebra and its Applications
影响因子：
1.1
作者：
Koji Kikuchi;Koji Kikuchi;Koji Kikuchi;Koji Kikuchi;菊地光嗣;菊地光嗣;Edward Effros and Frank Hansen;Frank Hansen;Frank Hansen;Frank Hansen
通讯作者：
Frank Hansen

Expected utility with subjective events

主观事件的预期效用

DOI：
发表时间：
2012
期刊：
The Australian Journal of Mathematical Analysis and Applications
影响因子：
0
作者：
Koji Kikuchi;Koji Kikuchi;Koji Kikuchi;Koji Kikuchi;菊地光嗣;菊地光嗣;Edward Effros and Frank Hansen;Frank Hansen;Frank Hansen;Frank Hansen;Frank Hansen;Frank Hansen
通讯作者：
Frank Hansen

The fast track to Loewner's theorem

洛纳定理的快速通道

DOI：
10.1016/j.laa.2013.01.022
发表时间：
2013
期刊：
Linear Algebra and its Applications
影响因子：
1.1
作者：
Koji Kikuchi;Koji Kikuchi;Koji Kikuchi;Koji Kikuchi;菊地光嗣;菊地光嗣;Edward Effros and Frank Hansen;Frank Hansen;Frank Hansen;Frank Hansen;Frank Hansen
通讯作者：
Frank Hansen

WYD-like Skew Information Measures