Quantum inequalities and completely positive maps
This course is a continuation of the course from last semester. It is divided into three main parts. First, we will introduce the fundamental theory of completely positive maps, such as the dilation theorem. Next, we will discuss quantum inequalities related to positive maps, such as Kadison's inequality and Jensen's inequality. Finally, we will explore the applications of completely positive maps in quantum information theory.
讲师
日期
2024年09月11日 至 12月04日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周三 | 13:30 - 16:55 | A3-4-301 | ZOOM 05 | 293 812 9202 | BIMSA |
修课要求
Mathematical Analysis, Linear Algebra
课程大纲
1.An introduction to C^*-algebras
2.Generalities for (Completely) Positive Maps
3.Dilation Theorems
4.Choi Matrices and Dual Functionals
5.States and Norms of Positive Maps
6.Inequalities and Positive Maps
7.Completely Positive Maps into Mn
8.Arveson’s Extension Theorems
9.Completely Bounded Maps
10.Completely Positive Maps in Quantum Information Theory
2.Generalities for (Completely) Positive Maps
3.Dilation Theorems
4.Choi Matrices and Dual Functionals
5.States and Norms of Positive Maps
6.Inequalities and Positive Maps
7.Completely Positive Maps into Mn
8.Arveson’s Extension Theorems
9.Completely Bounded Maps
10.Completely Positive Maps in Quantum Information Theory
参考资料
[1] E. Størmer, Positive Linear Maps of Operator Algebras[M], Berlin: Springer, 2013.
[2]V. Paulsen, Completely bounded maps and operator algebras[M], Cambridge University Press, 2002.
[3] Michael A. Nielsen, Isaac L. Chuang, Quantum computation and quantum information[M], Cambridge university press, 2010.
[2]V. Paulsen, Completely bounded maps and operator algebras[M], Cambridge University Press, 2002.
[3] Michael A. Nielsen, Isaac L. Chuang, Quantum computation and quantum information[M], Cambridge university press, 2010.
听众
Advanced Undergraduate
, Graduate
, 博士后
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语言
中文