BIMSA > Quantum inequalities and completely positive maps \(ICBS\)
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.
Lecturer
Lin Zhe Huang
Date
11th September ~ 4th December, 2024
Location
Weekday Time Venue Online ID Password
Wednesday 13:30 - 16:55 A3-4-301 ZOOM 05 293 812 9202 BIMSA
Prerequisite
Mathematical Analysis, Linear Algebra
Syllabus
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
Reference
[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.
Audience
Advanced Undergraduate , Graduate , Postdoc
Video Public
No
Notes Public
No
Language
Chinese