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Unit M15: Professorship for Optimization and Data Analysis

John von Neumann Professor Marius Junge

Junge image
E-mail jungeematmath.uiuc.edu
Homepage https://faculty.math.illinois.edu/~mjunge/

John von Neumann Lecture

Operator Algebra Techniques in Quantum Information Theory (MA 5920)

Contents:
The aim is to cover enough material to present some recent results in Quantum Information Theory. In the given time frame it will impossible to cover all foundational material from physics, math and quantum probability thoroughly. Instead, the course will selectively choose some foundational material. In a second step this material will be used to demonstrate how concept from one are can be used to make progress in a more quantized environment.
(1) Basics on quantum mechanics, states and measurement (2 lectures);
(2) Basics on Banach space theory, including interpolation (3 lectures);
(3) Channels, Kraus operators and Stinespring's theorem and Stinespring spaces (3 lectures);
(4) Relative Entropy, Interpolation and Recovery (4 lectures).

Educational objectives:
After successful completion of this module, students will be able to
(1) Explain and apply basic concepts from quantum mechanics including measurements and channels;
(2) Explain the historical connection between the notion of a channel and tools from operator algebras;
(3) Formulate, apprehend, and analyze the concept of entropy in connection with transmitted information;
(4) Analyze problems in quantum information theory with a broader understanding of probabilistic events;
(5) independently read, understand, and present a research article on the topic;
(6) prove inequalities between different entropic quantities.

Educational methods: TBA
Media: TBA

Level: Master
Duration: 1 Semester (Summer 18), lectures will be held on Tuesdays and Wednesdays from May 15 to June 20, 2018
Language: English
Exam: TBA

Prerequisites (recommended): none

Literature: TBA

-- FelixKrahmer - 10 May 2018