## Quantum Information Theory

Module Number: EI76471

Duration: 1 Semester

Occurence: Summer semester

Language: English

Number of ECTS: 5

## Staff

Professor in charge: Holger Boche

## Amount of Work

Contact hours: 60

Self-study hours: 90

Total: 150

## Description of achievement and assessment methods

Succesful attendance of the module is assessed via oral exams. The student should prove his/her understanding of basic conceptual and mathematical aspects of the Shannon-theoretic description of quantum communication systems. In addition, the student should know the communication scenaria and relevant results regarding their abilities presented in the course, such that he/she is able to reflect them. Supporting materials are not allowed within the exams.

## (Recommended) requirements

Interest in mathematical modelling, basic knowledge of linear algebra, basic knowledge of classical information theory, Combination with at least one of the following related modules is recommended

EI7431 – Information Theory

EI7344 – Informationstheoretische Grundlagen der Informationsforensik und biometrische Sicherheit

EI7345 - Informationstheoretische Sicherheit“

EI7353 - Multi-User Information Theory

## Contents

Over the last decades, the theoretical possibility of transmission and storage of data using quantum mechanical properties of physical systems created whole areas of theoretical as well experimental research. The present module aims to introduce to mathematical modelling of Quantum communication systems in spirit of Shannon's conception of information theory. Regarding the choice of topics treated as well as the methodological approach pursued, the module is intended as a continuation of the corresponding modules covering classical information theory . Topics covered in the lecture are - mathematical and conceptual basics of the description of quantum systems with finite degrees of freedom. - Quantum hypothesis testing, Quantum Stein's Lemma - Source coding for memoryless quantum sources - Coding Theorems for classical message transmission over quantum and classical-quantum memoryless channels. - Selected advanced topics covering topics such as information-theoretic security for quantum channels and sources, entanglement theory, optimal protocols for generation of classical and quantum communication resources.

## Learning outcomes

Having successfully accomplished the module, students have basic expertise regarding the mathematical and conceptual methods to describe memoryless semi-classical quantum and quantum communication scenaria. They know the most prominent basic scenaria and the correspoding coding theorem as well as general and special strategies for proving them.

## Teaching and Learning methods

During the lecture and by means of a blackboard presentation, the mathematical/theoretical methods to describe semi-classical and quantum mechanical systems are presented and fundamental coding theorems are proved in detail.

In the exercise classes, the students will solve independently and with the aid of the instructor problems from exercise sheets. Therein, the learned proof techniques should be applied to derive and to prove coding theorems for specific communication scenario.

## Media

blackboard presentation

exercise sheets

## Literature

M. M. Wilde, "Quantum Information Theory", Cambridge University Press, 2012

T. Heinosaari, M. Ziman, „The Mathematical Language of Quantum Theory – From Uncertainty to Entanglement“, Cambridge University Press, 2012

I. Csiszar, J. Körner, „Information Theory – Coding Theorems for Discrete Memoryless Systems“, 2nd Ed., Cambridge University Press, 2011"