## Quantum information theory (Exercise)

Lecturer (assistant) | |
---|---|

Number | 0000004709 |

Type | Exercise |

Duration | 2 SWS |

Term | Wintersemester 2020/21 |

Language of instruction | English |

Position within curricula | See TUMonline |

Dates | See TUMonline |

### Dates

### Admission information

### Objectives

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.

### Description

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.

### Prerequisites

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

### Examination

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 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"