**Lecture "Quantum Information"** (winter term 2018/19)

Lecturer: Norbert Schuch

__Overview__

Quantum Information is concerned with the study of quantum mechanics from the point of view of information theory, as well as with the use of quantum mechanical systems for the purpose of information processing and computation. On the one hand, this includes quantum information theory, with topics such as quantum teleportation, the transmission of information through quantum channels, quantum cryptography, and the quantification of quantum entanglement as a resource for the aforementioned tasks. On the other hand, it involves quantum computation, i.e., computation based on the laws of quantum mechanics, covering topics such as quantum algorithms, quantum error correction, and the physical realization of quantum computers.

This lecture will provide a comprehensive introduction to the field of Quantum Information. Planned topics include

- States, evolution, and measurement
- Quantum entanglement
- Quantum channels
- Quantum cryptography
- Quantum computation and quantum algorithms
- Quantum error correction

__Prerequisites__

Solid knowledge of Linear Algebra is essential for this lecture. Knowledge of quantum mechanics is useful, but not necessary. (However, *please* let me know in advance if you have no prior knowledge of quantum mechanics.)

__Material__

Lecture notes

Lecture 1 (19.10.): | I. Introduction. |

Lecture 2 (26.10.): | II. The formalism: States, measurements, evolution. Pure states, unitary evolution, projective measurements. Composite systems. Mixed states. |

Lecture 3 ( 9.11.): | II. The formalism: States, measurements, evolution. Mixed states. The Schmidt decomposition and purifications. |

Lecture 4 (16.11.): | II. The formalism: States, measurements, evolution. The Schmidt decomposition and purifications. POVM measurements. General evolution: Superoperators. |

Lecture 5 (23.11.): | II. The formalism: States, measurements, evolution. General evolution: Superoperators. III. Entanglement. Introduction. Bell inequalities. |

Lecture 6 (30.11.): | III. Entanglement. Bell inequalities. Applications of entanglement: Teleportation, Dense coding. |

Lecture 7 ( 7.12.): | III. Entanglement. Applications of entanglement: Teleportation, Dense coding. Entanglement conversion and quantification (See also this review by Nielsen and Vidal). |

Lecture 8 (14.12.): | III. Entanglement. Entanglement conversion and quantification. Mixed state entanglement. |

Lecture 9 ( 11.1.): | IV. Quantum Computation. The circuit model. |

Lecture 10 (18.1.): | IV. Quantum Computation. Oracle-based algorithms. Grover's algorithm. |

Lecture 11 (25.1.): | IV. Quantum Computation. Grover's algorithm. The Quantum Fourier transform, period finding, and Shor's algorithm. |

Lecture 12 ( 1.2.): | IV. Quantum Computation. The Quantum Fourier transform, period finding, and Shor's algorithm. V. Quantum Error Correction. Introduction. The 9-qubit Shor code. |

Exercise sheets

__Literature__

**Main texts**

- J. Preskill, Quantum Computation lecture notes.
- M. Nielsen and I. Chuang, Quantum Information and Computation. (Cambridge University Press, 2010)

**Other lecture notes:** Mark Wilde, Reinhard Werner

**Further reading:**

- A. Peres, Quantum Theory: Concepts and Methods (Kluver Academic Press, 2002)

__Organisatorial issues__

The lecture takes place Friday 14:00-16:00 in Lecture Hall 2 (Hörsaal 2).

Tutorials for the lecture are offered on a voluntary basis. The tutorials will take place every Friday after the lecture from 16:00-17:00, starting Oct. 26th, in room PH2271, and will be given by David Stephen. In the tutorial, every other week a new exercise sheet will be handed out and an introduction to the problems will be given, and the following week, solutions to the exercise problems and questions relating to them will be discussed.

See also the TUM Online entry for this lecture.