## QST-Theory: Quantum Information [PH1010]

### Wintersemester 2020/21

The course, which is part of the Master’s Program

Quantum Science & Technology, will be entirely online. Registered students can find the course material on the

moodle page.

### Content

Quantum Information offers an introduction to the theoretical foundations of Quantum Science and Technology. The course starts with a brief motivation and an introduction to fundamental concepts and the basic formalism (pure/mixed states, evolution, completely positive maps, measurements Schmidt decomposition, tomography, quantum estimation, hypothesis testing). Then the concept of entanglement is discussed in detail, including the distinction between pure and mixed-state entanglement, entanglement entropy, quantification and conversion. Subsequently, some of the revolutionary promises of exploiting entanglement are presented, including dense coding, quantum teleportation and quantum cryptography. Next the Bell inequalities, characterizing the quantum weirdness of entanglement and non-locality, are introduced and discussed in detail. Subsequent chapters cover central applications of quantum information theory: quantum computation, quantum algorithms such as those of Deutsch, Shor and Grover, and quantum simulation. Final core topics are decoherence, Lindbladian descriptions thereof, and error correction schemes to counteract the consequences of decoherence and protect fragile quantum information. The module will typically also include one or more optional topics, such as many-body entanglement, topological quantum computation, quantum complexity, or tensor networks, which link quantum information theory to many-body physics.

### Literature

Standard articles, textbooks and lecture notes on Quantum Information, for example:

- Quantum Computing
^{}, an article by J.Eisert and M.M.Wolf.
- Quantum Computation
^{} (Lecture Notes), John Preskill. A famous set of lecture notes, continually being refined throughout the last 20 years.
- Quantum Computation and Quantum Information
^{}, 10th Anniversary Edition, Michael A. Nielsen, Isaac L. Chuang, Cambridge University Press, 2010. One of the most cited books in physics of all time, providing a general, accessible and wide-ranging introduction to the topic.